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Modify the DFT such that the frequency components are computed from $n=-\frac{N}{2}, \ldots, 0, \ldots, \frac{N}{2}-1$. Why is this approach useful in sinusoidal analysis-synthesis?

   Modify the DFT such that the frequency components are computed from $n=-\frac{N}{2}, \ldots, 0, \ldots, \frac{N}{2}-1$. Why is this approach useful in sinusoidal analysis-synthesis?

Audio Signal Processing and Coding

Audio Signal Processing and Coding

Andreas Spanias, Ted… 1st Edition

Chapter 9, Problem 1

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The standard DFT is defined for a sequence \( x[n] \) of length \( N \) as: \[ X[k] = \sum_{n=0}^{N-1} x[n] e^{-j \frac{2\pi}{N} kn} \] where \( k = 0, 1, \ldots, N-1 \). Show more…

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Modify the DFT such that the frequency components are computed from $n=-\frac{N}{2}, \ldots, 0, \ldots, \frac{N}{2}-1$. Why is this approach useful in sinusoidal analysis-synthesis?

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