MATLAB: How to stack 10 shots from seismic source to produce a resultant signature with greater signal/noise ratio

signal processingstacking

This bolt gun signal (attached) shoots a seismic source every ten seconds. You can see the signature dramatically changes as the ship passes over the geophones. How do I stack the shots fired in this interval to produce a new signal with a greater signal to noise ratio?

Best Answer

What result do you want? You already seem to have removed the 0.1 Hz bolt gun signal, since it does not appear in your Fourier transformed signal (at least that I can see).

I would just use a filter (highpass, lowpass, bandpass or bandstop) to pass your frequencies-of-interest, eliminating everything else. The signals from the ship appear to have a frequency range of about 0.8 to 1.2 Hz, so filtering those in or out — depending on what you want — would likely be easiest.

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step 1: analyze the signal and see if you can determine what frequencies are to be kept and what frequencies are to be discarded. FFTs as well as possibly short-time fourier transforms will be helpful here. You will also need some a priori knowledge of the problem domain (i.e. what frequencies are typically contained in human speech). Your instructor has been kind enough to give you versions with and without the noise, so comparison between the two should show you the frequency cutoff.

step 2: design a filter. start with a first order butterworth lowpass filter, with a cutoff frequency that is between the frequency you think should be kept and the frequency you think should be discarded.

step 3: analyze the filtered signal the same way you analyzed the original signal to see what changed. Also play it back to hear the difference.

step 4: try some other types of filters to see if you can get something better than a 1st order butterworth. e.g. try higher orders, different cutoff frequencies, and different filter types.

Some of the tutorials on my webpage may be helpful to you: http://mechanicalvibration.com/tutorial.html

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The best answer to your question is, “don’t use ‘normrnd’ for that purpose!” It is very much the wrong distribution for that.

You should use ‘rand’ as follows:

x = 0.5*rand(m,n)-0.25;

This will give you a statistically uniform distribution between -0.25 and +0.25, and nowhere else.

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