[SOLVED] convolution of two sine waves

[preethi19]

Hi i am trying to convolve two sine waves of the same freq 5KHz. I am able to multiply both in time domain and when i convert i am able to get the spectrum at 10KHz. But rather i want to try for obtaining two 5KHz spectrum and convolving them and checking the result. I tried conv() function in matlab but the spectrum is wrong. Here is my matlab code. Can someone pls let me know the correction. Thank you!!!!

Fs = 150; % Sampling frequency
t = 0:1/Fs:1; % Time vector of 1 second
f = 5; % Create a sine wave of f Hz.
x = sin(2*pi*t*f);
y = sin(2*pi*t*f);
nfft = 1024; % Length of FFT
X = fft(x,nfft);
Y = fft(y,nfft);

X = X(1:nfft/2);
Y = Y(1:nfft/2);

mx = abs(X);
my = abs(Y);

f = (0:nfft/2-1)*Fs/nfft;
figure(1);
plot(t,x);
figure(2);
plot(t,y);
 % plotting both sine waves of 5KHz

figure(3);
plot(f,mx);
figure(4);
plot(f,my);
%plotting their spectrum

Later if i do simple multiplication "z=x.*y;"
i am able to multiply the waves and then take fft of it. But when i do "sp=conv(mx,my);"
i am not getting desired output spectrum. Can anyone pls tell how to go about. Thank you!!!

 

[c_mitra]

What you are trying to do with plot (f,mx); check both arguments.

 

[preethi19]

plot(f,mx) is just to see the freq spectrum of the individual sine waves which comes out fine as 5KHz in freq spectrum. But ultimately i am trying to convolve these two 5K and 5K (in freq domain ) to get the resultant 10K spectrum.

 

[yavuzyaman]

Hi,

As you know, regular convolution of function1 and function2 results with the length of function1+function2 -1. And in matlab, conv(func1, func2) gives the same length. However, if you work with DFT, you use rather CIRCULAR CONVOLUTION. So try CCONV function in matlab.

And as far as I see, you use conv(mx,my) namely convolution of amplitudes of FTs. This is not correct either. You have to convolve X and Y themselves. The right one should be cconv(X,Y).

Hope this helps.

-yaman

 

[c_mitra]

I do not have matlab but I use octave. It is working as expected (the code you have pasted). Please be specific and tell what is expected and what is found.

- - - Updated - - -

You are trying the convolution of two identical functions, right? I see that mx and my are same as per the graph.

 

[preethi19]

Yes you are right.. I am trying to convolve two identical functions and to see the result of the convolution. Just trying to see when i convolve two 5KHz signal to get result of 10KHz.
And i tried cconv(X,Y).. I am still not able to obtain a output figure of 10KHz spectrum..Thank you for the reply so far!!!!

 

[c_mitra]

I used octave and conv(X,Y,"same") returned an array with the same size as X or Y and I could plot that against t or f. Please check the documentation for conv in your setup.

 

[FvM]

But ultimately i am trying to convolve these two 5K and 5K (in freq domain ) to get the resultant 10K spectrum.

Did you consider the possibility that your expectation is wrong?

 

[yavuzyaman]

Yes you are right.. I am trying to convolve two identical functions and to see the result of the convolution. Just trying to see when i convolve two 5KHz signal to get result of 10KHz.
And i tried cconv(X,Y).. I am still not able to obtain a output figure of 10KHz spectrum..Thank you for the reply so far!!!!

first of all, sinus signal with 5khz frequency will give you two dirac delta at 5KHz and -5KHz. similarly if you multiply two 5KHz sinus signal, you'd get two cos at the frequencies of 0KHz and 10KHz which means you would have 3 delta functions in frequency spectrum at 0, 10KHz and -10KHz. So you should understand that those frequencies(5KHz, 10KHz) are not bandwidths just will dirac deltas.

I add cconv to your code and it worked.

Fs = 150; % Sampling frequency
t = 0:1/Fs:1; % Time vector of 1 second
f = 5; % Create a sine wave of f Hz.
x = sin(2*pi*t*f);
y = sin(2*pi*t*f);
nfft = 1024; % Length of FFT
X = fft(x,nfft);
Y = fft(y,nfft);
Z= CCONV(X,Y,size(X,2));

X = X(1:nfft/2);
Y = Y(1:nfft/2);
Z= Z(1:nfft/2);

mx = abs(X);
my = abs(Y);
mz=abs(Z);

f = (0:nfft/2-1)*Fs/nfft;
figure(1);
plot(t,x);
figure(2);
plot(t,y);
 % plotting both sine waves of 5KHz

figure(3);
plot(f,mx);
figure(4);
plot(f,my);
figure (5);
plot(f,mz);
%plotting their spectrum