### Block Diagram Interpretation of Time-Varying STFT Modifications

Assuming is causal gives

This is depicted in Fig.8.17.

The term
can be interpreted as the FIR filter tap
at time
. Note how each tap is *lowpass filtered* by the FFT window
. The window thus enforces *bandlimiting* each filter tap to
the bandwidth of the window's main lobe. For an
-term length-
Blackman-Harris window, for example, the main-lobe reaches zero at
frequency
(see Table 5.2 in §5.5.2
for other examples). This bandlimiting places a limit on the *bandwidth expansion*
caused by time-variation of the filter coefficients, which in turn places a limit
on the maximum STFT hop-size that can be used without frequency-domain aliasing.
See Allen and Rabiner 1977
[9] for further details on the bandlimiting
property.

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