LinearSystems::BilinearPrewarp Function

double BilinearPrewarp(double Freq, double FS = 2);

Prewarp an analog (s-domain) cutoff so it maps to the requested digital frequency under the bilinear transform.

#NameTypeDescription
1FreqdoubleDesired digital cutoff frequency, in the range 0 < Freq < 1 (normalised so the Nyquist frequency is 1, i.e. sampling frequency 2). At Freq toward 1 the result grows without bound (tan -> inf).
2FS = 2doubleSampling frequency; default 2. $T = 1/FS$.

Returns: The prewarped analog radian frequency omega_a.

Remarks:

Returns the analog frequency omega_a whose image, after the bilinear transform with sampling frequency FS, is the digital frequency Freq. This is the inverse of the bilinear frequency warp and is computed as omega_a = 2 FS tan( (pi Freq)/2 ) . Design an analog prototype at omega_a so that, once Bilinear is applied, the cutoff lands exactly at Freq. The sample period is T=1/FST = 1/FS.

References:

[1] Digital signal processing, Vinay K. Ingle and John G. Proakis, Brooks-Cole, 2000

See Also: LinearSystems::Bilinear, LinearSystems::BilinearUnwarp
Declared in Dew::Signal::Units::LinearSystems · Dew.Signal/Units.LinearSystems.h · Cross-compiler