Multi-resolution Analysis
TFDs, Wavelets Etc.
PCG applications
Heart Sound Introduction
Recording PCG
S2 signal


Occurs because of blood flow and closure of
Aortic and Pulmonary valves.
Is composed of two sub signals



A2 – created because of Aortic valve closure
P2 - created because of Pulmonary valve closure
A2 is characterized with
lower frequencies than
P2 and is usually
precedes it in time.
FT – Fourier Transform


Fourier Transform
returns the frequency
components of the
signal globaly.
For example:

S2 signal
filtered in
[20,120]
FT – Fourier Transform



The corresponding
FT:
What does this give
us?
No Temporal info!
Short Time FT for changing
signals

FT windowed:
Window size 64
Window size 128
Window size 256
Short Time FT for changing
signals

Uncertainty Principle



Each window N samples.
N/2 coefficients signifying 0-fs/2 frequencies.
Space between coefficients
fs / 2
fs

( N / 2  1) N
Multi-Resolution Analysis
Wavelet Transform - Intro

Basis functions are compact in time and
frequency.

Basis function are created basic function
called “Mother Wavelet”
Wavelet Transform - Intro

Basis function are created from mother wavelet
through scaling and shifting
Wavelet Transform
CTW
Discrete
Wavelet Transform –
PCG applications

Obaidat M.S., J. Med. Eng. Tech., 1993
Used wavelet transform for HS analysis:
Wavelet Transform –
PCG applications

Reed T.R et al. Proceeding
Signal and Image
Processing -2005
Used Wavelet
decomposition and
reconstruction for PCA
feature extraction and
segmentation to Diastolic
and systolic parts
Wavelet Transform –
PCG applications


Liang, H. Hartimo, I.
Signal Process. & Comput. Technol. Lab., Helsinki Univ.
of Technol., Espoo
Used Wavelet Decomposition and Reconstruction of PCG
as input to an ANN for study of murmurs.
There are several other works doing the same for detection
of different HS conditions
Wavelet Transform - Applications

Image Analysis:

Feature Extraction

Wavelet and Fractal
connection – Self
similarity
S-Transform

CTW with mother wavelet:

Properties:


Not Orthogonal
Directly invertible into the Fourier Transform
Spectrum
S-Transform – PCG Application

G Livanos*, N Ranganatha, J
Jiang, Computers in Cardiology
2000.
Showed that S-Transform can
perform best for the needs of a
user who needs a simple and
clear display of intensity,
frequency and timing, in
comparison to Morlet wavelet
and STFT.
Wigner-Ville Distribution

Mathematical definition:

Valuable:


because of preserving FT essence:
Is always pure real
Wigner-Ville Distribution

Problematic:

Cross components unlimited
Wigner-Ville Distribution – PCG
Applications

Xu, Durand et al,
IEEE transactions on
biomedical
engineering 2000,
used WVD to extract
A2 and P2 from S2
signals and used this
to estimate A2-P2
interval
Wigner-Ville Distribution – PCG
Applications

Seedahamed S.M. et al, Biomedical Signal Processing and
control (Feb 2006).
Use WVD to estimate IF (instantaneous frequency).
Chirplet Transform

Instead of wavelet
basis function that can
be scaled and shifted
Chirplet Transform
uses basis functions
that derive for chirps
where the phase
changes too.
Chirplet Transform - Applications

O’Neill J.C. et al gave and algorithm to create sparse
representation of signal using max likelihood estimation of
chirplets
Chirplet Transform - Applications
My work

Currently trying to use TFDs and wavelet
transform to extract interval time of A2-P2.

Currently working on using S-Transform for
basis for a feature extraction algorithm