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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

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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