Determine if the data contains a 50 Hz sine wave and if so, over what time period..

Question: The file prob2_33_data.mat contains a signal x (fs = 500 Hz). Determine if this signal contains a 50-Hz sine wave and if so over what time periods. Do I determine it is a sone wave by finding the correlation coefficient?

Code + data:

% Problem2_33.mat
% Determine if this signal contains a 50-Hz sine wave and if so ...
% over what time periods.

clear all;
close all;
clc;

fs = 500; % Sample frequency
load prob2_33_data.mat; % get data of input signal from file

figure;
subplot(2,1,1);
plot(x); % Plot of input signal x(t)
xlabel('Time (sec)','FontSize',18);
ylabel('Signal (milli volts)','FontSize',18);
title('Random input signal x(t) ','FontSize',18);
grid on;

f = 50;
t = (1:fs/f)/fs; % Generate only 1 cycle
y = sin(2*pi*f*t); % Generate a sine wave
subplot(2,1,2);

plot(t,y); % Plot the 50Hz
xlabel('Time (sec)','FontSize',18);
ylabel('Signal (milli volts)','FontSize',18);
title('50 Hz signal y(t) ','FontSize',18);
grid on;
[rxy, lags] = crosscorr(x,y,'p'); % compute the cross correlation of the signal x and y

figure(2);
plot(lags,rxy); % Plot of auto corleation between 2 signal x and y
xlabel('Lags (n)','FontSize',14);
ylabel('r_x_y','FontSize',14);
title('Cross corelation between x(t), y(t) ','FontSize',18);
grid on;
[max_corr1, max_shift1] = max(rxy(1:1500)); % Plot show two possible peaks

figure(3);
plot( [max_corr1 max_shift1]);
[max_corr2, max_shift2] = max(rxy(1500:2500)); % Toward begining and middle of data
[max_corr3, max_shift3] = max(rxy(2500:4000)); % Plot show two possible peaks

Td1 = lags(max_shift1)/fs; % Time shift 1
Td2 = lags(max_shift2+1500)/fs; % Time shift 2
Td3 = lags(max_shift3+2500)/fs; % Time shift 3

disp('Max corr ');
disp([max_corr1 max_corr2 max_corr3 ]);
disp(' Times (sec)');
disp([ Td1 Td2 Td3]);

[dpb]

What is the signature for the function <crosscorr>?

There is no named parameter 'p' and even if were, it would need a value to go along with it as the error message says...look at the examples for the function that illustrate using those.

Answer 1

[Image Analyst]

Have you tried periodogram and spectrogram?

[Image Analyst]

Or pwelch?

[dpb]

As it is homework, will leave specific code to the student; I'd venture there's a section towards the beginning of the signal that has a decent 50 Hz energy content, but beyond that, there's not a lot too choose...some content but nothing very dominant...