LinearSystems::LowpassToBandpassZ Function

Apply frequency band transformation from lowpass to bandpass in the z-domain.

Freq is the center frequency of the passband with width BW of the new filter. The function returns modified num and den. PrototypeFreq is the cutoff frequency of the prototype lowpass filter after it has been mapped to z-domain. Freq, BW and PrototypeFreq must be between 0 and 1 (Sampling frequency = 2). The transformation is defined with the following mapping ([1] p. 260 and [2] p. 434, [3] p. 352): z^(-1) -> (-a2 + a1 z^(-1) - z^(-2))/(1 - a1 z^(-1) + a2 z^(-2)) beta = (cos((w2 + w1)/2))/(cos((w2 - w1)/2)) k1 = cot((w2 - w1)/2)tan(wc/2) a1 = (2 beta k1)/(k1 + 1), a2 = (k1 - 1)/(k1 + 1)

wc - old cutoff frequency
w2 - desired upper cutoff frequency
w1 - desired lower cutoff frequency

References:

[1] Theory and application of digital signal processing, Lawrence R. Rabiner and Bernard Gold. Prentice-Hall, 1975

[2] Discrete-time signal processing, Oppenheim and Schafer, Prentice-Hall, 1989

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

The function returns modified z (zeros), p (poles) and k (gain).