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| WaveWarp 2.0 Example DrawingBoard
PolyphaseVersusDirectResamplingEducationalExample1_2
Description
Polyphase versus direct implementation of a downsampler followed by an upsampler: direct case
This is an elaboration of "PolyphaseVersusDirectDownsamplingEducationalExample1.dwb" whereby the signal is
downsampled by a factor of 4 with an anti-aliasing filter (imported from an off-line design), then upsampled by a factor of 4
with an anti-imaging filter (imported from an off-line design created using the MATLAB code in the script-file "wwxmpl12.m"
located in the wwmatlab directory). The net result is a low-pass filtering of the original signal. The point of the DrawingBoard
is to demonstrate the "duality" between anti-aliasing-followed-by-downsampling, and upsampling-followd-by-anti-imaging.
Play the DrawingBoard with the sinusoidal test signal (from the Combo Wave Generator) and observe the output on the
oscilloscope. You will see that the ouput is a restored sinusoidal signal, almost identical to the input for signal frequencies
below (approx) 5512 Hz, the low-pass filter cut-off frequency. Now gradually increase the signal frequency. As it
approaches and exceeds 5512, the ouput amplitude is suppressed due to the action of the low-pass filtering.
A key point to notice in this example is that the entire re-sampling chain is implemented in the "direct" (straightforward)
implementation. In other words, the anti-alias filtering is performed before the downsampling, and the up-sampling is
perfomed before the anti-image filtering. This is wasteful bearing in mind that the 4-factor downsampler "throws
away" 3 out of 4 samples, and the 4-factor upsampler adds 3 zero-values between successive inputs. All these values are
included in the filter computations but don't contribute to the filter outputs ! There is, in fact, a considerably more efficient
implementation which gives identical results. It is known as the polyphase implementation, and is demonstrated in the
companion ExampleDrawingBoard
"PolyphaseVersusDirectResamplingEducationalExample2.dwb" .
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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