Which of the following is the expression for \(\frac{∂p_i}{∂a_k}\)?(a) \(\frac{-p_i^{N+k}}{\prod_{l=1}^n p_i-p_l}\)(b) \(\frac{p_i^{N-k}}{\prod_{l=1}^n p_i-p_l}\)(c) \(\frac{-p_i^{N-k}}{\prod_{l=1}^n p_i-p_l}\)(d) None of the mentionedI had been asked this question in class test.My query is from Quantization of Filter Coefficients in chapter Digital Filters Design of Digital Signal Processing

Which of the following is the expression for \(\frac{∂p_i}{∂a_k}\)

1.	Which of the following is the expression for \(\frac{∂p_i}{∂a_k}\)?(a) \(\frac{-p_i^{N+k}}{\prod_{l=1}^n p_i-p_l}\)(b) \(\frac{p_i^{N-k}}{\prod_{l=1}^n p_i-p_l}\)(c) \(\frac{-p_i^{N-k}}{\prod_{l=1}^n p_i-p_l}\)(d) None of the mentionedI had been asked this question in class test.My query is from Quantization of Filter Coefficients in chapter Digital Filters Design of Digital Signal Processing
Answer» Right option is (c) \(\frac{-p_i^{N-k}}{\prod_{l=1}^n p_i-p_l}\) For explanation I WOULD SAY: The EXPRESSION for \(\frac{∂p_i}{∂a_k}\) is GIVEN as follows \(\frac{∂p_i}{∂a_k}=\frac{-p_i^{N-k}}{\prod_{l=1}^n p_i-p_l}\)

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