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Math Help - Convolution of wave with self

  1. #1
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    Convolution of wave with self

    Can anyone enlighten me on what will happen for convolution of a wave with itself? Thanks in advance
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  2. #2
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    Quote Originally Posted by boredaxel View Post
    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
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    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
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    Quote Originally Posted by boredaxel View Post
    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
    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
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    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
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  6. #6
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    Quote Originally Posted by boredaxel View Post
    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
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  7. #7
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    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?
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