Exp 1-Discrete Convolution and Correlation

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Discrete Convolution

Convolution is a common mathematical way of combining two signals, input, and impulse- to form a third signal, the output signal.




  • The condition for the length of the output of Linear Convolution is greater than or equal to one less the sum of the length of an input signal and impulse response signal(N>=L+M-1).
  • Circular convolution gives an aliased output.

Correlation

Correlation gives a measure of similarity between two data sequences. In this process, two signals are compared and the degree to which the two signals are similar is computed.

In cross-correlation, the output sequence gets affected when the input signal is delayed.

Autocorrelation


The correlation of a function with itself is called its autocorrelation.


In Autocorrelation, the delay in the input signal would make no difference in the output signal i.e Autocorrelation of x[n-1] is same as autocorrelation of x[n].

Comments

  1. Gopala15 May 2018 at 06:58

    This comment has been removed by a blog administrator.

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    1. Unknown15 May 2018 at 21:30

      This comment has been removed by the author.

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  2. Rutwik Pandit15 May 2018 at 07:09

    Why do we use discrete convolution

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    Replies
    1. Unknown15 May 2018 at 21:30

      What we are actually doing in transform just to change the domain of signal information,may be in time or frequency.suppose we are dealing in time domain, let's we have a situation in which two signal get mixed up and we want to know what will be output of mixing all that,to do so we just have to find overlapped area( but by change its phase characteristics ) so we flipped any one of them and find its overlapped area and shifted untill there will be no overlapping in between and in last all result get addded and operation known is convolution while similar things get easily solve by just multiplication of two signal in case of frequency domain that's why we requires a process known as transform. Hope you will understand.

      Delete
  3. Anonymous15 May 2018 at 07:42

    Well illustrated. It can also be shown that correlation and convolution are equivalent under reflection of the filter response, leading to interesting insight in fields like image processing.

    ReplyDelete
  4. Anonymous15 May 2018 at 08:43

    Correlation is indeed very useful measure as it can also be used for detecting a known waveform in random white noise.

    ReplyDelete
  5. Unknown15 May 2018 at 21:22

    Well put. I always got confused before

    ReplyDelete

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