Question

If the poles are tightly clustered as they are in a narrow band filter, the lengths of |pi-pl| are large for the poles in the vicinity of pi.

(a) True

(b) False

This question was posed to me in exam.

My enquiry is from Quantization of Filter Coefficients topic in chapter Digital Filters Design of Digital Signal Processing

Answer 1

Correct option is (b) False

Best explanation: If the poles are tightly clustered as they are in a narrow band filter, the lengths of |pi-pl| are small for the poles in the vicinity of pi. These small lengths will contribute to large errors and hence a large perturbation error results.