convolution of fourier property

[gareth1983]

Hi all,

I would like to prove the convolution property of the fourier transform. as shown in my attached VI file, i'm supposed to display 4 graphs.

1) display the 2 type of signals generated x(t) and y(t), and signal x(t)*y(t) (top left corner)

2) FT of convoluted signal in graph 1 (top right corner)

3) display x(t)y(u-t) (bottom left corner)

4) display X(ejw)Y(ejw), which is also the FT for graph 3 (bottom right corner)

The result should show that the FT shown in graph 2 and graph 4 are the same to ensure that the property is proven.

http://www-structmed.cimr.cam.ac.uk/Course/Convolution/convolution.html#commut

The above link shows the method being employed to get the results. Can someone help me please?

[gareth1983]

i think i should rephrase. I would like to show the FFT convolution as well as the linear convolution. I'd completed the portion to perform FFT convolution, but am not sure how to do the linear part. Can someone advise?

[altenbach · Accepted solution]

The quoted web page does not mention the word "linear convolution", but if you simply want to do it without any fourier transforms, you could multiply and sum in a loop as in the attached demo. It gives the same result as the stock convolution VI (within ~10e-15). There are many other ways to do this, of course.

(There are a couple of things wrong with your VI, so I don't quite know what you want at the end. For example you are graphing complex arrays in a plain graph, so you are losing the imaginary part. You also need a small wait in the loop, else the VI consumes all CPU, recalculating the same over and over again. Ideally the loop only needs to spin when an input changes.)

Message Edited by altenbach on 04-18-2009 11:04 AM

[gareth1983]

thanks a lot altenbach. I had found another way to do it and it works just as required.

[Mathan]

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gareth1983 wrote:

I had found another way to do it and it works just as required.

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Could you please tell that another way here so that other people will get benefitted a lot by your help in the future.

Thanks,

Mathan

[gareth1983]

Hi Mathan,

well, for the benefit for everyone, just like what I'd benefited from this forum.

1) using the WDT Append Waveforms DBL which was used to 'merge' the 2 signals together.

2) retrieve the length of this waveform and connected to the FFT size input of both FT.vi. In doing this, I'm getting the length of the entire signal. For example, if the length of signal 1 and signal 2 is 100 samples each, the length retrieved would be 200 samples.

3) Connect the waveforms to the FT.vi inputs to perform a Fourier transform of both the signals, multiply the transformed waveforms together to get the frequency domain signals.

4) Do a inverse FFT of part 3 to retrieve back the convoluted time domain signal.

Regards,

Gareth.

[Mathan]

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gareth1983 wrote:

Hi Mathan,

well, for the benefit for everyone, just like what I'd benefited from this forum.

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Thanks a lot. Surely it will help lot of people. Please continue this service. Thanks again.

Mathan