Question

What is the expression for the perturbation error Δpi?

(a) \(\sum_{k=1}^N \frac{∂p_i}{∂a_k} \Delta a_k\)

(b) \(\sum_{k=1}^N p_i \Delta a_k\)

(c) \(\sum_{k=1}^N \Delta a_k\)

(d) None of the mentioned

I had been asked this question during an interview for a job.

Origin of the question is Quantization of Filter Coefficients in division Digital Filters Design of Digital Signal Processing

Answer 1

Right choice is (a) \(\sum_{k=1}^N \frac{∂p_i}{∂a_k} \Delta a_k\)

The best explanation: The perturbation error Δpi can be expressed as

Δpi=\(\sum_{k=1}^N \frac{∂p_i}{∂a_k} \Delta a_k\)

Where \(\frac{∂p_i}{∂a_k}\), the partial derivative of pi with respect to ak, represents the incremental change in the pole pi due to a change in the coefficient ak. Thus the total error Δpi is expressed as a sum of the incremental errors due to changes in each of the coefficients ak.