Note that the FFT algorithm MATLAB uses does not depend upon

Note that the FFT algorithm MATLAB uses does not depend upon the length of the data being 2^n

Given the two four-point sequences x[n] = [-2, -1, 0, 2] and y[n] = [-1, -2, -1, -3] use DFTs to find (a) the circular convolution; (b) the linear convolution.

Solution

Matlab Code:

x= [-2 -1 0 2];
y = [-1,-2,-3,-3];
circularconv = cconv(x,y,4);
linearconv = conv(x,y);
disp(circularconv);
disp(linearconv);

Output:

1 -1 2 7

2 5 8 7 -1 -6 -6