Wearable EMG System with Signal
Compression and Decompression
Related reading: Effective Low-Power Wearable Wireless
Surface EMG Sensor Design Based on Analog-Compressed
Sensing, Balouchestani & Krishnan (2014). Sensors 14: 2430524328.
W. Rose 201704011
Background
“sEMG signals exhibit good level of sparsity in the
time and frequency domains.”
“Conventional data acquisition approaches rely on
the Shannon sampling theorem, which says a signal
must be sampled at least twice its bandwidth in
order to be represented without error.”
Sparse signal = a signal with most values zero or
lacking information
Drawbacks of conventional approach
Generates huge intolerable number of samples for
many applications with a large bandwidth. Even for
low signal bandwidths, including some biomedical
signals, this produces a large number of redundant
digital samples.
Cure
Use compressive sampling to reduce the number of
acquired samples by utilizing sparsity.
Specifically, use analog compressive sampling before
the analog-to-digital conversion step
Balouchestani & Krishnan (2014)
1. No compression
2. Digitize, then compress (more common than #3)
3. Compress, then digitize
Question for the Authors
Balouchestani & Krishnan (2014) say they apply
compressive sampling to the analog signal before Ato-D conversion. (See bottom part of figure in
previous slide.) But they implement their
compression algorithm in computer code (C, hSpice,
or Matlab). And their sample signals are from online
databases. The fact that they implement in code (not
with a circuit) and that their test data is already
digitized means the ADC has already happened.
How do they account for this discrepancy?
How did they get it published?
L-1 norm
The L1 norm is a way of measuring the “length of a
vector” by the sum of the absolute values of its
components.
𝑘
𝑥
1
=
𝑥𝑘
𝑖=1
𝑛
𝑥
𝑛
𝑘
=
𝑥𝑘
𝑖=1
𝑛
L-2 norm
The L2 norm is the Euclidean norm, in which we
measure the length by the square root of the sum of
the squares of the components.
2
𝑥
2
𝑘
=
𝑥𝑘
𝑖=1
2
L- norm
The L- norm means measuring the length of a
vector by the length of it longest component.
𝑛
𝑥
𝑛
𝑘
= lim
𝑛→∞
𝑥𝑘
𝑖=1
𝑛
= 𝑚𝑎𝑥 𝑥𝑘
L-n norm
The L-n norm is a way of measuring the “length of a
vector” by the nth root of the sum of the nth power of
each element.
𝑛
𝑥
𝑛
𝑘
=
𝑥𝑘
𝑖=1
𝑛
BSBL
Block-sparse Bayesian Learning
Data Compression Examples
No compression: standard audio CD, .wav, .aiff
44.1
𝐾𝑠𝑎𝑚𝑝𝑙𝑒𝑠
𝑏𝑦𝑡𝑒𝑠
𝑠𝑒𝑐
𝑀𝐵
×2
× 60
× 2𝑐ℎ𝑎𝑛𝑛𝑒𝑙𝑠 = 10
𝑠𝑒𝑐
𝑠𝑎𝑚𝑝𝑙𝑒
𝑚𝑖𝑛
𝑚𝑖𝑛
Lossy compression: MP3, AAC
Decompressed signal is not perfect, but very close
Typical compression factor = 4 to 20
Lossless compressed audio formats
Decompressed signal is perfect copy
Typical compression factor = 2
Codec
Software or hardware to compress and decompress
Balouchestani &
Krishnan (2014)
Transmitter and Receiver Design
Eq. 7 in Balouchestani & Krishnan (2014) should be*
𝑇𝑃
𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 =
𝑇𝑃 + 𝐹𝑁
Sensitivity = % of “positives” that are correctly identified.
𝑇𝑁
𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐𝑖𝑡𝑦 =
𝑇𝑁 + 𝐹𝑃
Specificity = % of “negatives” that are correctly identified.
TP = true positive; FN = false negative, etc.
* B.&K. 2014, eq.7, says: Sens. = TP / (TP+TN) (wrong)
Step 7 of Table 2 in Balouchestani & Krishnan (2014) says
sparsity level is given by
Sp = (N/N-K)
which is an unclear or wrong choice of parentheses, and
K is undefined, and it is inconsistent with later figures,
which show that Sparsity is a percentage that is 100% or
less – which will not be true if computed with the
equation above.
Fig. 10 does not make sense. It indicates that
the accuracy is highest when sampling rate is
lowest, just 10% of the Nyquist rate.