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| WaveWarp 2.0 Example DrawingBoard
PolyphaseVersusDirectDownsamplingEducationalExample2_2
Description
Polyphase versus direct implementation of a downsampler: polyphase case
Demonstrates how to build an anti-aliasing downsampler in the "polyphase" implementation. In this example,
the sample rate is reduced by a factor of 4 (via the Simple DownSampler). An FIR anti-aliasing low-pass filter is
constructed in polyphase form, i.e. from 4 parallel filter "branches" (or "phases") fed with successively delayed versions of
the input. The filters in each branch (imported from off-line designs created using the MATLAB code in the script-file
"wwxmpl12.m" located in the wwmatlab directory) comprise the exact polyphase representation of the corresponding
"direct" low-pass filter (demonstrated in the companion ExampleDrawingBoard
"PolyphaseVersusDirectDownsamplingEducationalExample1.dwb").
Play the DrawingBoard and note that the audio sounds reasonable, despite the significant degree of downsampling. The
"high frequencies" have, however, been attenuated as expected from the low-pass filtering (compare with the original by
temporarily bypassing the entire downsampling chain to appreciate the difference). Now compare the output of this
downsampler with that of the "direct" implementation of the same anti-aliasing filter (from
"PolyphaseVersusDirectDownsamplingEducationalExample1.dwb"). You will observe that the ouputs are identical for the
two implementations (this is most easily appreciated by temporarily connecting up the ASCII input /output files -- which are
included in both DrawingBoards -- and disconnecting the WAV file and soundcard. The ASCII files can be opened with a
text editor and allow convenient and accurate comparison since they offer direct access to the exact numerical input
/output data without the scaling inherent to the WAV I/O interface).
The important point about the polyphase structure is that all the filters are executed at the low sample rate. This
implementation is therefore considerably more efficient than the direct implementation where the filter is executed at the
high sample rate. Even with the overhead associated with the extra components in the polyphase implementation, you will
observe (e.g. from a CPU resource monitor) a considerable performance gain (speed improvement) over the direct method.
This is the entire motivation for using the polyphase method. Moreover, when the polyphase structure is implemented in the
most efficient manner (i.e. without separate multiple components, but coded together within a single component), drastic
improvements in efficiency can be achieved. Such a "self-contained" internal polyphase architecture is the basis of many
of the pre-built down- (up-) samplers in the mutirate category of the Component Library.
For a thorough discussion on polyphase filtering, see "Wavelets and Filter Banks" by Gilbert Strang and Truong Nguyen,
Wellesley-Cambridge Press, 1996, and "Multirate Digital Signal Processing" by Ronald E Crochiere and Lawrence R
Rabiner, Prentice Hall, 1983.
This DrawingBoard nicely illustrates the power and versatility of WaveWarp's sample-by-sample multirate audio engine.
Components used:
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