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How do I compute power spectrograms in MATLAB?

Hi there, 

I'm currently trying to validate an approach previously published for the automatic interpretation of ECGs. One of the main steps described in this paper concerns computing the power spectrograms of the detail and approximate coefficients. 

(paper ref: Automatic detection of atrial fibrillation using stationary wavelet transform and support vector machine, Computers in Biology and Medicine 2015, Asgari et al. Available online using pubmed)

While the paper describes the steps completed reasonably well, there are a few points I need second opinions on:

1. It defines the aforementioned spectrograms as follows

Sd(f) = E{|D(f)|^2}
Sa(f) = E{|A(f)|^2}

Where Sd, Sa are the power spectrums of detail and approximate coefficients respectively, D and A are fourier transforms of the detail and approximate coefficients and E in the expectation operation. 

First Question: What is E and how do I obtain it? I have done lots of searching but can't find anything. 

Second Question: Is there a way of computing the power spectrum another way in matlab?


Any help would be appreciated 

Kind regards

Dr. Nicholas D'Elia
0
Nicholas
12/19/2016 12:42:03 AM
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I don't know anything about this paper, but I give some hint on the wording I read:

> 
> First Question: What is E and how do I obtain it? I have done lots of searching but can't find anything. 

https://en.wikipedia.org/wiki/Expected_value

> 
> Second Question: Is there a way of computing the power spectrum another way in matlab?

help periodogram

if you have a signal processing toolbox
0
Bruno
12/19/2016 10:53:03 AM
On Monday, December 19, 2016 at 1:42:07 PM UTC+13, Nicholas wrote:
> Hi there, 
> 
> I'm currently trying to validate an approach previously published for the automatic interpretation of ECGs. One of the main steps described in this paper concerns computing the power spectrograms of the detail and approximate coefficients. 
> 
> (paper ref: Automatic detection of atrial fibrillation using stationary wavelet transform and support vector machine, Computers in Biology and Medicine 2015, Asgari et al. Available online using pubmed)
> 
> While the paper describes the steps completed reasonably well, there are a few points I need second opinions on:
> 
> 1. It defines the aforementioned spectrograms as follows
> 
> Sd(f) = E{|D(f)|^2}
> Sa(f) = E{|A(f)|^2}
> 
> Where Sd, Sa are the power spectrums of detail and approximate coefficients respectively, D and A are fourier transforms of the detail and approximate coefficients and E in the expectation operation. 
> 
> First Question: What is E and how do I obtain it? I have done lots of searching but can't find anything. 
> 
> Second Question: Is there a way of computing the power spectrum another way in matlab?
> 
> 
> Any help would be appreciated 
> 
> Kind regards
> 
> Dr. Nicholas D'Elia

Actually, it should be:
Sd(f) = E{|D(t,f)|^2}
in other words D is a function of frequency and time.
The operator E{} just means take the mean, so you square the coefficients and take the mean over time.
Another (better?) way of doing it is to use var(D) in Matlab.  In this case the sum of the variances will be the variance of the original time signal (Parseval's Law). 
0
TideMan
12/19/2016 10:49:20 PM
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