2.70 Circular convolution of two sequences

  2.70.1 example 1. The sequences are of equal length
  2.70.2 example 2. The sequences are of unequal length

Problem: Given 2 sequences \(x_{1}[n]\) and \(x_{2}[m]\), determine the circular convolution of the 2 sequences.

2.70.1 example 1. The sequences are of equal length



Mathematica





 


Matlab





 


Maple

Note: had to figure the correct normalization to get same answer as Matlab. Also, the input has to be type Array. list is not accepted.


\[ \left [\begin {array}{cccc} 14.0 & 16.0 & 14.0 & 16.0 \end {array}\right ] \]



 

2.70.2 example 2. The sequences are of unequal length



Mathematica





 


Matlab





 


Maple

Padding zeros to make the two list same was a little tricky. Find if there is a better way.


\[ \left [\begin {array}{ccccc} 53.0 & 43.0 & 28.0 & 43.0 & 58.0 \end {array}\right ] \]