Show that: (a) The DCT of a length- (N) sequence (x(n)) corresponds to the Fourier transform of

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Show that:

(a) The DCT of a length- $N$ sequence $x(n)$ corresponds to the Fourier transform of the length- $2 N$ sequence $\tilde{x}(n)$ consisting of $x(n)$ extended symmetrically; that is:

\[\tilde{x}(n)= \begin{cases}x(n), & \text { for } 0 \leq n \leq N-1 \\ x(2 N-n-1), & \text { for } N \leq n \leq 2 N-1 .\end{cases}\]

(b) The DCT of $x(n)$ can be computed from the DFT of $\tilde{x}(n)$.

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Related Book For answer-question

Digital Signal Processing System Analysis And Design

ISBN: 9780521887755

2nd Edition

Authors: Paulo S. R. Diniz, Eduardo A. B. Da Silva , Sergio L. Netto

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Question Posted: Mar 27, 2024 02:00 AM

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Show that: (a) The DCT of a length- (N) sequence (x(n)) corresponds to the Fourier transform of

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Digital Signal Processing System Analysis And Design

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