How to compare two signal

 I have two signal. One is original signal and other is reconstruction of that signal. Reconstruction is done by some algorithms. My doubt is how to compare of that two signal to show that reconstructed signal has approximately same as original signal.

Answer 1

[Hugo]

The comparison can be done in several different ways. Suppose that X is the original signal and that XR is its reconstruction. You can compare them by calculating

mean( (X(:)-XR(:)).^2)

which represents the mean of the squared differences between both signals. This quantity will be zero only if both signals are exactly the same.

You could also calculate

mean( (X(:)-XR(:)).^2) / mean( (X(:).^2 )

which will give you an idea on the size of the differences between the two signals compared to the variance of the original signal.

You may well be interested in other ways of measuring the reconstruction error as well. The possibilities are too vast depending on what the signal is about. You can read more about this by looking for words like "reconstruction error" and "distance measures" in google. Any book about pattern recognition will provide you with good material too.

Hope this helps.

[Tinkul]

thank you..

Answer 2

[Image Analyst]

If they're images or 2D arrays, you can use psnr() or ssim() (both are now in the Image Processing Toolbox). Check wikipedia for definitions. I have a manual method for psnr and MSE if you need it. You could also use SAD or MAD (sum or mean of absolute differences).

[Tinkul]

no sir, signal is 1D signal...

[Image Analyst]

Well psnr, MSE, MAD, and SAD all work for 1D signals. Try them. They have different uses. For example the MSE (Hugo's answer) really blows up for big outliers, while MAD doesn't so much. And there are others that are really a lot better behaved in the presence of outliers like Median Absolute Deviation http://en.wikipedia.org/wiki/Median_absolute_deviation