Monday, 13 March 2017

Linear and Circular Convolution and Correlation

The aim of this experiment was to study linear convolution, circular convolution and linear convolution using circular convolution and correlation of signals.
Convolution is an mathematical expression used to express the relation between input and output of a system.
Mathematically, Linear convolution is expressed as y[n]=x[n]*h[n]
Where x[n] is the input to the system and h[n] is the impulse response of the system.
Linear convolution is use to find the output of the system.
The length of the output signal obtained was the one less than the addition of the length of the 2 input signals. 
In case of Circular convolution the length of the output signal is chosen as maximum length of both the signals.
Circular convolution gives alliased output.
Correlation is use to find the degree of similarity of two signals.
Auto-correlation is an Even signal.

13 comments:

  1. In circular convolution,Length 2 signals should be exactly same. To obtain this zero padding is done.

    ReplyDelete
    Replies
    1. Yes circular convolution requires the length of two input signals to be exactly same. However as mentioned above the disadvantage of Circular convolution is that it provides alliased output.

      Delete
  2. What are the applications of co-relation?

    ReplyDelete
    Replies
    1. Co-relation is basically used in applications such as speech processing, image processing and radar systems.
      In radar system, the transmitted signal is correlated with the ehco signal to locate the position of the target.

      Delete
  3. Circular convolution is used only for periodic signals

    ReplyDelete
    Replies
    1. Yes. And in case of circular convolution the length of output signal is chose as max of the two input signals

      Delete
  4. Convolution is used to find output in time domain. For evaluating output in frequency domain,transfer functions are used.

    ReplyDelete
  5. The output of the convolution has the length L+M-1 (where L = Length of x[n] , M = Length of h[n] ).

    ReplyDelete
  6. correlation is widely used for speech recognition, image processing.

    ReplyDelete
    Replies
    1. Yes as it basically provides the similarity between two signals

      Delete