Find period cycle and frequency for signal

Hi,

And For 50Hz frequency, need to plot 1000 cycles, with varrying frequency of 49.97/49.98/50.01.50.02 adn show the varrying load on graph i.e.

(Period cycle and measured frequency)

How do i need to find period and frequency of signal?

clc;
clear all;
close all;

% CONSTANTS
fs=2400;
fo=50;
t=0:1000;
t2=0.5; 

% Geneeration of sine wave
 xp=sin(2*pi*(fo/fs)*t);

% upward zero crossing detector
UpZC = @(a) find(a(1:end-1) <= 0 & a(2:end) > 0);	
% downward zero crossing detector
DownZC = @(a) find(a(1:end-1) >= 0 & a(2:end) < 0);  
% interploator formula
ZeroX = @(x0,y0,x1,y1) x0 - (y0.*(x0 - x1))./(y0 - y1); 
ZXi = sort([UpZC(xp),DownZC(xp)]);
% zerocrossing detector with interpolation
ZX = ZeroX(t(ZXi),xp(ZXi),t(ZXi+1),xp(ZXi+1));
if xp(end)==0
    ZX(end+1) = t(end);
end
xx= zeros(1,length(ZX));
xx1= zeros(1,length(ZX));

for i=1:length(ZX)
    if rem(i,2)==1
        xx(1,i)=ZX(i)+t2;
        xx1(1,i)=ZX(i)-t2;
    else
        xx(1,i)=ZX(i)-t2;
          xx1(1,i)=ZX(i)+t2;
    end
end

y1= sin(2*pi*(fo/fs)*t2);

figure(1)
plot(t,xp, '-b')
hold on
plot(ZX,zeros(1,length(ZX)),'go')
hold on;
plot(xx,zeros(1,length(ZX))+y1,'r*')
hold on
plot(xx1(2:end),zeros(1,length(ZX)-1)-y1,'r*')
grid on;
legend('Sine wave Signal', 'zero crossing point','Interpolated Zero-Crossing')
xlabel('Time');
ylabel('Amplitude');

Answer 1

[Star Strider]

Finding the approximate zero-crossings is straightforward, and the subsequent interpolation involves a loop to get the exact zero-crossings —

% CONSTANTS
fs=2400;
fo=50;
t=0:1000;
t2=0.5; 
N = numel(t);
% Geneeration of sine wave
xp=sin(2*pi*(fo/fs)*t);

zxi = find(diff(sign(xp)));                                             % Approximate Indices Of Zero-Crossings

for k = 1:numel(zxi)
    idxrng = max(1,zxi(k)-1) : min(N,zxi(k)+1);                         % Index Range For Interpolation
    txc(k) = interp1(xp(idxrng), t(idxrng), 0);                         % Interpolate
end

figure
plot(t, xp, 'DisplayName','Data')
hold on
plot(txc, zeros(size(txc)), 'rs', 'DisplayName','Zero-Crossings')
hold off
grid
xlabel('t')
ylabel('xp')

for k = 1:numel(zxi)
    idxrng = max(1,zxi(k)-2) : min(N,zxi(k)+2);                         % Index Range For Interpolation
    DM = [t(idxrng); ones(size(idxrng))].';                             % Design Matrix
    B = DM \ xp(idxrng).';                                              % Parameter Vector
    txv(k) = -B(2) / B(1);                                              % Interpolate
end

figure
plot(t, xp, 'DisplayName','Data')
hold on
plot(txv, zeros(size(txv)), 'rs', 'DisplayName','Zero-Crossings')
hold off
grid
xlabel('t')
ylabel('xp')

The first loop uses the interp1 function and the second uses simple linear regression.

.

[Shanmuka]

But, I want to plot rate of change of frequency for 3 frequencies which are added to single sine signal and find out difference in plot with respect to different frequencies

[Star Strider]

It is not easy to follow your code.

If you have more periodic (or aperiodic) curves to analyse, run my code for each one of them, or if they all have the same time vector, the sum or product of them as well, if that is what you are doing. You can combine them easily if they have different frequecies, however not if they have different time vectors.

If they have different time vectors, you will have to analyse each one individually. That should be straightforward by just repeating my code with each of them.