Time-Varying Delay Effects
Delay-Line Interpolation
Linear InterpolationSearch Physical Audio Signal Processing
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Linear interpolation works by effectively drawing a straight line between two neighboring samples and returning the appropriate point along that line.
More specifically, let
be a number between 0 and 1 which
represents how far we want to interpolate a signal
between time
and time
. Then we can define the linearly interpolated
value
as follows:
Note that by factoring out
, we can obtain a one-multiply
form,
A linearly interpolated delay line is depicted in Fig.3.2.
The C++ class implementing a linearly interpolated delay line in the Synthesis Tool Kit (STK) is called DelayL.
The frequency response of linear interpolation for fixed fractional
delay (
fixed in Fig.3.2) is shown in Fig.3.3.
From inspection of Fig.3.2, we see that linear interpolation is
a one-zero FIR filter. When used to provide a fixed fractional delay,
the filter is linear and time-invariant (LTI). When the delay
provided changes over time, it is a linear time-varying filter.