peeasa at sat

1
?pe?e??as?a ß???at????? s?µat??

• ?????a ???ßa?d?

2
??at?

• ?ata???s? ?d??t?t?? s?µat??
• ???es? ?a?a?t???st????
• ???te??p???s?
• ?a????µ?s?

3
?a?a?t???st???

• ?d??t?te? st? ped?? t?? ??????
• ?d??t?te? st? ped?? t?? s????t?t??
• ?????-fasµat???? ?d??t?te?
• ??p

4
?????? p??et??µas?a - Preprocessing

• ??????s?
• BASELINE
• TREND
• ?p?????ß?p???s?
• Gaussian noise
• 50 Hz line interference
• Other specific interferences

5
Preprocessing

• ?fa??es? t?? bias - µ?s?? t?µ?
• Trend removal
• ?fa??es? ??aµµ??
• ??de??µ????, afa??es? p??? ?aµ???? fasµat????
  s???st?s??
• ?a??????p???s? s?µata ?d?a? e????e?a?

6
pa??de??µa

• load fantasia.txt ascii
• test_ecgfantasia(11000,3)
• mnmean(test_ecg)
• y test_ecg -mn
• plot(test_ecg)
• hold on
• plot(y, r)
• y1 detrend(y)
• plot(y)
• hold on
• plot(y1, r)
• http//lomiweb.med.auth.gr/xml_output/sigproc/

7
Filters in matlab

• FIR
• b fir1(48,0.35 0.65)
• f 0 0.3 0.4 0.6 0.7 1 a 0 0 1 1 0 0 b
  remez(17,f,a)
• IIR
• Butterworth n 5 Wn 100 200/500 b,a
  butter(n,Wn)
• Chebyshev n 10 Rp 0.5 Wn 100 200/500
  b,a cheby1(n,Rp,Wn)
• Elliptic For data sampled at 1000 Hz, design a
  sixth-order lowpass elliptic filter with a cutoff
  frequency of 300 Hz, 3 dB of ripple in the
  passband, and 50 dB of attenuation in the
  stopband
• b,a ellip(6,3,50,300/500)
• http//users.ece.gatech.edu/bonnie/book/TUTORIAL/
  tut_4.html
• http//www.dsptutor.freeuk.com/digfilt.pdf

8
Filters in matlab

• The frequency response of all the classic
  electronic filters. The first one is the
  Butterworth filter, that is the smoothest one but
  it has no ripples. The last one is the Elliptic
  filter it is the sharpest one but it shows
  ripples in both the pass-band and the stop-band.
  The two Chebyshev filter in the middle have an
  average behavior, being quite sharp with ripples
  in part of the spectrum. All the plots have been
  obtained using the same parameters and the same
  number of coefficients, thus showing only the
  properties of the different filters.
• http//en.wikipedia.org/wiki/ImageElectronic_line
  ar_filters.svg

9
?a??de??µa

• load fantasia.txt ascii
• test_ecgfantasia(13000,3)
• b,a butter(9,3/125 50/125)
• y1 filtfilt(b,a,y)
• plot(test_ecg)
• plot(y1)

?????? epe?e??as?a ??a ?a????sµa t??
s?µat??. ???? ?fa????µe t?? p??? ?aµ????
s????t?te? trend ?fa????µe t?? ????? s????t?te?
- ????ß??
10
pa??de??µa

• ?????? ????ß??
• Download the ECG signal from the web
  http//www.oersted.dtu.dk/ftp/jaj/31610/data/data4
  /ecg.mat
• Sampling frequency 500 Hz. Values in volts.
  Amplification factor on the electrode signals
  500.
• load ecg.mat
• plot(ecg)

11
pa??de??µa

• ?a??? t? ?p??e?µe?? ??????ta? e?af??,
  ?ata???feta? ??a ?aµ???? s????t?ta? µ???? s?µa
  p?? ep????eta? st? ECG ?a? ?a??st? p?? d?s????
  t? µe??t? t??.
• ?? s?µa p?? ape?????saµe e??a? ??a t?t???
  pa??de??µa. G?a ?a ap?µa???????? ?? µ?????
  s???st?se?
• set frequencies below 0.5 Hz to zero
• b,a butter(7,0.6/250 200/250)
• Y FILTFILT(b, a, ecg)

12
pa??de??µa

• ?a?at????µe t?? d?af???? t?? a?????? ?a? te?????
  s?µat??.  
• plot(Y,'r')hold onplot(ecg)

13
Increasing the signal-to-noise ratio

• The ECG signal is also contaminated with noise.
  The amount of noise is proportional to the
  measurement bandwidth.
• A higher bandwidth will give more noise in the
  signals, and limiting the bandwidth can obscure
  details in the ECG.
• Try to find a compromise on the cut-off
  frequency, where the shape of the ECG signal is
  preserved and the noise reduced. Try different
  choices and plot and comment on the results.
• Make a plot of one period of the new filtered
  signal ecg3 and identify as many intervals in the
  ECG as you can.  

14
Increasing the signal-to-noise ratio

• b,a butter(3,0.6/250 10/250)
• Y1 FILTFILT(b, a, Y)
• figure
• plot(Y1(11000),'r')hold onplot(Y(11000))title
  ('10Hz')
• b,a butter(3,0.6/250 20/250)
• Y1 FILTFILT(b, a, Y)
• figure
• plot(Y1(11000),'r')hold onplot(Y(11000))title
  ('20Hz')
• b,a butter(3,0.6/250 50/250)
• Y1 FILTFILT(b, a, Y)
• figure
• plot(Y1(11000),'r')hold onplot(Y(11000))title
  ('50Hz')
• b,a butter(3,0.6/250 100/250)
• Y1 FILTFILT(b, a, Y)
• figure
• plot(Y1(11000),'r')hold onplot(Y(11000))title
  ('100Hz')

15
(No Transcript)
16
Removing 50 Hz interference

• Often the ECG is contaminated with 50 Hz noise
  from the power outlet, which overlaps the ECG.
  This interference should be removed.
• Szsize(Y,1)
• for i1Sz, Y50(i,1)Y(i,1)0.1cos(2pii50/500)
  end
• plot(Y50(11000))
• Design a filter for removing 50 Hz noise as a
  Notch filter with a zero at 50 Hz. A Notch filter
  is an all-pass filter with a zero at one given
  frequency.
• Apply the filter to the signal and generate a new
  signal ecg2. Plot the new signal and note the
  difference.
• n 5
• Wn 1 45/500
• b,a butter(n,Wn)
• Y1 FILTFILT(b, a, Y)
• n 5
• Wn 55 150/500
• b,a butter(n,Wn)
• Y2 Y1FILTFILT(b, a, Y1)
• hold on

17
ped?? t?? ?????? Crosscorrelation-S?s??t?s?

• ? s?s??t?s? d?? s??a?t?se?? x(t) ?a? y(t)
  ????eta? se s??s? µe t? ??????? ?a??st???s? t
• ???s?µ?p??e?ta? ??a ?a µet??se? t? ßa?µ? st??
  ?p??? s?s?et????ta?- µ??????? ta d?? s?µata.

18
Cross-correlation

• ? s?s??t?s? ?a??????p??e?ta? st?? pe????? ap? -1
  (complete anti-synchronization) ??? 1 (complete
  synchronization). ??µ? s?s??t?s?? ???t? st? µ?d??
  de???e? ??aµµ??? a?e?a?t?s?a t?? d?? s?st?µ?t??.
• ?p?te?e? ??a ap? ta ap???ste?a ?a? p??
  s?????sµ??a µ?t?a t?? s???????sµ?? d??
  s?st?µ?t??, a? ?a? de? e??a? e?a?s??t? se
  µ?-??aµµ??? e???t?s?.

19
crosscorrelation

• St?? efa?µ???? s?????? ????µe ??a? pepe?asµ???
  a???µ? µet??se??.
• ?st? x0 xN-1 ?a? y0 yN-1 d??
  ?????se???? p?? ?ata???f??a? ta?t?????a, µe
  µ?de???? µ?s? t?µ? ?a? µ??ad?a?a variance. ?
  s?s??t?s? µp??e? ?a ???ste? sa s????t?s? t?? t
  -(N - 1) 0 N - 1

20
S?s??t?s? ?? e??a?e?? ??a t? st????s? s?µ?t??

• ??? pa?µ?? ?a? ? s?s??t?s? t???. ?? s?µe??
  µ???st?? s?s??t?s?? µp??e? ?a ???s?µ?p????e? ??a
  ?a st???????? ?? d?? pa?µ??.

Superimposition of the previous traces properly
aligned
21
S?s??t?s? ??a t?? e??es? transients

• the upper trace represents the original trace,
• the middle trace the signal masked with noise
• the lower trace the correlation between the
  transient and the signal contaminated with noise

22
??t?s?s??t?s? -Autocorrelation

• ? s?s??t?s? µ?a? s????t?s?? µe t?? ea?t? t??
  ???µ??eta? a?t?s?s??t?s?.
• ???a? ??a? t??p?? ??a ?a a????e??e? pe???d???t?ta
  se ??a s?µa.

23
??t?s?s??t?s? ?e???? ????ß??

• ? ?e???? ??a??s?a??? ????ß?? ??e? µ?de????
  a?t?s?s??t?s?

nnrandn(1000,1) plot(nn) crxcorr(nn,nn,1000,c
oeff) plot(cr)
24

• The autocovariance function will be written as

25
pa??de??µa

• load fantasia.txt ascii
• test_ecgfantasia(13000,3)
• b,a butter(9,3/125 50/125)
• y1 filtfilt(b,a,test_ecg)
• crxcorr(y1,y1, 1000,'coeff')
• plot(cr)
• mx,psmax(cr)
• mx 1.0000
• ps 1001
• for i12001
• if( cr(i) lt 0.2) cr(i)0
• end end
• plot(cr)

??s?? fa??eta? ?a e??a? ? ?a?d?a??? ???µ?? 250
samples -gt 1 sec - gt 60 beats/min
26

• ??? s?s?et????ta? t? ?a?d?????f?µa µe t??
  a?ap?e?st??? ???µ? (st? a??e?? fantasia )
• load fantasia.txt ascii
• test_ecgfantasia(,3)
• b,a butter(3,0.01/125 30/125)
• y1 filtfilt(b,a,test_ecg)
• test_ecgy1
• test_respfantasia(,2)
• b,a butter(3,0.01/125 30/125)
• y1 filtfilt(b,a,test_resp)
• test_respy1
• crxcorr(test_ecg, test_resp, 9000,'coeff')
• plot(cr)
• mx,psmax(cr)

? s?s??t?s? de? p????pte? ap? t?? ap?? ?µ???t?ta
t?? µ??f??
27
cross-spectrum function

• St? ped?? t?? s????t?t?? ????eta? t?
  cross-spectrum, µ?a µ??ad??? s????t?s?,
• ?p?? s??????.
• ? s??s? a?t? a?t?st???e? st? s?s??t?s?.
• ? a?t?s?s??t?s? a?t?st???e? st? autospectrum.

28
coherence

• ?? ?a??????p???µ??? cross-spectrum, ???µ??eta?
  coherence function.
• ???a? t? cross-spectrum ?a??????p???µ??? µe ta
  autospectra ???e s????t?s??

where ltgt denotes the ensemble average.
29
coherence

• The estimation of the coherence function is not
  easy. The ensemble averaging is not possible and
  we have to replace it by the time average
  assuming the stationarity of underlying dynamics.
• Usually one divides time series into segments
  and estimates the cross-spectrum and the
  autospectra for each segment, and then takes the
  average over these segments. The choice of the
  segment length, a window function (e.g.,
  Bartlett, Welch) is not always obvious and
  depends on the problem in hand.
• While the coherence function is a function of the
  frequency , it is a very useful measure when one
  is interested in the synchronization related to
  certain frequency ranges only, e.g., in the
  classical EEG frequency bands.

30
?fa?µ???

• St? p??????µe??pa??de??µa ??? s?s?et????ta? t?
  ?a?d?????f?µa µe t?? a?ap?e?st??? ???µ? (st?
  a??e?? fantasia )
• Cxy,Fcohere(test_resp, test_ecg, 256,250)

31
?fa?µ???

• Coherence between 2 eeg channels. Se d?? pe??????
  t?? e??ef????, eµfa?????ta? ?? ?d?e? s????t?te?
• ???s? t??
• ???e??? C3, C4
• S????t?s?? cohere

32

• load A1_C3.txt
• load A1_C4.txt
• c3detrend(A1_C3)
• c4detrend(A1_C4)
• b,a butter(7,3/125 17/125)
• y2 filtfilt(b,a,c4)
• y1 filtfilt(b,a,c3)
• Cxycohere(y1, y2, 256, 128)
• plot(Cxy)

33
Power Spectrum Analysis

• ?? power spectrum de???e? t?? ?s?? ???e
  fasµat???? s???st?sa? t?? ??µat?µ??f??.
• ?? power spectrum ???s?µ?p??e?ta? s???? ??a t??
  a????s? f?s????????? s?µ?t??, ?p?? ECG (rate) ?a?
  EEG .

34
Power Spectrum Analysis

• ?? power spectrum (PS) ????eta? ?? t? tet??????
  t?? µ?t??? t?? f?sµat??

35
?fa?µ???

• Analysis of variations in the instantaneous heart
  rate time series using the beat-to-beat
  RR-intervals (the RR tachogram) is known as Heart
  Rate Variability (HRV) analysis.
• HRV analysis has been shown to provide an
  assessment of cardiovascular disease. The heart
  rate may be increased by slow acting sympathetic
  activity or decreased by fast acting
  parasympathetic (vagal) activity.
• The balance between the effects of the
  sympathetic and parasympathetic systems, the two
  opposite acting branches of the autonomic nervous
  system, is referred to as the sympathovagal
  balance and is believed to be reflected in the
  beat-to-beat changes of the cardiac cycle.

36
?fa?µ???

• The heart rate is given by the reciprocal of the
  RR-interval in units of beats per minute.
• Spectral analysis of the RR tachogram is
  typically used to estimate the effect of the
  sympathetic and parasympathetic modulation of the
  RR-intervals.
• The two main frequency bands of interest are
  referred to as the Low-Frequency (LF) band (0.04
  to 0.15 Hz) and the High-Frequency (HF) band
  (0.15 to 0.4 Hz) .
• Sympathetic tone is believed to influence the LF
  component whereas both sympathetic and
  parasympathetic activity have an effect on the HF
  component.
• The ratio of the power contained in the LF and HF
  components has been used as a measure of the
  sympathovagal balance .

37
?fa?µ???

• Respiratory Sinus Arrhythmia (RSA) is the name
  given to the oscillation in the RR tachogram due
  to parasympathetic activity which is synchronous
  with the respiratory cycle. The RSA oscillation
  manifests itself as a peak in the HF band of the
  spectrum.
• For example, 15 breaths per minute corresponds to
  a 4 second oscillation with a peak in the power
  spectrum at 0.25 Hz.
• A second peak is often found in the LF band of
  the spectrum at approximately 0.1 Hz.
• While the cause of this 10 second rhythm is
  strongly debated, one possible explanation is
  that it may be due to baroreflex regulation which
  creates the so-called Mayer waves in the blood
  pressure signal .

38
Finding the heart rate using autocorrelation

• The heart rate can be found from the
  autocorrelation function of the signal. This is
  done be finding the first local maximum after the
  global maximum at tau 0 in the autocorrelation
  function. Make a procedure for doing this
  automatically and use it on ECG signal ecg. Limit
  your search interval for the maximum to the
  possible range for the heart rate. Does your
  program find the right pulse rate? Document your
  program with plots of the autocorrelation
  functions found.
• crxcorr(Y2,1200,'coeff')
• plot(cr)

39
Periodogram - about HRV analysis

• load thr01.txt
• Pxx, wperiodogram(thr01)
• plot(w,Pxx)
• plot(w(120),Pxx(120))

40
?s??s? 1

• 1. This collection consists of 10 heart beat time
  series 5 young subjects (Y1.txt, Y2.txt, etc)
  and 5 elderly subjects (O1.txt, O2.txt, etc) from
  the Fantasia Database.
• http//www.physionet.org/physiobank/database/fanta
  sia/subset/
• ?a ???e? a????s? t?? µetaß??t?t?ta? t?? ?a?d?a???
  ???µ?? (stat?st??? ?a? µe ß?s? t? power spectrum)
  ?a? ?a d?ap?st??e? e?? ?p?????? d?af???p???se??
  a??µesa st?? d?? ?µ?de?

41
?s??s? 2

• G?a ta EEGs p?? d?a??tete,
• ????sete t?? µp??te? a ?a? ß,
• ß?e?te se µ???? tµ?µata t?? 2 sec p??
  µetaß???eta? ? ?s??? se ???e µp??ta, ?a? ?at?
  p?s? ?? s????t?te? s???p?????? ta?t?????a sta d??
  ?a????a