Algorithm to locate local maxima

Question

I have data that always looks something like this:

alt text http://michaelfogleman.com/static/images/chart.png

I need an algorithm to locate the three peaks.

Answer 1

You could try a band-pass filter to reject the noise and make it easier to reliably select those maxima.

The point of a band-pass (rather than low-pass) is to pull nearly-constant down to zero. That way, the highest values you find in the filtered result will probably be the clearest peaks.

Certainly if you can define a narrow frequency-range for your signal and apply a very selective filter, it should make a fairly unsophisticated maxima-finding algorithm practical - e.g. a simple sample-thats-higher-than-either-neighbour scan.

A sophisticated filter might not be necessary - you could get away with a mexican hat wavelet at a single well-chosen scale. One scale probably means it's not really a wavelet any more - just a band-pass FIR filter.

EDIT

There's an asymmetric wavelet (I forget the name) which, if the mexican hat is analogous to a cosine, takes the role of the sine. I mention it as it combines band-pass filtering with a kind of derivative - the zero-crossings in the result are the stationary-points of a band-pass filtered version of the original signal.

A "debounced" scan could then identify reliable maxima by looking for crossing points in this "derivative" signal.