Question

What is the value of x(n)*h(n), 0≤n≤11 for the sequences x(n)={1,2,0,-3,4,2,-1,1,-2,3,2,1,-3} and h(n)={1,1,1} if we perform using overlap save fast convolution technique?

(a) {1,3,3,-1,1,3,5,2,-2,2,3,6}

(b) {1,2,0,-3,4,2,-1,1,-2,3,2,1,-3}

(c) {1,2,0,3,4,2,1,1,2,3,2,1,3}

(d) {1,3,3,1,1,3,5,2,2,2,3,6}

I had been asked this question by my college director while I was bunking the class.

My question comes from Linear Filtering Methods Based on DFT topic in division Discrete Fourier Transform – Properties and Applications of Digital Signal Processing

Answer 1

The correct option is (a) {1,3,3,-1,1,3,5,2,-2,2,3,6}

Easy explanation: Since M=3, we chose the transform length for DFT and IDFT computations as L=2^M=2^3=8.

Since L=M+N-1, we get N=6.

According to Overlap save technique, we get

x1‘(n)={0,0,1,2,0,-3,4,2} and h'(n)={1,1,1,0,0,0,0,0}

=>y1(n)={1,3,3,-1,1,3}

x2‘(n)={4,2,-1,1,-2,3,2,1} and h'(n)={1,1,1,0,0,0,0,0}

=>y2(n)={5,2,-2,2,3,6}

=>y(n)= {1,3,3,-1,1,3,5,2,-2,2,3,6}.