Generate trapezoidal waveform from a square waveform using convolution
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Hello,
I try to generate a trapezoidal waveform from a square waveform using convolution using rectpuls() and fft() but I don't manage to obtain the good result with correct amplitude (i.e. same as the original signal). Could you please help me ?
Thank you !
Example:
t = 0:10e-6:10;
signal = 270*square(t);
trise=100e-6;
x = rectpuls(t-trise/2,trise);
conv = ifft(fft(signal).*fft(x));
figure
plot(t,signal,'k-+'); hold on
plot(t,conv,'r-s'); hold on
legend('signal', 'conv')
xlabel('Time (s)')
ylabel('Signal (-)')
采纳的回答
William Rose
2023-3-9
编辑：William Rose
2023-3-9
0 个投票
[edit correct capitalization errors]
Your convolution worked and it did produce a trapezoidal signal. You just need to zoom in more on the transitions to see the trapezoidal shape. See zoomed-in plot below.
If you want wider transitions, then you need to make the signal x have a wider pulse. In its present form, the pulse in x is only 0.0001 time units long.
4 个评论
@William Rose @Abhijeet Thanks for your answers, I know the convolution worked but as you can see the amplitude of the convolution signal does not match the square one.
t = 0:10e-6:10;
amplitude = 270;
signal = amplitude*square(t);
trise = 30e-6;
x = amplitude*rectpuls(t-trise/2,trise);
conv = (1/length(signal))*ifft(fft(signal).*fft(x));
figure
plot(t,signal,'k-+'); hold on
plot(t,conv,'r-s'); hold on
legend('signal', 'conv')
xlabel('Time (s)')
ylabel('Signal (-)')
@Victor Dos Santos, if you want the convolution to have the same amplitude as the original signal, then divide by the sum of the valyues in x:
t=0:.01:10; signal=270*square(t);
trise=0.3; x=rectpuls(t-trise/2,trise);
conv=ifft(fft(signal).*fft(x))/sum(x);
figure
subplot(211), plot(t,signal,'-r.',t,conv,'-b.'); legend('signal','conv')
subplot(212), plot(t,x,'-g.'); legend('x')
Or you can normalize x before using it in the convolution, so that the area under the curve in x is one:
x=x/sum(x);
Then do the convolution, and you won't need to divide by sum(x):
conv=ifft(fft(signal).*fft(x));
Victor Dos Santos
2023-3-9
William Rose
2023-3-9
@Victor Dos Santos, you're welcome.
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