LinearSystems.LowpassToHighpassZ Method (TVec, TVec, TSample, TSample)

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

public LowpassToHighpassZ(TVec num, TVec den, double Freq, double PrototypeFreq);

Remarks

Freq is the cutoff frequency 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 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) + a
  z^(-1) --->  - -------------
                  1 + a*z^(-1)

        cos((wc - wn)/2)
  a = -------------------
        cos((wc + wn)/2)

  wc - old cutoff frequency
  wn - new (desired) 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