#### Index Ranges for Zero-Phase Zero-Padding

Having looked at zero-phase zero-padding ``pictorially'' in matlab
buffers, let's now specify the index-ranges mathematically. Denote
the window length by
(an odd integer) and the FFT length by
(a power of 2). Then the windowed data will occupy indices 0
to
(positive-time segment), and
to
(negative-time segment). Here we are assuming a 0-based indexing
scheme as used in C or C++. We add 1 to all indices for matlab
indexing to obtain `1:(M-1)/2+1` and `N-(M-1)/2+1:N`,
respectively. The zero-padding zeros go in between these ranges,
*i.e.*, from
to
.

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