Getting the Period in an audio file

Question

I have an audio file , which represent the sound of a motor running at 2500rpm my aim is to get the period of this signal, so I can automaticlly tell what is the motor speed is. To do that I take a part of the signal and run get it autocorrelation , hopping that this willl tell the period of the singal! but I just don't get it : here is a part of my code :

clear;
clc;
[x0,Fs] = audioread('_2500.wav');
x= x0(1:2000,1);
xc = xcorr(x);
clf; 
subplot(3,1,1);
plot(x);

subplot(3,1,2);
plot(xc);

[peaks,locs] = findpeaks(xc);
hold on 
subplot(3,1,3)
plot(xc(locs),'ro');

and here are the plot :

and how should I consider the sampling frequency, which is : 44100 ?

Answer 1

You can use the autocorrelation or FFT of the signal to find where is the maximum:

% Parameters
Fc = 1e1;
Fs = 1e3;

% Signal
t = 0:1/Fs:1;
x = sin(2*pi*Fc*t);

% FFT
Y = abs(fft(x));
[~,I] = max(Y(1:floor(end/2)));

% Frequency and period
F = I-1;
T = 1/F;

% Plot
figure; 
subplot(2,1,1); plot(t,x);
subplot(2,1,2); plot(Y);
disp(['The frequency is ',mat2str(F),'Hz, and the period is ',mat2str(T),'sec.']);

This and this post are related.

Answer 2

To go from your auto-correlation function xc to an estimate of the fundamental frequency, do:

fs = 44100; % Unit: Hz
xc = xc((length(xc) - 1) / 2 + 1: end); % Get the half on the positive time axis. 
[~, pidx] = findpeaks(xc);
period = (pidx(1) - 1) / fs;
F0 = 1 / period; % Estimated fundamental frequency. 

Note that there are other potentially more robust fundamental frequency / pitch estimation algorithms. Doing a google scholar search on "fundamental frequency estimation" or "pitch estimation" will lead you to some good reviews.

Answer 3

you find all peaks using "findpeaks" funciton, now compute the difference between each peak

P=diff(locs)

your period can be :

max(P)

The peiod of 250hz sine at 22050 sample rate, is about 88, the Frequency of your signal is equivalent at the Period if you do (Fs/Period) == Frequency

If you Know the frequency of your signal you can find the period just do Fs/Frequency