how to multiply two signals given step signal of duration 0.2 and cosine wave ,and i need to plot the spectrogram of the output ,some how managed to get product but spectrogram is happening

Question

chiranjeevi A 2021-1-15

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/717605-how-to-multiply-two-signals-given-step-signal-of-duration-0-2-and-cosine-wave-and-i-need-to-plot-th

回答： Dev 2025-8-26

fs=1000;

t=0:1/fs:2.0-1/fs;

Z=length(t);

f1=20;

f2=30;

f3=40;

x=3*cos(2*pi*f1*(t)+0.2)+cos(2*pi*f2*(t)-0.3)+2*cos(2*pi*f3*(t)+2.4);

subplot(3,3,1);

plot(t,x);

title(['inputwave']);

xlabel('time');

ylabel('amplitude');

f=fft(x);

m=length(f);

xmag=abs(f);

subplot(3,3,2);

plot(xmag);

title(['fft of input']);

xlabel('hz');

ylabel('magnitude');

fs1=1000; %sampling frequency

T=0.2; %width of the rectangule pulse in seconds

m=-1:1/fs1:1-1/(fs1); %time base

z=length(m);

r=rectpuls(m-(T)/2,T); %generating the square wave

subplot(3,3,3);

plot(m,r,'k');

title(['Rectangular Pulse width=', num2str(T),'s']);

xlabel('Time(s)');

ylabel('Amplitude');

s=transpose(r)*(m);%multiplying both waves

subplot(3,3,4);

plot(t,s);

title(['multiplied output']);

xlabel('time(s)');

ylabel('amp');

k=fft(s);%fft of the windowed signal

kmag=abs(k);

subplot(5,1,5);

plot(kmag);

title(['fft of output']);

xlabel('frquency');

ylabel('amplitude');

spectrum of input and output

subplot(3,3,5);

title('spectro gram of input ');

spectrogram(x)

subplot(3,3,6);

title('spectro gram of output or product siganl');

spectrogram(s)

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Answer 1

Dev 2025-8-26

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/717605-how-to-multiply-two-signals-given-step-signal-of-duration-0-2-and-cosine-wave-and-i-need-to-plot-th#answer_1569735

Hi @chiranjeevi A,

In the code provided in the question, you're trying to multiply a step signal with a cosine wave and analyse the results. This code has some issues, particularly with the multiplication step and spectrogram plotting. Please find below the required improvements in the code:

Fixed multiplication: Use element-wise multiplication (.*) instead of matrix multiplication.
Proper time alignment: Both signals should use the same time vector “t”.
Improved FFT plotting: We can use the “fftshift” function available in MATLAB to centre the spectrum around 0 Hz.

For more information on the usage of this function, please refer to the link below-

https://www.mathworks.com/help/releases/R2024b/matlab/ref/fftshift.html

After making the above modifications, we can expect the input signal to be three constant frequency lines at 20Hz, 30Hz, and 40Hz throughout the duration. Also, the output signal will have the same three frequencies, but only visible during the 0.2s window when the rectangular pulse is active (1), and silent elsewhere (0). Please refer to the attached spectrogram plotted below-