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| WaveWarp 2.0 Example DrawingBoard
AliasingAndImagingEducationalExample2
Description
Aliasing and Imaging Educational Example 2
Illustrates the classic phenomenon of "imaging" associated with digital up-sampling (interpolation). Imaging is the dual
phenomenon to Aliasing (demonstrated in the Aliasing AndImagingEducationalExample1 DrawingBoard). Imaging occurs
whenever a digital signal is up-sampled to a higher sample rate without adequate interpolation to embed the new samples
smoothly amongst the old. Undesirable spectral "images" of the original low-frequency signal are introduced as high
frequency content in the new up-sampled audio stream. This is the phenomenon illustrated in this DrawingBoard.
Open the Parameter Window of the upper Spectrum Analyser and start the DrawingBoard. Two spikes will appear in the
display. The left-most spike occurs at 6700 Hz and corresponds to the input pure tone (the Sine Wave Generator output
frequency is set to 6700 Hz). This is no surprise. The spike on the right, however, occurs at about 15000 Hz, well above
the original Nyquist rate of 11025 Hz (half the sample rate of the Sine Wave Generator which is running at 22050 Hz). This
spike is precisely due to "imaging". It is an undesirable "image" of the legitimate low-frequency spike, introduced by the
imperfect up-sampler (the Simple Up:2 block)
The only way to avoid imaging is to filter out all those frequencies above half the new Nyquist rate, after carrying out the
up-sampling. This process, commonly referred to as "anti-image filtering", is built in to WaveWarp's Nyquist Interpolating
Up:2 block which, in essence, performs half-band FIR low-pass filtering (i.e. with an edge frequency at half of the
new Nyquist rate) followed by the up-sampling by a factor of 2. To observe the effect of the anti-imaging filter, open
the Parameter Window of the lower Spectrum Analyser and start the DrawingBoard. You will notice that the imaged spike
at 15000 Hz has been drastically reduced. In fact, if you connect the output of the Nyquist Interpolating Up:2 block to the
soundcard, you will not be able to hear the imaged tone, such is the power of the filtering !
Although this example used a pure tone as a test signal in order to clearly demonstrate the imaging phenomenon, imaging
occurs with all digital audio signals (e.g. music) which are up-sampled without adequate filtering. The undesirable audio
artefacts will always occur, though the extent to which they are perceived can depend on the material itself. In any case, it
is generally recommended to perform anit-image filtering whenever the material is up-sampled. To this end, WaveWarp has
a wide range of anti-image up-samplers (and anti-aliasing down-samplers) allowing total flexibility in on-the-fly sample rate
conversion by any integer factor. Furthermore, some of these (such as the Nyquist Interpolator shown here) are
implemented in the highly-efficient polyphase structure (a neat trick whereby the anti-image filtering is actually implemented
as a multiple branch filter bank which runs at the low rate before the up-sampling). You can also build your own up-(and
-down)-samplers from scratch using WaveWarp's wide range of Digital Filter components in combination with the simple up -
(and -down)-samplers. You can even build parallel branch filter banks and create polyphase re-samplers from scratch !
Finally, if you want to use your own filters, you may import them easily into WaveWarp (and routines are provided for
import/export to MATLAB).
Components used:
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