# If yk(n) is the convolution of the finite duration input sequence

If yk(n) is the convolution of the finite duration input sequence x(n) of length N, then what is the impulse response of the filter?

A. WN-kn

B. WN-kn u(n)

C. WNkn u(n)

D. None of the mentioned

I got this question during an online interview.

This key question is from Linear Filtering Approach to Computation of DFT in chapter DFT Efficient Computation – Fast Fourier Transform Algorithms of Digital Signal Processing

The correct option is B. WN-kn u(n)

The best I can explain: We know that yk(n)=$$\sum_{m=0}^{N-1} x(m)W_N^{-k(n-m)}$$

The above equation is of the form yk(n)=x(n)*hk(n)

Thus we obtain, hk(n)= WN^-kn u(n).