How to extract a frequency from a signal

问题

Is there a simple way to extract the main frequency/period from a signal (without resorting to the FFT)?

For my requirements, this can result in either a value for the main frequency (e.g. 3Hz) or a value representing the strength of a target frequency. For example, in the following 1-D signal the frequency is about 4Hz, assuming the sampling rate is 50ms.

How can this be extracted from the data programmatically?

10 2 1 2 8 10 8 2 1 1 8 10 7 1 1 2 7 10 5 1

回答1:

Use Auto Correlation !

%using Matlab

%convert sample rate to hertz

fs = 1/(50/1000) % result = 20hz

vector = [10 2 1 2 8 10 8 2 1 1 8 10 7 1 1 2 7 10 5 1];

R = xcorr(vector);

[pks,locs]=findpeaks(R);

%result in hertz

fs./(diff(locs))

ans =

3.3333    4.0000    3.3333    3.3333    4.0000    3.3333

max(fs./diff(locs))

ans =

4

• Apply Autocorrelation on the signal, you can find a lot of source code in the web in defferent languages to do autocorrelation, a pseudo code:

  TotalSamples = length(signal)
  for z=1:TotalSamples
   sum = 0;
  
   for i=1:TotalSamples
  
             sum = sum + (signal(i)*signal(i + pos));
  
   end
  
   Xcorre(z) = Xcorre(z) + sum;
  end
  

• Find all local peaks from result of autocorrelation

• Compute the difference between local peaks locs[k+1] - locs[k]

• Divide your frame rate by the difference between local peaks

• The Frequency is the Maximum value

来源：https://stackoverflow.com/questions/18145936/how-to-extract-a-frequency-from-a-signal