Question

Find the convolution of x(n)=[1,1,1,1,2,2,2,2] with h(n)=[3,3,0,0,0,0,3,3] by using matrix method.

Answer 1

To find the convolution of two sequences using the matrix method, create a matrix and calculate the dot product of each row with one of the sequences.

Step-by-step explanation:

To find the convolution of two sequences using the matrix method, we need to create a matrix with dimensions (m+n-1) x n, where m is the length of the first sequence and n is the length of the second sequence. In this case, the length of x(n) is 8 and the length of h(n) is also 8. Therefore, the dimensions of the matrix will be 15 x 8.

We then fill the matrix with the values of the two sequences. Since the convolution operation involves shifting and multiplying the sequences, we need to replicate the shifted versions of the sequences in the matrix.

Next, we calculate the dot product of each row in the matrix with the sequence h(n). Finally, we get the convolution by adding up the dot products.