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What is the equation for average power of discrete time periodic signal x(n) with period N in terms of Fourier series coefficient ck?(a) \(\sum_{k=0}^{N-1}|c_k|\)(b) \(\sum_{k=0}^{N-1}|c_k|^2\)(c) \(\sum_{k=0}^N|c_k|^2\)(d) \(\sum_{k=0}^N|c_k|\)I have been asked this question by my college director while I was bunking the class.The query is from Frequency Analysis of Discrete Time Signal in division Frequency Analysis of Signals and Systems of Digital Signal Processing |
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Answer» CORRECT choice is (b) \(\sum_{k=0}^{N-1}|c_k|^2\) For EXPLANATION: We know that Px=\(\frac{1}{N} \sum_{n=0}^{N-1}|x(n)|^2\) =\(\frac{1}{N} \sum_{n=0}^{N-1}x(n).x^*(n)\) =\(\frac{1}{N} \sum_{n=0}^{N-1}x(n) \sum_{k=0}^{N-1}c_k * e^{-j2πkn/N}\) =\(\sum_{k=0}^{N-1}c_k * \frac{1}{N} \sum_{n=0}^{N-1}x(n)e^{-j2πkn/N}\) =\(\sum_{k=0}^{N-1}|c_k |^2\) |
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