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| WaveWarp 2.0 Component
      
Multirate:
Functional Description
Reduces the sample rate of the input by an integer factor, with
a built-in anti-aliasing filter based on an FIR Nyquist design.
The currently available downsampling factors are
2 and 3. Separate components are provided for each.
The output sample rate is a factor of 2 (or 3, respectively) lower than the
input sample rate.
Algorithm
In the current implementation, the FIR low-pass
anti-aliasing filters are "hard-wired"
(i.e. cannot be changed by the user). The filter lengths are
83 for the 2-factor downsampler, and 155 for the 3-factor downsampler.
These are found to give reasonable performance.
The particular type of filters used are
"Nyquist filters" (also known as an "Mth-band filters"),
and have been designed according to the eigenfilter method
described in
[VaNg].
Mth-band filters are highly suitable for downsampling (and upsampling)
applications
since their cut-off frequency is located at
Fs/2M (where Fs is the sample rate),
which is precisely what is required of an anti-aliasing (or anti-imaging)
filter
for a down-(or up-)sampling factor of M.
Furthermore, an Mth-band FIR filter has the useful property that every Mth
coefficient is identically zero, which can lead to greater computational
efficiency since the filter implementation can
be coded such that zero coefficients are not included in the real-time
computation.
For further efficiency,
the combined FIR filtering and downsampling operations are internally implemented in the
polyphase structure
(2 branches for the 2-factor downsampler,
3 branches for the 3-factor downsampler, etc.)
such that the filtering is computed at the lower
(i.e. the output) sample rate. The end result is the same as if the
filtering was performed first (i.e. at the higher sample rate), followed
by the downsampling (retaining only every Mth filtered sample).
The output from each polyphase FIR filter branch is computed by direct convolution in
real-time, taking advantage of the efficiency gained by
ignoring the zero coefficients.
See
[CrRa]
and
[StNg]
for a detailed treatment
of multirate signal processing.
For a specific discussion
on downsampling by an integer factor, see
section 2.3.2 of
[CrRa]
and chapters 1 & 3 of
[StNg].
For a specific discussion
on the polyphase implementation, see
section 3.3.2 of
[CrRa]
and section 3.4 of
[StNg].
For design methodologies for FIR Nyquist filters, see, for example,
[VaNg]
[SaNe],
and
[Mi];
and likewise for IIR (recursive) Nyquist filters, see, for example,
[ReSa1]
and
[ReSa2].
Signal Implementations
| Audio signals | Control signals | Description |
|---|
| Single input mono single output mono | n/a | Converts the sample rate of the mono signal |
| Single input stereo single output stereo | n/a | Converts the sample rate of the stereo signal |
Related components:
Example DrawingBoards illustrating usage:
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