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Time Varying OLA Modifications
In the preceding sections, we assumed that the spectral modification
did not vary over time. We will now examine the implications of
timevarying spectral modifications. The derivation below
follows [9], except that we'll keep our previous
notation:
Using
in our OLA formulation with a hop size
results in
Define
to get

(9.42) 
Let's examine the term
in more detail:

describes the time variation of the
tap.

is a filtered version of the
tap
. It is
lowpassfiltered by w and delayed by
samples.
 Denote the
th timevarying, lowpassfiltered, delayedby
filter tap by
. This can be interpreted
as the weighting in the output at time
of an impulse entering
the timevarying filter at time
.
Using this, we get
This is a superposition sum for an arbitrary linear, timevarying filter
.
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