- ... Abel
^{1}
- Work supported in part
by San Jose State University Cooperative Agreement NCC-2-327.
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- ... plane
^{2}
- Note that the image of the conformal map
corresponds to the
*domain* variable of the allpass
transformation, while the input of the map corresponds to the
*range* variable *z*.
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- ... desired.
^{3}
- In
general, the unit circle is mapped once to itself by any allpass
transformation for which the number of poles
*N*_{p} minus the number of
zeros *N*_{z} inside the unit circle is |N_{p}-*N*_{z}|=1. Therefore, higher
order allpass transfer functions can be used having *N*_{p} poles inside the
unit circle, say, and
poles *outside* the unit circle.
However, such a transformation cannot be used for audio digital filter
design, our principle application, because it results in an *unstable* final
filter
. It similarly cannot be used in any
applications requiring time-domain implementation of the unstable allpass
filter in place of a unit delay element.
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- ... Barks
^{4}
- The
normalized warped-frequency interval
was converted to
Barks
*b* by the affine transformation
,
where *N*_{b} is the number of Bark bands in use. For example, *N*_{b}=25 for
a 31 kHz sampling rate.
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- ...JOST:
^{5}
- Matlab functions
*bark2lin.m* and *lin2bark.m* for transforming between linear and bark-warped frequency
representations are available on the internet at *http://ccrma.stanford.edu/~jos/bbt/bbt.html*.
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