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How to write code for a composite signal with instantaneous frequency

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Jan Ali
Jan Ali on 20 Nov 2020
Commented: Jan Ali on 10 Jan 2021
Anyone can help me with writing code for this function?

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Accepted Answer

Swetha Polemoni
Swetha Polemoni on 23 Nov 2020
Hi Jan Ali,
It is my understanding that you want to add three signals that are defined only in particular intervels of time. Following code might help you.
t = (-1:0.01:1); % defining time axis
unitstep1=t>=0; % unitsetp1 takes 1 only when t is greater than equal to 0
unitstep2=t>=0.1; % unitsetp2 takes 1 only when t is greater than equal to 0.1
unitstep3=t>=0.18;% unitsetp3 takes 1 only when t is greater than equal to 0.18
unitstep4=t>=0.3; % unitsetp4 takes 1 only when t is greater than equal to 0.3
rect1=unitstep1-unitstep2; % rect1 takes 1 only when 0<=t<0.1
rect2=unitstep2-unitstep3; % rect2 takes 1 only when 0.1<=t<0.18
rect3=unitstep3-unitstep4; % rect2 takes 1 only when 0.18<=t<0.3
% taking three random sine siganls
Signal1=sin(2*pi*50*t);
Signal2=sin(2*pi*150*t);
Signal3=sin(2*pi*500*t);
% Composite signal
Sc= Signal1*rect1+Signal2*rect2+Signal3*rect3;

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Swetha Polemoni
Swetha Polemoni on 9 Dec 2020
Hi Jan Ali,
t = 0:0.0000001:0.3; % defining time axis
unitstep1=t>=0; % unitsetp1 takes 1 only when t is greater than equal to 0
unitstep2=t>=0.1; % unitsetp2 takes 1 only when t is greater than equal to 0.1
unitstep3=t>=0.18;% unitsetp3 takes 1 only when t is greater than equal to 0.18
unitstep4=t>=0.3; % unitsetp4 takes 1 only when t is greater than equal to 0.3
rect1=unitstep1-unitstep2; % rect1 takes 1 only when 0<=t<0.1
rect2=unitstep2-unitstep3; % rect2 takes 1 only when 0.1<=t<0.18
rect3=unitstep3-unitstep4; % rect2 takes 1 only when 0.18<=t<0.3
% taking three random sine siganls
Signal1=sin(2*pi*50*t)+0.2*sin(2*pi*250*t);
Signal2=sin(2*pi*50*t)+0.2*sin(2*pi*250*t)+sin(2*pi*500*t).*exp(-30*t-0.1);
Signal3=sin(2*pi*50*t)+0.2*sin(2*pi*250*t);
% Composite signal
Sc= Signal1.*rect1+Signal2.*rect2+Signal3.*rect3;
plot(t,Sc);
This is the plot I got when I tried to implement the composite signal you have provided. I can notice there is bit difference. I have plotted to check if rect1, rect2 and rect3 are in the given range and those are in correct range. Check if there is any change in signals to get the plot you are expecting.
Jan Ali
Jan Ali on 9 Dec 2020
Thanks so much dear Swetha. As you notice, there is a transient in the 0,1 to 0,18 s time interval. I also got the same plat as you did, however not able to get the same as the picture above. Anyway, I really appreciate your effort and the time you spent to get the same result.
Wish you all the bests!
Warm regards,
Ali
Jan Ali
Jan Ali on 10 Jan 2021
Dear Swetha,
I found a workaround for this problem :)
fs=2000;
t = linspace(0,0.3,1000);
s1 = sin(2*pi*30*t) + 0.2*sin(2*pi*70*t);
s2 = sin(2*pi*30*t) + 0.2*sin(2*pi*70*t) + sin(2*pi*500*t).*exp(-30*t-0.1);
s3 = sin(2*pi*30*t) + 0.2*sin(2*pi*70*t);
if 0.1 > t >= 0
s1;
elseif 0.18 > t >= 0.1
s2;
else
s3;
end
s=[s1 s2 s3];
t = linspace(0,0.3,3000);
plot(t, s, 'b')
I really appreciate your kind support and the time you spent for coding.
Wish you all the best

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