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 mentionedI 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

What is the expression for the perturbation error Δpi?(a) \(\sum_{k=1

1.	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 mentionedI 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» 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.

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