# Convolution of wave with self

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• Sep 25th 2010, 12:23 AM
boredaxel
Convolution of wave with self
Can anyone enlighten me on what will happen for convolution of a wave with itself? Thanks in advance
• Sep 26th 2010, 12:56 AM
CaptainBlack
Quote:

Originally Posted by boredaxel
Can anyone enlighten me on what will happen for convolution of a wave with itself? Thanks in advance

Look at the definition of convolution and tell us what kind of wave you have in mind.

CB
• Sep 26th 2010, 05:43 AM
boredaxel
I imagined 2 square waves convoluting and I get a feeling that the result will be a smoother wave. Is that so? I couldnt imagine the convolution of sinuosoidal wave with itself. Its too confusing to me(Doh)
• Sep 26th 2010, 07:39 AM
CaptainBlack
Quote:

Originally Posted by boredaxel
I imagined 2 square waves convoluting and I get a feeling that the result will be a smoother wave. Is that so? I couldnt imagine the convolution of sinuosoidal wave with itself. Its too confusing to me(Doh)

When you sort out what you are asking about you will find the convolution of a square wave with itself is a triangular wave.

CB
• Sep 26th 2010, 08:40 AM
boredaxel
I know that the result is a triangular wave, that is why I said it seems to be a smoother wave. Therefore if it is really is a smoother wave, can I say that the convolution of other waves with itself will be a smoother wave? Or am I mistaken and the result is something else. Please enlighten me. I have given much thought to this and I am still lost
• Sep 26th 2010, 11:02 AM
CaptainBlack
Quote:

Originally Posted by boredaxel
I know that the result is a triangular wave, that is why I said it seems to be a smoother wave. Therefore if it is really is a smoother wave, can I say that the convolution of other waves with itself will be a smoother wave? Or am I mistaken and the result is something else. Please enlighten me. I have given much thought to this and I am still lost

You have not yet defined what you mean by a convolution, are we talking of convolution over some space of functions on the Reals, are we talking of circular convolutions, are we talking about sampled data circular convolutions.

CB

CB
• Sep 29th 2010, 10:17 AM
boredaxel
I am unfamiliar with the different convolutions you listed but from what I gathered from google, it seems that it should be circular convolution. The convolution that I learnt and am referring to for this question is the type where the convolution of 2 signal waveforms is the multiplication of their fourier transform. I hope that can clarify what you meant?