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| WaveWarp 2.0 Example DrawingBoard
DigitalClippingEducationalExample_2
Description
Digital Clipping Educational Example
Illustrates the phenomenon of digital clipping using a sinusoidal test signal (produced by the Sine Wave Generator block).
Start by playing the DrawingBoard with the default settings which correspond to an amplitude of approximately 0.24. As
observed in the digital displays and in the LED indicator, the corresponding rms amplitude and dB levels are approximately
0.170 and -12.4 dB, respectively. The audio sounds smooth, as expected from a pure sinusoidal tone.
Now gradually increase the amplitude of the signal via the Gain slider of the Large gain block. The displays will reflect the
corresponding increase in signal level, and the audio output will remain smooth, but will become successively louder (no
surprise !). However, as soon as the signal amplitude exceeds unity (or the dB level exceeds 0, or the rms amplitude
exceeds 0.707) , the signal will immediately become distorted and will sound unpleasant. This is because of digital clipping
which is an unavoidable by-product of the process of converting an analog signal into a digital representation.
Distortion due to clipping is not unique to digital audio. For example, when the amplitude of an analog signal is successively
increased, ultimately the amplifier or speakers will become "over-driven" when they exceed their maximum range of
operability. However, this process is generally gradual, and can even be beneficial e.g. the nice distortion obtained when
over-driving a guitar amplifier (especially of the tube [or valve!] variety). The fact that an analog system exhibits this useful
characteristic of graceful degradation when over-driven, leads to the term "headroom" when describing the available useful
amplitude range beyond the onset of nonlinear amplitude distortion. Unfortunately with digital systems, there is no such
graceful degradation. The onset of unpleasant distortion is instantaneous once the clipping threshold has been crossed (i.e.
there is no "headroom" in a digital system). The reason is that once the clipping threshold has been crossed, the digital
representation of the amplitude is no longer unique (due to finite word length) and can be mapped on to any value, leading
to unpleasant distortion. In the worst case, the slightest amount of "over-drive" will map the amplitude on to a completely
different numerical value (because of digital word-wrapping). This means that great care must be taken when working with
digital audio. The basic rule is that digital clipping should be avoided at all cost (except on those rare occasions when the
associated distortion is desired as a special effect!). The "clip" LED in the Decibel Audio LED window provides a useful
and accurate indication of the presence of digital clipping. Whenever this LED lights up, clipping has occured. When this
happens, reduce the amplitude of the signal, and re-play the DrawingBoard. Repeat this procedure until the "clip" LED is
never activated for a given soundtrack. Ideally, the signal amplitude should be adjusted to be as large as possible without
causing clipping. This maximises the signal-to-noise-ratio.
Note that, generally speaking, the numerical value of amplitude corresponding to the digital clipping threshold is essentially
arbitrary since any finite range of numbers can be used to represent the signal in the digital domain. However, in any
implemented digital system, there will be an adopted convention which defines the numerical range for that system. The
clipping threshold is then defined relative to that convention. In WaveWarp, the adopted convention is that all audio
signals are mapped on to the amplitude range from -1 to 1. Any signal outside this range will, by definition, be digitally
clipped. Again, merely by by convention, the extrema of the range -- i.e. the values -1 and 1 -- are mapped in
WaveWarp on to the decibel value of 0.Hence, any signal above 0 dB in WaveWarp, will, be definition, be subject to
digital clipping. (Note: other digital audio systems may use different conventions, so care should be taken when comparing
them with WaveWarp!)
A final related comment on the resolution of the digital representation: once a numerical range has been established for a
given digital system, the A/D conversion maps the analog signal on to a fixed number of digital values over the established
range. For example, in WaveWarp, the adopted (floating point) range of -1 to 1 contains 256 discrete values for an 8-bit
digital signal, 65536 discrete values for a 16-bit quantised digital signal, 1048576 discrete values for a 20-bit
quantised digital signal, 16777216 discrete values for a 24-bit quantised digital signal, and 4294967296 discrete values for
a 32-bit quantised digital signal. Hence the accuracy of the digital representation increases with the number of bits in the
quantised representation., even though the adopted amplitude range of -1:1 is used for all representations. Furthermore,
WaveWarp uses 32-bit representation in all its internal calculations, so very high accuracy (low noise) is maintained even
for 24-bit audio files!
Components used:
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