Hindawi Publishing Corporation
EURASIP Journal on Advances in Signal Processing
Volume 2008, Article ID 672941, 13 pages
doi:10.1155/2008/672941
Research Article
A Window Width Optimized S-Transform
Ervin Sejdić,1 Igor Djurović,2 and Jin Jiang1
1 Department
2 Electrical
of Electrical and Computer Engineering, The University of Western Ontario, London, Ontario, Canada N6A 5B9
Engineering Department, University of Montenegro, 81000 Podgorica, Serbia and Montenegro
Correspondence should be addressed to Jin Jiang, [email protected]
Received 14 May 2007; Accepted 15 November 2007
Recommended by Sven Nordholm
Energy concentration of the S-transform in the time-frequency domain has been addressed in this paper by optimizing the width
of the window function used. A new scheme is developed and referred to as a window width optimized S-transform. Two optimization schemes have been proposed, one for a constant window width, the other for time-varying window width. The former is
intended for signals with constant or slowly varying frequencies, while the latter can deal with signals with fast changing frequency
components. The proposed scheme has been evaluated using a set of test signals. The results have indicated that the new scheme
can provide much improved energy concentration in the time-frequency domain in comparison with the standard S-transform.
It is also shown using the test signals that the proposed scheme can lead to higher energy concentration in comparison with other
standard linear techniques, such as short-time Fourier transform and its adaptive forms. Finally, the method has been demonstrated on engine knock signal analysis to show its effectiveness.
Copyright © 2008 Ervin Sejdić et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1.
INTRODUCTION
In the analysis of the nonstationary signals, one often needs
to examine their time-varying spectral characteristics. Since
time-frequency representations (TFR) indicate variations of
the spectral characteristics of the signal as a function of time,
they are ideally suited for nonstationary signals [1, 2]. The
ideal time-frequency transform only provides information
about the frequency occurring at a given time instant. In
other words, it attempts to combine the local information
of an instantaneous-frequency spectrum with the global information of the temporal behavior of the signal [3]. The
main objectives of the various types of time-frequency analysis methods are to obtain time-varying spectrum functions
with high resolution and to overcome potential interferences
[4].
The S-transform can conceptually be viewed as a hybrid
of short-time Fourier analysis and wavelet analysis. It employs variable window length. By using the Fourier kernel, it
can preserve the phase information in the decomposition [5].
The frequency-dependent window function produces higher
frequency resolution at lower frequencies, while at higher
frequencies, sharper time localization can be achieved. In
contrast to wavelet transform, the phase information pro-
vided by the S-transform is referenced to the time origin, and
therefore provides supplementary information about spectra
which is not available from locally referenced phase information obtained by the continuous wavelet transform [5].
For these reasons, the S-transform has already been considered in many fields such as geophysics [6–8], cardiovascular
time-series analysis [9–11], signal processing for mechanical
systems [12, 13], power system engineering [14], and pattern
recognition [15].
Even though the S-transform is becoming a valuable tool
for the analysis of signals in many applications, in some
cases, it suffers from poor energy concentration in the timefrequency domain. Recently, attempts to improve the timefrequency representation of the S-transform have been reported in the literature. A generalized S-transform, proposed
in [12], provides greater control of the window function, and
the proposed algorithm also allows nonsymmetric windows
to be used. Several window functions are considered, including two types of exponential functions: amplitude modulation and phase modulation by cosine functions. Another
form of the generalized S-transform is developed in [7],
where the window scale and shape are a function of frequency. The same authors introduced a bi-Gaussian window
in [8], by joining two nonsymmetric half-Gaussian windows.
2
EURASIP Journal on Advances in Signal Processing
Since the bi-Gaussian window is asymmetrical, it also produces an asymmetry in the time-frequency representation,
with higher-time resolution in the forward direction. As a result, the proposed form of the S-transform has better performance in detection of the onset of sudden events. However,
in the current literature, none has considered optimizing the
energy concentration in the time-frequency domain directly,
that is, to minimize the spread of the energy beyond the actual signal components.
The main approach used in this paper is to optimize the
width of the window used in the S-transform. The optimization is performed through the introduction of a new parameter in the transform. Therefore, the new technique is referred
to as a window width optimized S-transform (WWOST).
The newly introduced parameter controls the window width,
and the optimal value can be determined in two ways. The
first approach calculates one global, constant parameter and
this is recommended for signals with constant or very slowly
varying frequency components. The second approach calculates the time-varying parameter, and it is more suitable for
signals with fast varying frequency components.
The proposed scheme has been tested using a set of synthetic signals and its performance is compared with the standard S-transform. The results have shown that the WWOST
enhances the energy concentration. It is also shown that the
WWOST produces the time-frequency representation with a
higher concentration than other standard linear techniques,
such as the short-time Fourier transform and its adaptive
forms. The proposed technique is useful in many applications where enhanced energy concentration is desirable. As
an illustrative example, the proposed algorithm is used to
analyze knock pressure signals recorded from a Volkswagen
Passat engine in order to determine the presence of several
signal components.
This paper is organized as follows. In Section 2, the concept of ideal time-frequency transform is introduced, which
can be compared with other time-frequency representations
including transforms proposed here. The development of
the WWOST is covered in Section 3. Section 4 evaluates the
performance of the proposed scheme using test signals and
also the knock pressure signals. Conclusions are drawn in
Section 5.
2.
ENERGY CONCENTRATION IN
TIME-FREQUENCY DOMAIN
The ideal TFR should only be distributed along frequencies
for the duration of signal components. Thus, the neighboring frequencies would not contain any energy; and the energy
contribution of each component would not exceed its duration [3].
For example, let us consider two simple signals: an
FM signal, x1 (t) = A(t) exp ( jφ(t)), where |dA(t)/dt | |dφ(t)/dt | and the instantaneous frequency is defined as
f (t) = (dφ(t)/dt)/2π; and a signal with the Fourier
transform given as X( f ) = G( f ) exp ( j2πχ( f )), where
the spectrum is slowly varying in comparison to phase
|dG( f )/df | |dχ( f )/df |. Further, A(t) and G(t) The ideal
TFRs for these signals are given, respectively, as shown in [16]
ITFR(t, f ) = 2πA(t)δ f −
1 dφ(t)
,
2π dt
ITFR(t, f ) = 2πG( f )δ t +
(1)
dχ( f )
,
df
(2)
where ITFR stands for an ideal time-frequency representation. These two representations are ideally concentrated
along the instantaneous frequency, (dφ(t)/dt)/2π, and on
group delay −dχ( f )/df . Simplest examples of these signals
are the following: a sinusoid with A = const. and dφ(t)/dt =
const. depicted in Figure 1(a); and a Dirac pulse x2 (t) =
δ(t − t0 ) shown in Figure 1(b). The ideal time-frequency representations are depicted in Figures 1(c) and 1(d). These two
graphs are compared with the TFRs obtained by the standard
S-transform in Figures 1(e) and 1(f).
For the sinusoidal case, the frequencies surrounding
(dφ(t)/dt)/2π also have a strong contribution, and from (1),
it is clear that they should not have any contributions. Similarly, for the Dirac function, it is expected that all the frequencies have the contribution but only for a single time instant. Nevertheless, it is clear that the frequencies are not only
contributing during a single time instant as expected from
(2), but the surrounding time instants also have strong energy contribution.
The examples presented here are for illustrations only,
since a priori knowledge about the signals is assumed. In
most practical situations, the knowledge about a signal is
limited and the analytical expressions similar to (1) and (2)
are often not available. However, the examples illustrate a
point that some modifications to the existing S-transform
algorithm, which do not assume a priori knowledge about
the signal, may be useful to achieve improved performance
in time-frequency energy concentration. Such improvements
only become possible after modifications to the width of the
window function are made.
3.
THE PROPOSED SCHEME
3.1.
Standard S-transform
The standard S-transform of a function x(t) is given by an
integral as in [5, 7, 12]
Sx (t, f ) =
+∞
−∞
x(τ)w t − τ, σ( f ) exp (− j2π f τ)dτ
(3)
with a constraint
+∞
−∞
w t − τ, σ( f ) dτ = 1.
(4)
Ervin Sejdić et al.
3
1
Amplitude
Amplitude
1
0
−1
0
0.2
0.4
0.6
0.8
0.5
0
1
0
0.2
Time (s)
(a)
0
0.2
0.4
0.6
0.8
50
0
1
0
0.2
0.4
Time (s)
0.6
0.8
1
0.6
0.8
1
Time (s)
(c)
(d)
100
Frequency (Hz)
100
Frequency (Hz)
1
(b)
50
50
0
0.8
100
Frequency (Hz)
Frequency (Hz)
0.6
Time (s)
100
0
0.4
0
0.2
0.4
0.6
0.8
50
0
1
Time (s)
0
0.2
0.4
Time (s)
(e)
(f)
Figure 1: Comparison of the ideal time-frequency representation and S-transform for the two simple signal forms: (a) 30 Hz sinusoid; (b)
sample Dirac function; (c) ideal TFR of a 30 Hz sinusoid; (d) ideal TFR of a Dirac function; (e) TFR by standard S-transform for a 30 Hz
sinusoid; and (f) TFR by standard S-transform of the Dirac delta function.
A window function used in S-transform is a scalable Gaussian function defined as
w t, σ( f ) =
1
t2
√ exp −
.
2σ 2 ( f )
σ( f ) 2π
(5)
The advantage of the S-transform over the short-time
Fourier transform (STFT) is that the standard deviation σ( f )
is actually a function of frequency, f , defined as
σ( f ) =
1
|f|
.
The disadvantage of the current algorithm is the fact that
the window width is always defined as a reciprocal of the
frequency. Some signals would benefit from different window widths. For example, for a signal containing a single sinusoid, the time-frequency localization can be considerably
improved if the window is very narrow in the frequency domain. Similarly, for signals containing only a Dirac impulse,
it would be beneficial for good time-frequency localization
to have very wide window in the frequency domain.
(6)
Consequently, the window function is also a function of time
and frequency. As the width of the window is dictated by the
frequency, it can easily be seen that the window is wider in
the time domain at lower frequencies, and narrower at higher
frequencies. In other words, the window provides good localization in the frequency domain for low frequencies while
providing good localization in time domain for higher frequencies.
3.2.
Window width optimized S-transform
A simple improvement to the existing algorithm for the Stransform can be made by modifying the standard deviation
of the window to
σ( f ) =
1
|f|
p.
(7)
4
EURASIP Journal on Advances in Signal Processing
1
0.9
Normalized amplitude
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Time (s)
p = 0.5
p=1
p=2
Figure 2: Normalized Gaussian window for different values of p.
Based on the above equation, the new S-transform can be
represented as
p
Sx (t, f )
p
+∞
2π
−∞
|f|
= √
x(τ) exp
(t − τ)2 f 2p
−
exp (− j2π f τ)dτ.
2
(8)
The parameter p can control the width of the window.
By finding an appropriate value of p, an improved timefrequency concentration can be obtained. The window functions with three different values of p are plotted in Figure 2,
where p = 1 corresponds to the standard S-transform window. For p < 1, the window becomes wider in the time domain, and for p > 1, the window narrows in the time domain. Therefore, by considering the example from Section 2,
for the single sinusoid, a small value of p would provide
almost perfect concentration of the signal, whereas for the
Dirac function, a rather large value of p would produce a
good concentration in the time-frequency domain. It is important to mention that in the case of 0 < f < 1, the opposite
is true.
The optimal value of p will be found based on the concentration measure proposed in [17], which has some favorable performance in comparison to other concentration
measures reported in [18–20]. The measure is designed to
minimize the energy concentration for any time-frequency
representation based on the automatic determination of
some time-frequency distribution parameter. This measure
is defined as
CM(p) = +∞ +∞ −∞ −∞
1
,
p
Sx (t, f )
dt df
where CM stands for a concentration measure.
(9)
There are two ways to determine the optimal value of p.
One is to determine a global, constant value of p for the entire signal. The other is to determine a time-varying p(t),
which depends on each time instant considered. The first approach is more suitable for signals with the constant or slowly
varying frequency components. In this case, one value of p
will suffice to give the best resolution for all components.
The time-varying parameter is more appropriate for signals
with fast varying frequency components. In these situations,
depending on the time duration of the signal components,
it would be beneficial to use lower value of p (somewhere
in the middle of the particular component’s interval), and
to use higher values of p for the beginning and the end of
the component’s interval, so the component is not smeared
in the time-frequency plane. It is important to mention that
both proposed schemes for determining the parameter p are
the special cases of the algorithm which would evaluate the
parameter on any arbitrary subinterval, rather than over the
entire duration of the signal.
3.2.1. Algorithm for determining the time-invariant p
The algorithm for determining the optimized time-invariant
value of p is defined through the following steps.
(1) For p selected from a set 0 < p ≤ 1, compute Sp
transform of the signal Sx (t, f ) using (8).
(2) For each p from the given set, normalize the energy of
the S-transform representation, so that all of the representations have the equal energy
p
Sx (t, f )
p
.
Sx (t, f ) = 2
+∞ +∞ p
−∞ −∞ Sx (t, f ) dt df
(10)
(3) For each p from the given set, compute the concentration measure according to (9), that is,
CM(p) = +∞ +∞ −∞ −∞
1
Sx (t, f )
dt df
p
.
(11)
(4) Determine the optimal parameter popt by
popt = max CM(p) .
p
(12)
p
(5) Select Sx (t, f ) with popt to be the WWOST
p
p
Sx (t, f ) = Sx opt (t, f ).
(13)
As it can be seen, the proposed algorithm computes the
S-transform for each value of p and, based on the computed representation, it determines the concentration measure, CM(p), as an inverse of L1 norm of the normalized
S-transform for a given p. The maximum of the concentration measure corresponds to the optimal p which provides
p
the least smear of Sx (t, f ).
It is important to note that in the first step, the value of
p is limited to the range 0 < p ≤ 1. Any negative value of p
corresponds to an nth root of a frequency which would make
the window wider as frequency increases. Similarly, values
Ervin Sejdić et al.
5
greater than 1 provide a window which may be too narrow in
the time domain. Unless the signal being analyzed is a superposition of Delta functions, the value of p should not exceed
unity. As a special case, it is important to point out that for
p = 0, the WWOST is equivalent to STFT with a Gaussian
window with σ 2 = 1.
In the case of a time-invariant p, it can be shown that
W(0, f ) = 1. In a general case, the Fourier transform of the
proposed modified window can only be determined numerically.
3.2.2. Algorithm for determining p(t)
In this section, the performance of the proposed scheme is
examined using a set of synthetic test signals first. Furthermore, the analysis of signals from an engine is also given.
The first part includes two cases: (1) a simple case involving
three slowly varying frequencies and (2) more complicated
cases involving multiple time-varying components. The goal
is to examine the performance of WWOST in comparison
to the standard S-transform. The proposed algorithm is also
compared to other time-frequency representations, such as
the short-time Fourier transform (STFT) and adaptive STFT
(ASTFT), to highlight the improved performance of the Stransform with the proposed window width optimization
technique. In particular, the proposed algorithm can be used
for some classes of the signals for which the standard Stransform would not be suitable.
As for the synthetic signals, the sampling period used in
the simulations is Ts = 1/256 seconds. Also, the set of p
values, used in the numerical analysis of both test and the
knock pressure signals, is given by p = {0.01n : n ∈ N and
1 ≤ n ≤ 100}. The ASTFT is calculated according to the concentration measure given by (9). In the definition of the measure, a normalized STFT is used instead of the normalized
WWOST. The standard deviation of the Gaussian window,
σ gw , is used as the optimizing parameter, where the window
is defined as
The time-varying parameter p(t) is required for signals with
components having greater or abrupt changes. The algorithm for choosing the optimal p(t) can be summarized
through the following steps.
(1) For p selected from a set 0 < p(t) ≤ 1, compute Sp
transform of the signal Sx (t, f ) using (8).
(2) Calculate the energy, E1 , for p = 1. For each p from the
set, normalize the energy of the S-transform representation to E1 , so that all of the representations have the
equal energy, and the amplitude of the components is
not distorted,
p
p
Sx (t, f )
Sx (t, f ) = E1 +∞ +∞
−∞ −∞
.
p
Sx (t, f )
2 dt df
(14)
(3) For each p from the set and a time instant t, compute
CM(t, p) = +∞ −∞
1
p
Sx (t,
f )
df
.
(15)
(4) Optimal value of p for the considered instant t maximizes concentration measure CM(t, p),
popt (t) = arg max CM(t, p) .
p
4.
WWOST PERFORMANCE ANALYSIS
(16)
wSTFT (t) =
(5) Set the WWOST to be
p
p
(t)
Sx (t, f ) = Sx opt (t, f ).
(17)
The main difference between the two techniques lies in
step (3). For the time invariant case, a single value of p is
chosen, whereas in the time-varying case, an optimal value of
p(t) is a function of time. As it is demonstrated in Section 4,
the time-dependent parameter is beneficial for signals with
the fast varying components.
Similarly to the standard S-transform, the WWOST can be
used as both an analysis and a synthesis tool. The inversion
procedure for the WWOST resembles that of the standard
S-transform, but with one additional constraint. The specp
trum of the signal obtained by averaging Sx (t, f ) over time
must be normalized by W(0, f ), where W(α, f ) represents
the Fourier transform (from t to α) of the window function,
w(t, σ( f )). Hence, the inverse WWOST for a signal, x(t), is
defined as
x(t) =
+∞ +∞
−∞
−∞
1
p
Sx (τ, f ) exp ( j2π f t)dτ df . (18)
W(0, f )
√
σ gw 2π
exp −
t2
.
2σ 2gw
(19)
The optimization for synthetic signals is performed on the
set of values defined by
σ gw = {n/128 : n ∈ N, 1 ≤ n ≤ 128}
(20)
and both the time-invariant and time-varying values of σ gw
are calculated.
4.1.
3.2.3. Inverse of the WWOST
1
Synthetic test signals
Example 1. The first test signal is shown in Figure 3(a). It has
the following analytical expression:
x1 (t) = cos 132πt + 14πt 2 + cos 10πt − 2πt 2
+ cos 30πt + 6πt 2 ,
(21)
where the signal exists only on the interval 0 ≤ t < 1. The signal consists of three slowly varying frequency components.
It is analyzed using the STFT (Figure 3(b)), ASTFT with
time-invariant optimum value of σ gw (Figure 3(c)), standard S-transform (Figure 3(d)), and the proposed algorithm
(Figure 3(f)). A Gaussian window is also used in the analysis by the STFT, with standard deviations equal to 0.05. The
6
EURASIP Journal on Advances in Signal Processing
Frequency (Hz)
Amplitude
5
0
−5
0
0.2
0.4
0.6
0.8
100
50
0
1
0
0.2
0.4
Time (s)
100
50
0
0.2
0.8
1
0.6
0.8
1
(b)
Frequency (Hz)
Frequency (Hz)
(a)
0
0.6
Time (s)
0.4
0.6
0.8
100
50
0
1
0
0.2
0.4
Time (s)
Time (s)
(c)
(d)
Frequency (Hz)
Amplitude of CM
1
0.5
0
0
0.2
0.4
0.6
0.8
1
100
50
0
0
0.2
0.4
Time (s)
0.6
0.8
1
Time (s)
(e)
(f)
p
Figure 3: Test signal x1 (t): (a) time-domain representation; (b) STFT of x1 (t); (c) ASTFT of x1 (t) with σ opt ; (d) Sx (t, f ) of x1 (t) with p = 1
p
(standard S-transform); (e) concentration measure CM(p); (f) Sx (t, f ) of x1 (t) with the optimal value of p = .57.
optimum value of standard deviation for the ASTFT is calculated to be σ opt = 0.094. The colormap used for plotting the
time-frequency representations in Figure 3 and all the subsequent figures is a linear grayscale with values from 0 to 1.
The standard S-transform, shown in Figure 3(d), depicts
all three components clearly. However, only the first two
components have relatively good concentration, while the
third component is completely smeared in frequency. As
shown in Figure 3(b), the STFT provides better energy concentration than the standard S-transform. The ASTFT, depicted in Figure 3(c), shows a noticeable improvement for all
three components. The results with the proposed scheme is
shown in Figure 3(f) for p = 0.57. The value of p is found according to (12). For the determined value of p, the first two
components have higher concentration even than the ASTFT,
while the third component has approximately the same concentration.
In Figure 3(e), the normalized concentration measure is
depicted. The obtained results verify the theoretical predictions from Section 3.2. For this class of signals, that is, the
signals with slowly varying frequencies, it is expected that
smaller values of p will produce the best energy concentration. In this example, the optimal value, found according to
(12), is determined numerically to be 0.57.
Based on the visual inspection of the time-frequency representations shown in Figure 3, it can be concluded that the
proposed algorithm achieves higher concentration among
the considered representations. To confirm this fact, a performance measure given by
ΞTF =
+∞ +∞ −∞
−∞
TF(t, f )
dt df
−1
(22)
is used for measuring the concentration of the representation, where |TF(t, f )| is a normalized time-frequency representation. The performance measure is actually the concentration measure proposed in (9). A more concentrated representation will produce a higher value of ΞTF . Table 1 summarizes the performance measure for the STFT, the ASTFT,
the standard S-transform, and the WWOST.
Ervin Sejdić et al.
7
Table 1: Performance measure for the three time-frequency transforms.
TFR
STFT
ASTFT
Standard S-transform
WWOST
ΞTF
0.0119
0.0131
0.0080
0.0136
The value of the performance measure for the standard Stransform is the lowest, followed by the STFT. The WWOST
produces the highest value of ΞTF , and thus achieves a TFR
with the highest energy concentration amongst the transforms considered.
Example 2. The signal in the second example contains multiple components with faster time-varying spectral contents.
The following signal is used:
x2 (t) = cos 40π(t − 0.5) arctan (21t − 10.5)
2
− 20π ln (21t − 10.5) + 1 /21 + 120πt (23)
+ cos 40πt − 8πt 2 ,
where x2 (t) exists only on the interval 0 ≤ t < 1. This
signal consists of two components. The first has a transition region from lower to higher frequencies, and the second is a linear chirp. In the analysis, the time-frequency
transformations that employ a constant window exhibit a
conflicting issue between good concentration of the transition region for the first component versus good concentration for the rest of the signal. In order to numerically demonstrate this problem, the signal is again analyzed using the STFT (Figure 4(a)), ASTFT with the optimal time-invariant value of σ gw (Figure 4(c)), ASTFT with
the optimal time-varying value of σ gw (Figure 4(e)), standard S-transform (Figure 4(b)), the proposed algorithm
with both time-invariant (Figure 4(d)), and time-varying p
(Figure 4(f)). A Gaussian window is used for the STFT, with
σ = 0.03. The optimum time-invariant value of the standard
deviation for the ASTFT is determined to be σ opt = 0.055.
The standard deviation of the Gaussian window used
should be small in order for the STFT to provide relatively
good concentration in the transition region. However, as the
value of the standard deviation decreases, so is the concentration of the rest of the signal. To a certain extent, the standard
S-transform is capable of producing a good concentration
around the instantaneous frequencies at the lower frequencies and also in the transition region for the first component.
However, at the high frequencies, the standard S-transform
exhibits poor concentration for the first component. The
WWOST with a time-invariant p enhances the concentration of the linear chirp, as shown in Figure 4(d). However the
concentration of the transition region of the first component
has deteriorated in comparison to the standard S-transform.
The concentration obtained with the WWOST with the timeinvariant p for this transition region is equivalent to the
poor concentration exhibited by the STFT. Even though the
ASTFT with both time-invariant and time-varying optimum
Table 2: Performance measures for the time-frequency representations considered in Example 2.
ΞTF
0.0108
0.0115
0.0119
0.0116
0.0124
TFR
STFT
ASTFT with σ opt
ASTFT with σ opt (t)
WWOST with p
WWOST with p(t)
values of standard deviation provide good concentration of
the linear FM component and the stationary parts of the second component, the transition region of the second component is smeared in time.
Figure 4(f) represents the signal optimized S-transform
obtained by using p(t). A significant improvement in the energy concentration is easily noticeable in comparison to the
standard S-transform. All components show improved energy concentration in comparison to the S-transform. Further, a comparison of the representations obtained by the
proposed implementation of the S-transform and the STFT
shows that both components have higher energy concentration in the representation obtained by the WWOST with
p(t).
As mentioned previously, for this type of signals it is
more appropriate to use the time-varying p(t) rather than
a single constant p value in order to achieve better concentration of the nonstationary data. By comparing Figures 4(d)
and 4(f), the component with the fast changing frequency
has better concentration with p(t) than a fixed p, which is
calculated according to (12), while the linear chirp has similar concentration in both cases.
It would be beneficial to quantify the results by evaluating the performance measure again. The performance
measure is given by (22) and the results are summarized
in Table 2. A higher value of the performance measure for
WWOST with p(t) reconfirms that the time-varying algorithm should be used for the signals with fast changing components. Also, it is worthwhile to examine the value of (22)
for the STFT and the ASTFT. The time-frequency representations of the signal obtained by the STFT and ASTFT algorithms achieve smaller values of the performance measure
than WWOST. This supports the earlier conclusion that the
WWOST produces more concentrated energy representation
than the STFT and ASTFT. The WWOST with the timeinvariant value of p produces higher concentration than the
ASTFT with the optimum time-invariant value of σ gw , and
the WWOST with p(t) produces higher concentration than
the ASTFT with the optimum time-varying value of the
σ gw .
Example 3. Another important class of signals are those with
crossing components that have fast frequency variations. A
representative signal as shown in Figure 5(a) is given by
x3 (t) = cos 20π ln (10t + 1) + cos 48πt + 8πt 2
(24)
with x3 (t) = 0 outside the interval 0 ≤ t < 1. For this
class of signals, similar conflicting issues occur as in the
EURASIP Journal on Advances in Signal Processing
100
Frequency (Hz)
Frequency (Hz)
8
50
0
0
0.2
0.4
0.6
0.8
100
50
0
1
0
0.2
0.4
Time (s)
100
50
0
0.2
0.4
0.6
0.8
0
1
0
0.2
0.4
Frequency (Hz)
Frequency (Hz)
1
0.6
0.8
1
(d)
50
0.4
0.8
Time (s)
100
0.2
0.6
50
(c)
0
1
100
Time (s)
0
0.8
(b)
Frequency (Hz)
Frequency (Hz)
(a)
0
0.6
Time (s)
0.6
0.8
100
50
0
1
Time (s)
0
0.2
0.4
Time (s)
(e)
(f)
p
Figure 4: Comparison of different algorithms: (a) STFT of x2 (t); (b) Sx (t, f ) of x2 (t) with p = 1 (standard S-transform); (c) ASTFT of x2 (t)
p
p
with σ opt = 0.055; (d) Sx (t, f ) of x2 (t) with p = 0.73; (e) ASTFT of x2 (t) with σ opt (t); (f) Sx (t, f ) of x2 (t) with the optimal p(t).
previous example; however, here exists an additional constraint, that is, the crossing components. The time-frequency
analysis is performed using the STFT (Figure 5(b)), the
ASTFT with the time-varying σ gw (Figure 5(c)), the standard
S-transform (Figure 5(d)), and the proposed algorithm for
the S-transform (Figure 5(f)). In the STFT, a Gaussian window with a standard deviation of 0.02 is used. Due to the
time-varying nature of the frequency components present in
the signal, the time-varying algorithm is used in the calculation of the WWOST in order to determine the optimal value
of p.
The representation obtained by the STFT depicts good
concentration of the higher frequencies, while having relatively poor concentration at the lower frequencies. An improvement in the concentration of the lower frequencies
is obtained with the ASTFT algorithm. The standard Stransform is capable of providing better concentration for
the high frequencies, but for the linear chirp, the concentration is equivalent to that of the STFT.
From the time-frequency representation obtained by the
WWOST, it is clear that the concentration is preserved at
high frequencies, while the linear chirp has significantly
higher concentration in comparison to the other representations. It is also interesting to note how p(t) varies between
0.6 and 1.0 as a function of time shown in Figure 5(e). In particular, p(t) is close to 1 at the beginning of the signal in order
to achieve good concentration of the high-frequency component. As time progresses, the value of p(t) decreases in order
to provide a good concentration at the lower frequencies. Towards the end of the signal, p(t) increases again to achieve a
good time localization of the signal.
In Section 3, it has been stated that for the components
with faster variations, it is recommended that the timevarying algorithm with the WWOST be used. In order to
substantiate that statement, the performance measure implemented in the previous examples is used again and the results
are shown in Table 3. The optimized time-invariant value of
the parameter popt for this signal, found according to (12), is
determined numerically to be 0.71. These performance measures verify that the time-varying algorithm should be used
for the faster varying components. For comparison purposes,
the performance measures for the representations given by
Ervin Sejdić et al.
9
Frequency (Hz)
Amplitude
2
0
−2
0
0.2
0.4
0.6
0.8
100
50
0
1
0
0.2
0.4
Time (s)
100
50
0
0.2
0.8
1
0.6
0.8
1
0.6
0.8
1
(b)
Frequency (Hz)
Frequency (Hz)
(a)
0
0.6
Time (s)
0.4
0.6
0.8
100
50
0
1
0
0.2
0.4
Time (s)
Time (s)
(c)
(d)
Frequency (Hz)
Amplitude
1
0.5
0
0
0.2
0.4
0.6
0.8
100
50
0
1
Time (s)
0
0.2
0.4
Time (s)
(e)
(f)
Figure 5: Time-frequency analysis of signal with fast variations in frequency: (a) time-domain representation; (b) STFT of x3 (t); (c) ASTFT
p
p
of x3 (t) with σ opt (t); (d) Sx (t, f ) of x3 (t) with p = 1 (standard S-transform); (e) p(t); (f) Sx (t, f ) of x3 (t) with the optimal p(t).
Table 3: Performance measures for the time-frequency representations considered in Example 3.
TFR
STFT
ASTFT with σ opt
ASTFT with σ opt (t)
WWOST with p
WWOST with p(t)
ΞTF (noise-free)
0.0106
0.0121
0.0122
0.0122
0.0126
ΞTF (SNR = 25 dB)
0.0100
0.0114
0.0113
0.0110
0.0116
the STFT and its time-invariant (σ opt = 0.048) and timevarying adaptive algorithms are calculated as well. By comparing the values of the performance measure for different
time-frequency transforms, these values confirm the earlier
statement which assures that each algorithm for the WWOST
produces more concentrated time-frequency representation
in its respective class than the ASTFT.
In the analysis performed so far, it was assumed that the
signal-to-noise ratio (SNR) is infinity, that is, the noise-free
signals were considered. It would be beneficial to compare
the performance of the considered algorithms in the presence of additive white Gaussian noise in order to understand
whether the proposed algorithm is capable of providing the
enhanced performance in noisy environment. Hence, the signal x3 (t) is contaminated with the additive white Gaussian
noise and it is assumed that SNR = 25 dB. The results of such
an analysis are summarized in Table 3. Even though, the performance has degraded in comparison to the noiseless case,
the WWOST with p(t) still outperforms the other considered
representations.
4.2.
Demonstration example
In order to illustrate the effectiveness of the proposed
scheme, the method has been applied to the analysis of engine knocks. A knock is an undesired spontaneous autoignition of the unburned air-gas mixture causing a rapid increase in pressure and temperature. This can lead to serious problems in spark-ignition car engines, for example,
EURASIP Journal on Advances in Signal Processing
1
Frequency (kHz)
Amplitude (kPa)
10
0
−1
0
2
4
Time (ms)
3
2
1
0
6
0
2
3
2
1
0
0
2
4
Time (ms)
3
2
1
0
6
0
2
3
2
1
0
2
4
Time (ms)
4
Time (ms)
6
(d)
Frequency (kHz)
Frequency (kHz)
(c)
0
6
(b)
Frequency (kHz)
Frequency (kHz)
(a)
4
Time (ms)
6
(e)
3
2
1
0
0
2
4
Time (ms)
6
(f)
Figure 6: Time-frequency analysis of engine knock pressure signal (17th trial): (a) time-domain representation; (b) STFT; (c) ASTFT with
p
p
p
σ opt (t); (d) Sx (t, f ) with p = 1 (standard S-transform); (e) Sx (t, f ) with p = 0.86; (f) Sx (t, f ) with the optimal p(t).
environment pollution, mechanical damages, and reduced
energy efficiency [21, 22]. In this paper, a focus will be on
the analysis of knock pressure signals.
It has been previously shown that high-pass filtered pressure signals in the presence of knocks can be modeled as
multicomponent FM signals [22]. Therefore, the goal of this
analysis is to illustrate how effectively the proposed WWOST
can decouple these components in time-frequency representation. A knock pressure signal recorded from a 1.81 Volkswagen Passat engine at 1200 rpm is considered. Note that the
signal is high-pass filtered with a cutoff frequency of 3000 Hz.
The sampling rate is fs = 100 kHz and the signal contains 744
samples.
The performance of the proposed scheme in this case is
evaluated by comparing it with that of the STFT, the ASTFT,
and the standard S-transform. The results are shown in Figures 6 and 7. These results represent two sample cases from
fifty trials. For the STFT, a Gaussian window, with a standard
deviation of 0.3 milliseconds, is used for both cases. The optimization of the standard deviation for the ASTFT is per-
formed on the set of values defined by σ gw = {0.01n : n ∈
N and 1 ≤ n ≤ 744} milliseconds.
A comparison of these representations show that the
WWOST performs significantly better than the standard Stransform. The presence of several signal components can be
easily identified with the WWOST, but rather difficult with
the standard S-transform. In addition, both proposed algorithms produce higher concentration than the STFT and the
corresponding class of the ASTFT. This is accurately depicted
through the results presented in Table 4. The best concentration is achieved with the time-varying algorithm, while
the time invariant value p produces slightly higher concentration than the ASTFT with the time-invariant value of
σ gw (σ opt = 0.2 milliseconds for the signal in Figure 6 and
σ opt = 0.19 milliseconds for the signal in Figure 7).
The direct implication of the results is that the WWOST
could potentially be used for the knock pressure signal analysis. A major advantage of such an approach in comparison to some existing methods is that the signals could be
modeled based on a single observation, instead of multiple
Ervin Sejdić et al.
11
Frequency (kHz)
Amplitude (kPa)
1
0
−1
0
2
4
Time (ms)
3
2
1
0
6
0
2
3
2
1
0
0
2
4
Time (ms)
3
2
1
0
6
0
2
3
2
1
0
2
4
Time (ms)
4
Time (ms)
6
(d)
Frequency (kHz)
Frequency (kHz)
(c)
0
6
(b)
Frequency (kHz)
Frequency (kHz)
(a)
4
Time (ms)
6
(e)
3
2
1
0
0
2
4
Time (ms)
6
(f)
Figure 7: Time-frequency analysis of engine knock pressure signal (48th trial): (a) time-domain representation; (b) STFT; (c) ASTFT with
p
p
p
σ opt (t); (d) Sx (t, f ) with p = 1 (standard S-transform); (e) Sx (t, f ) with p = 0.87; (f) Sx (t, f ) with the optimal p(t).
Table 4: Concentration measures for the two sample trials.
Trial
ΞSTFT ΞASTFTσ opt ΞASTFTσ opt (t) Ξ p=1
Ξ popt Ξ popt (t)
17th trial 0.0057 0.0059
0.0068
0.0054 0.0065 0.0074
48th trial 0.0052 0.0054
0.0060
0.0053 0.0058 0.0069
realizations required by some other time-frequency methods
such as Wigner-Ville distribution [23], since the WWOST
does not suffer from the cross-terms present in bilinear transforms.
4.3. Remarks
It should be noted that, in some cases, when implementing
the proposed algorithm, it may be beneficial to window the
p
signal before evaluating Sx (t, f ) in step (1). This additional
step diminishes the effects of a discrete implementation. As
shown in [24], wideband signals might lead to some irregular
results unless they are properly windowed.
The STFT and the ASTFT are valuable signal decomposition-based representations, which can achieve good energy concentration for a wide variety of signals. However,
throughout this paper, it is shown that the proposed optimization of the window width used in the S-transform is
beneficial, and in presented cases, it outperforms other standard linear techniques, such as the STFT and the ASTFT.
It is also crucial to mention that the WWOST is designed
to achieve better concentration in the class of the timefrequency representations based on the signal decomposition.
In comparison to the standard S-transform or the STFT,
the WWOST does have a higher computational complexity.
The algorithm for the WWOST is based on an optimization procedure and requires a parameter tuning. However,
when compared to the transforms of similar group algorithms (e.g., ASTFT), the WWOST has almost the same degree of complexity.
The sampled data version of the standard S-transform
and their MATLAB implementations have been discussed in
12
EURASIP Journal on Advances in Signal Processing
several publications [5, 7, 25–27]. The WWOST is a straightforward extension of the standard S-transform. Therefore,
the sampled data version of the WWOST also follows the
steps presented in earlier publications.
5.
CONCLUSION
In this paper, a scheme for improvement of the energy
concentration of the S-transform has been developed. The
scheme is based on the optimization of the width of the window used in the transform. The optimization is carried out
by means of a newly introduced parameter. Therefore, the
developed technique is referred to as a window width optimized S-transform (WWOST). Two algorithms for parameter optimization have been developed: one for finding an optimal constant value of the parameter p for the entire signal;
while the other is to find a time-varying parameter. The proposed scheme is evaluated and compared with the standard
S-transform by using a set of synthetic test signals. The results have shown that the WWOST can achieve better energy
concentration in comparison with the standard S-transform.
As demonstrated, the WWOST is capable of achieving higher
concentration than other standard linear methods, such as
the STFT and its adaptive form. Furthermore, the proposed
technique has also been applied to engine knock pressure signal analysis, and the results have indicated that the proposed
technique provides a consistent improvement over the standard S-transform.
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
ACKNOWLEDGMENTS
Ervin Sejdić and Jin Jiang would like to thank the Natural Sciences and Engineering Research Council of Canada (NSERC)
for financially supporting this work.
REFERENCES
[1] L. Cohen, Time-Frequency Analysis, Prentice Hall PTR, Englewood Cliffs, NJ, USA, 1995.
[2] S. G. Mallat, A Wavelet Tour of Signal Processing, Academic
Press, San Diego, Calif, USA, 2nd edition, 1999.
[3] K. Gröchenig, Foundations of Time-Frequency Analysis,
Birkhäuser, Boston, Mass, USA, 2001.
[4] I. Djurović and LJ. Stanković, “A virtual instrument for timefrequency analysis,” IEEE Transactions on Instrumentation and
Measurement, vol. 48, no. 6, pp. 1086–1092, 1999.
[5] R. G. Stockwell, L. Mansinha, and R. P. Lowe, “Localization of
the complex spectrum: the S-transform,” IEEE Transactions on
Signal Processing, vol. 44, no. 4, pp. 998–1001, 1996.
[6] S. Theophanis and J. Queen, “Color display of the localized
spectrum,” Geophysics, vol. 65, no. 4, pp. 1330–1340, 2000.
[7] C. R. Pinnegar and L. Mansinha, “The S-transform with windows of arbitrary and varying shape,” Geophysics, vol. 68, no. 1,
pp. 381–385, 2003.
[8] C. R. Pinnegar and L. Mansinha, “The bi-Gaussian Stransform,” SIAM Journal of Scientific Computing, vol. 24,
no. 5, pp. 1678–1692, 2003.
[9] M. Varanini, G. De Paolis, M. Emdin, et al., “Spectral analysis of cardiovascular time series by the S-transform,” in Com-
[19]
[20]
[21]
[22]
[23]
[24]
puters in Cardiology, pp. 383–386, Lund, Sweden, September
1997.
G. Livanos, N. Ranganathan, and J. Jiang, “Heart sound analysis using the S-transform,” in Computers in Cardiology, pp.
587–590, Cambridge, Mass, USA, September 2000.
E. Sejdić and J. Jiang, “Comparative study of three timefrequency representations with applications to a novel correlation method,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP ’04),
vol. 2, pp. 633–636, Montreal, Quebec, Canada, May 2004.
P. D. McFadden, J. G. Cook, and L. M. Forster, “Decomposition of gear vibration signals by the generalized S-transform,”
Mechanical Systems and Signal Processing, vol. 13, no. 5, pp.
691–707, 1999.
A. G. Rehorn, E. Sejdić, and J. Jiang, “Fault diagnosis in machine tools using selective regional correlation,” Mechanical
Systems and Signal Processing, vol. 20, no. 5, pp. 1221–1238,
2006.
P. K. Dash, B. K. Panigrahi, and G. Panda, “Power quality analysis using S-transform,” IEEE Transactions on Power Delivery,
vol. 18, no. 2, pp. 406–411, 2003.
E. Sejdić and J. Jiang, “Selective regional correlation for pattern recognition,” IEEE Transactions on Systems, Man, and Cybernetics, Part A, vol. 37, no. 1, pp. 82–93, 2007.
LJ. Stanković, “Analysis of some time-frequency and timescale distributions,” Annales des Telecommunications, vol. 49,
no. 9-10, pp. 505–517, 1994.
LJ. Stanković, “Measure of some time-frequency distributions
concentration,” Signal Processing, vol. 81, no. 3, pp. 621–631,
2001.
D. L. Jones and T. W. Parks, “A high resolution data-adaptive
time-frequency representation,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 38, no. 12, pp. 2127–
2135, 1990.
T.-H. Sang and W. J. Williams, “Rényi information and signaldependent optimal kernel design,” in Proceedings of the 20th
IEEE International Conference on Acoustics, Speech and Signal
Processing (ICASSP ’95), vol. 2, pp. 997–1000, Detroit, Mich,
USA, May 1995.
W. J. Williams, M. L. Brown, and A. O. Hero III, “Uncertainty,
information, and time-frequency distributions,” in Advanced
Signal Processing Algorithms, Architectures, and Implementations II, vol. 1566 of Proceedings of SPIE, pp. 144–156, San
Diego, Calif, USA, July 1991.
M. Urlaub and J. F. Böhme, “Evaluation of knock begin in
spark-ignition engines by least-squares,” in Proceedings of the
IEEE International Conference on Acoustics, Speech and Signal
Processing (ICASSP ’05), vol. 5, pp. 681–684, Philadelphia, Pa,
USA, March 2005.
I. Djurović, M. Urlaub, LJ. Stanković, and J. F. Böhme, “Estimation of multicomponent signals by using time-frequency
representations with application to knock signal analysis,” in
Proceediongs of the European Signal Processing Conference (EUSIPCO ’04), pp. 1785–1788, Vienna, Austria, September 2004.
D. König and J. F. Böhme, “Application of cyclostationary and
time-frequency signal analysis to car engine diagnosis,” in Proceedings of IEEE International Conference on Acoustics, Speech,
and Signal Processing (ICASSP ’94), vol. 4, pp. 149–152, Adelaide, SA, Australia, April 1994.
F. Gini and G. B. Giannakis, “Hybrid FM-polynomial phase
signal modeling: parameter estimation and Cramér-Rao
bounds,” IEEE Transactions on Signal Processing, vol. 47, no. 2,
pp. 363–377, 1999.
Ervin Sejdić et al.
[25] R. G. Stockwell, S-transform analysis of gravity wave activity
from a small scale network of airglow imagers, Ph.D. dissertation, The University of Western Ontario, London, Ontario,
Canada, 1999.
[26] C. R. Pinnegar and L. Mansinha, “Time-local Fourier analysis
with a scalable, phase-modulated analyzing function: the Stransform with a complex window,” Signal Processing, vol. 84,
no. 7, pp. 1167–1176, 2004.
[27] C. R. Pinnegar, “Time-frequency and time-time filtering with
the S-transform and TT-transform,” Digital Signal Processing,
vol. 15, no. 6, pp. 604–620, 2005.
13
EURASIP Journal on Wireless Communications and Networking
Special Issue on
Fairness in Radio Resource Management for
Wireless Networks
Call for Papers
Radio resource management (RRM) techniques (such as admission control, scheduling, sub-carrier allocation, channel
assignment, power allocation, and rate control) are essential
for maximizing the resource utilization and providing quality of service (QoS) in wireless networks.
In many cases, the performance metrics (e.g., overall
throughput) can be optimized if opportunistic algorithms
are employed. However, opportunistic RRM techniques always favor advantaged users who have good channel conditions and/or low interference levels. The problem becomes
even worse when the wireless terminals have low mobility
since the channel conditions become slowly varying (or even
static), which might lead to long-term unfairness. The problem of fair resource allocation is more challenging in multihop wireless networks (e.g., mesh and multihop cellular networks).
The performance fairness can be introduced as one of
the QoS requirements (e.g., as a condition on the minimum
throughput per user). Fair RRM schemes might penalize advantaged users; hence, there should be a tradeoff between the
overall system performance and the fairness requirements.
We are soliciting high-quality unpublished research papers addressing the problem of fairness of RRM techniques
in wireless communication systems. Topics include (but are
not limited to):
• Fairness of scheduling schemes in wireless networks
• Tradeoff between maximizing the overall throughput
and achieving throughput fairness
• RRM fairness: problem definition and solution tech•
•
•
•
•
•
niques
Fairness performance in emerging wireless systems
(WiMAX, ad hoc networks, mesh networks, etc.)
Cross-layer RRM design with fairness
Short-term and long-term fairness requirements
Adaptive RRM to support fairness
Fairness in cooperative wireless communications
Issues and approaches for achieving fairness in multihop wireless networks
•
•
•
•
RRM framework and QoS architecture
Complexity and scalability issues
Experimental and implementation results and issues
Fairness in multiple-antenna transmission/reception
systems
• Fairness in end-to-end QoS provisioning
Authors should follow the EURASIP Journal on Wireless Communications and Networking manuscript format described at the journal site http://www.hindawi.com/
journals/wcn/. Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/,
according to the following timetable:
Manuscript Due
July 1, 2008
First Round of Reviews
October 1, 2008
Publication Date
January 1, 2009
Guest Editors
Mohamed Hossam Ahmed, Faculty of Engineering and
Applied Science, Memorial University of Newfoundland,
St. John’s, NF, Canada A1B 3V6; [email protected]
Alagan Anpalagan, Department of Electrical and
Computer Engineering, Ryerson University, Toronto, ON,
Canada M5G 2C5; [email protected]
Kwang-Cheng Chen, Department of Electrical
Engineering, National Taiwan University, Taipei, Taiwan;
[email protected]
Zhu Han, Department of Electrical and Computer
Engineering, College of Engineering, Boise State University
Boise, Idaho, USA; [email protected]
Ekram Hossain, Department of Electrical and Computer
Engineering, University of Manitoba, Winnipeg, MB,
Canada R3T 2N2; [email protected]
Hindawi Publishing Corporation
http://www.hindawi.com
EURASIP Journal on Advances in Signal Processing
Special Issue on
Signal Processing Advances in Robots and Autonomy
Call for Papers
The capabilities of robots and autonomous systems have increased dramatically over the past years. This success story
partly depends on advances in signal processing which provide appropriate and efficient analysis of sensor data and
enable autonomy. A key element of the transition of signal
processing output to its exploitation inside robots and autonomous systems is the way uncertainty is managed: uncertainty originating from insufficient sensor data, uncertainty
about effects of future autonomous actions and, in the case of
distributed sensors and actuators (like for a team of robots),
uncertainty about communication lines. The aim of this special issue is to focus on recent developments that allow passing this transition path successfully, showing either where
signal processing is used in robotics and autonomy or where
robotics and autonomy had special demands that had not
been fulfilled by signal processing before.
Topics of interest include, but are not limited to:
• Autonomous navigation:
◦ Outdoor navigation using geo-information and
dedicated indoor navigation solutions
◦ Collision avoidance/sense and avoid
◦ Dynamic feature maps, and simultaneous localization and mapping (SLAM)
• Path planning:
◦ Proactive, based on open-loop optimization
◦ Reactive, based on adaptive control or model
predictive control (MPC)
◦ Probabilistic approaches for maximizing the expected future information
• Exploration:
◦ Networked teams of robots
◦ Sensor networks which mix static sensors with
autonomous moving ones
◦ Distributed algorithms and communication
aspects
The special issue will focus on the one hand on the development and comparison of algorithmic approaches and on
the other hand on their currently ever-widening range of applications in any platform: underwater, surface, ground, and
airborne. Special interest lies in probabilistic approaches and
setups of distributed sensors and actuators.
Authors should follow the EURASIP Journal on Advances in Signal Processing manuscript format described
at http://www.hindawi.com/journals/asp/. Prospective authors should submit an electronic copy of their complete
manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/, according to the following
timetable:
Manuscript Due
August 1, 2008
First Round of Reviews
November 1, 2008
Publication Date
February 1, 2009
Guest Editors
Frank Ehlers, NATO Undersea Research Centre (NURC),
Viale S. Bartolomeo 400, 19138 La Spezia, Italy;
[email protected]
Fredrik Gustafsson, Department of Electrical Engineering,
Linköping University, 58183 Linköping, Sweden;
[email protected]
Matthijs Spaan, Instituto de Sistemas e Robótica, Instituto
Superior Técnico, Avenue Rovisco Pais 1, 1049-001 Lisboa,
Portugal; [email protected]
Hindawi Publishing Corporation
http://www.hindawi.com
EURASIP Journal on Image and Video Processing
Special Issue on
Patches in Vision
Call for Papers
The smallest primitive employed for describing an image is
the pixel. However, analyzing an image as an ensemble of
patches (i.e., spatially adjacent pixels/descriptors which are
treated collectively as a single primitive), rather than individual pixels/descriptors, has some inherent advantages (i.e.,
computation, generalization, context, etc.) for numerous image and video content extraction applications (e.g., matching, correspondence, tracking, rendering, etc.). Common descriptors in literature, other than pixels, have been contours,
shape, flow, and so forth.
Recently, many inroads have been made into novel tasks
in image and video content extraction through the employment of patch-based representations with machine learning
and pattern recognition techniques. Some of these novel areas include (but are not limited to):
• Object recognition/detection/tracking
• Event recognition/detection
• Structure from motion/multiview
In this special issue, we are soliciting papers from the image/video processing, computer vision, and pattern recognition communities that expand and explore the boundaries of
patch representations in image and video content extraction.
Relevant topics to the issue include (but are not limited
to):
• Novel methods for identifying (e.g., SIFT, DoGs, Har•
•
•
•
ris detector) and employing salient patches
Techniques that explore criteria for deciding the size
and shape of a patch based on image content and the
application
Approaches that explore the employment of multiple
and/or heterogeneous patch sizes and shapes during
the analysis of an image
Applications that explore how important relative patch
position is, and whether there are advantages in allowing those patches to move freely or in a constrained
fashion
Novel methods that explore and extend the concept of
patches to video (e.g. space-time patches/volumes)
• Approaches that draw upon previous work in struc-
tural pattern recognition in order to improve current
patch-based algorithms
• Novel applications that extend the concept of patchbased analysis to other, hitherto, nonconventional areas of image and video processing, computer vision,
and pattern recognition
• Novel techniques for estimating dependencies between
patches in the same image (e.g., 3D rotations) to improve matching/correspondence algorithmic performance
Authors should follow the EURASIP Journal on Image and
Video Processing manuscript format described at the journal site http://www.hindawi.com/journals/ivp/. Prospective
authors should submit an electronic copy of their complete
manuscripts through the journal Manuscript Tracking System at http://mts.hindawi.com/, according to the following
timetable:
Manuscript Due
May 1, 2008
First Round of Reviews
August 1, 2008
Publication Date
November 1, 2008
Guest Editors
Simon Lucey, Robotics Institute, Carnegie Mellon
University, Pittsburgh, PA, USA; [email protected]
Tsuhan Chen, ECE Department, Carnegie Mellon
University, Pittsburgh PA, USA; [email protected]
Hindawi Publishing Corporation
http://www.hindawi.com
EURASIP Journal on Bioinformatics and Systems Biology
Special Issue on
Applications of Signal Processing Techniques to
Bioinformatics, Genomics, and Proteomics
Call for Papers
The recent development of high-throughput molecular genetics technologies has brought a major impact to bioinformatics, genomics, and proteomics. Classical signal processing techniques have found powerful applications in extracting and modeling the information provided by genomic
and proteomic data. This special issue calls for contributions
to modeling and processing of data arising in bioinformatics, genomics, and proteomics using signal processing techniques. Submissions are expected to address theoretical developments, computational aspects, or specific applications.
However, all successful submissions are required to be technically solid and provide a good integration of theory with
practical data.
Suitable topics for this special issue include but are not
limited to:
•
•
•
•
•
•
•
•
•
•
Guest Editors
Erchin Serpedin, Department of Electrical and Computer
Engineering, Texas A&M University, College Station, TX
77843-3128, USA; [email protected]
Javier Garcia-Frias, Department of Electrical and
Computer Engineering, University of Delaware, Newark, DE
19716-7501, USA; [email protected]
Yufei Huang, Department of Electrical and Computer
Engineering, University of Texas at San-Antonio, TX
78249-2057, USA; [email protected]
Ulisses Braga Neto, Department of Electrical and
Computer Engineering, Texas A&M University, College
Station, TX 77843-3128, USA; [email protected]
Time-frequency representations
Spectral analysis
Estimation and detection
Stochastic modeling of gene regulatory networks
Signal processing for microarray analysis
Denoising of genomic data
Data compression
Pattern recognition
Signal processing methods in sequence analysis
Signal processing for proteomics
Authors should follow the EURASIP Journal on Bioinformatics and Systems Biology manuscript format described
at the journal site http://www.hindawi.com/journals/bsb/.
Prospective authors should submit an electronic copy of
their complete manuscript through the EURASIP Journal on
Bioinformatics and Systems Biology’s Manuscript Tracking
System at http://mts.hindawi.com/, according to the following timetable:
Manuscript Due
June 1, 2008
First Round of Reviews
September 1, 2008
Publication Date
December 1, 2008
Hindawi Publishing Corporation
http://www.hindawi.com
International Journal of Digital Multimedia Broadcasting
Special Issue on
Personalization of Mobile Multimedia Broadcasting
Call for Papers
In recent years, the widespread adoption of multimedia computing, the deployment of mobile and broadband networks,
and the growing availability of cheap yet powerful mobile
have converged to gradually increase the range and complexity of mobile multimedia content delivery services for devices
such as PDAs and cell phones. Basic multimedia applications
are already available for current generation devices, and more
complex broadcasting services are under development or expected to be launched soon, among which mobile and interactive television (ITV). Among the many challenging issues
opened by these developments is the problem of personalization of such services: adaptation of the content to the technical environment of the users (device and network type) and
to their individual preferences, providing personalized assistance for selecting and locating interesting programes among
an overwhelming number of proposed services.
This special issue is intended to foster state-of-the-art research contributions to all research areas either directly applying or contributing to solving the issues related to digital
multimedia broadcasting personalization. Topics of interest
include (but are not limited to):
•
•
•
•
•
•
•
•
•
•
•
•
Mobile TV
Mobile multimedia broadcasting personalization
Interactive broadcasting services/interactive television
Personalization and multimedia home platform
(MHP)
Multimedia content adaptation for personalization
User behavior and usage modelling
Standards for modelling and processing (MPEG-21,
CC/PP, etc.)
Personalization issues in DVB-H, DMB, MediaFLO,
CMMB, MBMS, and other systems
Mobile web initiative
Personalized multimedia and location-based services
Security and digital rights management
Applications for personalized mobile multimedia
broadcasting with cost-effective implementation
Authors should follow the International Journal of Digital Multimedia Broadcasting manuscript format described
at the journal site http://www.hindawi.com/journals/ijdmb/.
Prospective authors should submit an electronic copy of their
complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/ according to the following timetable:
Manuscript Due
March 1, 2008
First Round of Reviews
June 1, 2008
Publication Date
September 1, 2008
Guest Editors
Harald Kosch, University of Passau, 94030 Passau,
Germany; [email protected]
Jörg Heuer, Siemens AG, 80333 Munich, Germany;
[email protected]
Günther Hölbling, University of Passau, 94030 Passau,
Germany; [email protected]
László Böszörményi, University Klagenfurt, 9020
Klagenfurt, Austria; [email protected]
David Coquil, University of Passau, 94030 Passau,
Germany; [email protected]
Hindawi Publishing Corporation
http://www.hindawi.com
Research Letters in
Signal Processing
Why publish in this journal?
Research Letters in Signal Processing is devoted to very fast publication of short, highquality manuscripts in the broad field of signal processing. Manuscripts should not exceed
4 pages in their final published form. Average time from submission to publication shall
be around 60 days.
Research Letters in
Signal Processing
Hindawi Publishing Corporation
http://www.hindawi.com
Why publish in this journal?
Wide Dissemination
All articles published in the journal are freely available online with no subscription or registration
barriers. Every interested reader can download, print, read, and cite your article.
Quick Publication
The journal employs an online “Manuscript Tracking System” which helps streamline and speed
the peer review so all manuscripts receive fast and rigorous peer review. Accepted articles appear
online as soon as they are accepted, and shortly after, the final published version is released online
following a thorough in-house production process.
Research Letters in
Professional Publishing Services
The journal provides professional copyediting, typesetting, graphics, editing, and reference
validation to all accepted manuscripts.
Volume 2007
Editorial Board
Tyseer Aboulnasr, Canada
T. Adali, USA
S. S. Agaian, USA
Tamal Bose, USA
Jonathon Chambers, UK
Liang-Gee Chen, Taiwan
P. Dan Dan Cristea, Romania
Karen Egiazarian, Finland
Fary Z. Ghassemlooy, UK
Ling Guan, Canada
M. Haardt, Germany
Peter Handel, Sweden
Alfred Hanssen, Norway
Andreas Jakobsson, Sweden
Jiri Jan, Czech Republic
Soren Holdt Jensen, Denmark
Stefan Kaiser, Germany
C. Chung Ko, Singapore
S. Maw Kuo, USA
Miguel Angel Lagunas, Spain
James Lam, Hong Kong
Mark Liao, Taiwan Volume 2007
Stephen Marshall, UK
Stephen McLaughlin, UK
Antonio Napolitano, Italy
C. Richard, France
M. Rupp, Austria
William Allan Sandham, UK
Ravi Sankar, USA
John J. Shynk, USA
A. Spanias, USA
Yannis Stylianou, Greece
Jarmo Henrik Takala, Finland
S. Theodoridis, Greece
Luc Vandendorpe, Belgium
Jar-Ferr Kevin Yang, Taiwan
Signal Processing
Keeping Your Copyright
Authors retain the copyright of their manuscript, which is published using the “Creative Commons
Attribution License,” which permits unrestricted use of all published material provided that it is
properly cited.
Extensive Indexing
Hindawi Publishing Corporation
Articles published in this journal will be indexed in several major indexing databases to ensure
thehttp://www.hindawi.com
maximum possible visibility of each published article.
Submit your Manuscript Now...
In order to submit your manuscript, please visit the journal’s website that can be found at
http://www.hindawi.com/journals/rlsp/ and click on the “Manuscript Submission” link in the
navigational bar.
Should you need help or have any questions, please drop an email to the journal’s editorial office
at [email protected]
ISSN: 1687-6911; e-ISSN: 1687-692X; doi:10.1155/RLSP
Hindawi Publishing Corporation
410 Park Avenue, 15th Floor, #287 pmb, New York, NY 10022, USA