52
D. Rocchesso: Sound Processing
frequency warping
unwarping
the curve obtained by uniform distribution of the center frequencies of the Bark
scale
[99, 111] that are below the Nyquist rate.
A psychoacoustics-driven frequency warping is also useful to design digital
filters in such a way that the approximation error gets distributed on the fre-
quency axis in a way that is most tolerable by our ears. The procedure consists
in transforming the desired frequency response according to (53), and designing
a digital filter that approximates it using some filter design method [65]. Then
the inverse conformal mapping (unwarping) is applied on the resulting digital
filter. Some filter design techniques, beyond giving a better approximation in a
psychoacoustic sense, take advantage of the expansion of low frequencies induced
by the warping map, because low-frequency sharp transitions get smoother and
the design algorithms become less sensitive to numerical errors.
10
The center frequencies (in Hz) of the Bark scale are: 50, 150, 250, 350, 450, 570, 700, 840,
1000, 1170, 1370, 1600, 1850, 2150, 2500, 2900, 3400, 4000, 4800, 5800, 7000, 8500, 10500,
13500, 20500, 27000