Question

When |E(ω)|≤δ for all frequencies on the dense set, the optimal solution has been found in terms of the polynomial H(ω).

(a) True

(b) False

The question was asked in an online interview.

This key question is from Design of Optimum Equi Ripple Linear Phase FIR Filters topic in division Digital Filters Design of Digital Signal Processing

Answer 1

Correct choice is (a) True

Explanation: |E(ω)|≥δ for some frequencies on the dense set, then a new set of frequencies corresponding to the L+2 largest peaks of |E(ω)| are selected and computation is repeated. Since the new set of L+2 extremal frequencies are selected to increase in each iteration until it converges to the upper bound, this implies that when |E(ω)|≤δ for all frequencies on the dense set, the optimal solution has been found in terms of the polynomial H(ω).