Kurzweil K2661, Musician’S Reference Manual

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KDFX Reference
KDFX Algorithm Specifications
Clearly a one-bit word gives a very crude approximation to the original signal while four bits is beginning
to do a good job of reproducing the original decaying sine wave. When a good strong signal is being
quantized (its word length is being shortened), quantization usually sounds like additive noise. But notice
that as the signal decays in the above
fi gures, fewer and fewer quantization levels are being exercised
until, like the one bit example, there are only two levels being toggled. With just two levels, your signal has
become a square wave.
Controlling the bit level of the quantizer is done with the DynamRange parameter (dynamic range). At
0 dB we are at a one-bit word length. Every 6 dB adds approximately one bit, so at 144 dB , the word length
is 24 bits. The quantizer works by cutting the gain of the input signal, making the lowest bits fall off the
end of the word. The signal is then boosted back up so we can hear it. At very low DynamRange settings,
the step from one bit level to the next can become larger than the input signal. The signal can still make the
quantizer toggle between bit level whenever the signal crosses the zero signal level, but with the larger bit
levels, the output will get louder and louder. The Headroom parameter prevents this from happening.
When the DynamRange parameter is lower than the Headroom parameter, no more signal boost is added
to counter-act the cut used to quantize the signal. Find the DynamRange level at which the output starts to
get too loud, then set Headroom to that level. You can then change the DynamRange value without
worrying about changing the signal level. Headroom is a parameter that you set to match your signal
level, then leave it alone.
At very low DynamRange values, the quantization becomes very sensitive to DC offset. It affects where
your signal crosses the digital zero level. A DC offset adds a constant positive or negative level to the
signal. By adding positive DC offset, the signal will tend to quantize more often to a higher bit level than to
a lower bit level. In extreme cases (which is what we’re looking for, after all), the quantized signal will
sputter, as it is stuck at one level most of the time, but occasionally toggles to another level.
Aliasing is an unwanted artifact (usually!) of digital sampling. It’s an established rule in digital sampling
that all signal frequency components above half the sampling frequency (the Nyquist rate) must be
removed with a lowpass
fi lter (anti-aliasing fi lter). If frequencies above the Nyquist rate are not removed,
you will hear aliasing. A digital sampler cannot represent frequencies above the Nyquist rate, but rather
than remove the high frequencies, the sampler folds the high frequencies back down into the lower
frequencies where they are added to the original low frequencies. If you were to play a rising pure tone
through a sampler without an anti-alias
fi lter, you would hear the tone start to fall when it past the
Nyquist rate. The pitch will continue to drop as the input tone’s frequency increases until the input tone
reaches the sampling rate. The sampled tone would then have reached dc (frequency is 0) and will start to
rise again. Usually a lowpass anti-aliasing
fi lter is placed before the sampler to prevent this from
happening.
Figure 58 Spectra of (i) an analog signal and the (ii) same signal after sampling without
filtering
Fs Fn=Fs/2
(i)
Fs Fn=Fs/2
(ii)