Question

Which of the following is equal to the value of H(k+α)?

(a) H*(M-k+α)

(b) H*(M+k+α)

(c) H*(M+k-α)

(d) H*(M-k-α)

This question was addressed to me during an online interview.

This intriguing question originated from Design of Linear Phase FIR Filters by Frequency Sampling Method topic in portion Digital Filters Design of Digital Signal Processing

Answer 1

Right answer is (d) H*(M-k-α)

Explanation: Since {h(n)} is real, we can easily show that the frequency samples {H(k+α)} satisfy the symmetry condition

H(k+α)= H*(M-k-α).