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Discrete Fourier Series DTFT may not be practical for analyzing because is a function of the continuous frequency variable and we cannot use a digital 



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Prove (3 9) Summation by parts allows us to investigate the convergence of special type of trigonometric series Theorem 1 Suppose that cn > 0 



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Response to Complex Exponential Sequences Relation between DFS and the DT Fourier Transform Discrete Fourier series representation of a periodic signal



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The Fourier transform of a sum of discrete-time (aperiodic) signals is the respective sum of transforms Arun K Tangirala (IIT Madras) Applied Time- Series 



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The Discrete Fourier Transform (DFT) is the equivalent of the continuous Fourier Transform for signals known only at instants separated by sample times ¡ (i e



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Discrete–time Fourier Series and Fourier Transforms We now start considering discrete–time signals A discrete–time signal is a function (real or complex



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The Fourier Series (FS) and the Discrete Fourier Transform (DFT) should be thought of as playing similar roles for periodic signals in either continuous time ( FS) 



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Fourier series of discrete-time periodic signal An N-periodic discrete-time signal can be expanded as x(n) = N−1 ∑ k=0 dke j2πkn/N where dN−k = d ∗ k 9 



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Discrete Fourier Transform (DFT) Recall the DTFT: X(ω) = ∞ ∑ As a result, the summation in the Discrete Fourier Series (DFS) should contain only N terms:

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