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I am reading the book 'spectral audio signal processing'. It says when $n=LN-1$ for any integer $L$, the sliding DFT

$$X_n(k)=\sum_{m=0}^{N-1}x(n+m)e^{-j2\pi mk/N}$$

coincides with the DFT filter bank.

But at other times, they differ by a linear phase term. See here for the details.

  1. I cannot figure out why the above holds.

P.S., the DFT filter bank expression is given in this link.

  1. Another question is: In what situation can sliding DFT be used? Is it only meaningful for theoretical analysis?

Can you help with the above questions?

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