Find intersections of two sin wave function (2024)

clc

clearvars

f_1 = 12;

f = 0.79;

f1 = @(t) 35 * sin(2*pi*f_1*t + 0.08*pi).^2;

f2 = @(t) 35 * sin(2*pi*f*t + 0.08*pi).^2;

T=1;

Fs = 44100;

t = 0:1/Fs:T-1/Fs;

% % first solution

% tic

% [X0,Y0,I,J] = intersections(t, f1(t), t, f2(t),1);

% toc

%

% figure

% plot(t, f1(t), t, f2(t),X0,Y0,'dk');

% xlabel('Time (s)');

% ylabel('Amplitude');

% title('Potential Intersection Regions');

% legend('f1(t)', 'f2(t)' , ' intersections ' );

% second solution

tic

diff = f1(t) - f2(t);

[ZxP,ZxN] = find_zc(t,diff,0); % "zero crossing points with linear interpolation)

Xi = sort([ZxP;ZxN]);

Yi = interp1(t,f2(t),Xi);

toc

figure

plot(t, f1(t), t, f2(t),Xi,Yi,'dk');

xlabel('Time (s)');

ylabel('Amplitude');

title('Potential Intersection Regions');

legend('f1(t)', 'f2(t)' , ' intersections ' );

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [ZxP,ZxN] = find_zc(x,y,threshold)

% put data in rows

x = x(:);

y = y(:);

% positive slope "zero" crossing detection, using linear interpolation

y = y - threshold;

zci = @(data) find(diff(sign(data))>0); %define function: returns indices of +ZCs

ix=zci(y); %find indices of + zero crossings of x

ZeroX = @(x0,y0,x1,y1) x0 - (y0.*(x0 - x1))./(y0 - y1); % Interpolated x value for Zero-Crossing

ZxP = ZeroX(x(ix),y(ix),x(ix+1),y(ix+1));

% negative slope "zero" crossing detection, using linear interpolation

zci = @(data) find(diff(sign(data))<0); %define function: returns indices of +ZCs

ix=zci(y); %find indices of + zero crossings of x

ZeroX = @(x0,y0,x1,y1) x0 - (y0.*(x0 - x1))./(y0 - y1); % Interpolated x value for Zero-Crossing

ZxN = ZeroX(x(ix),y(ix),x(ix+1),y(ix+1));

end