You are here: Symbol Reference > Dew Namespace > Dew.Signal Namespace > Dew.Signal.Units Namespace > Classes > LinearSystems Class > LinearSystems Methods > LowpassToBandpassZ Method > LinearSystems.LowpassToBandpassZ Method ([In] TVec, [In] TVec, double, double, double)
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LinearSystems.LowpassToBandpassZ Method ([In] TVec, [In] TVec, double, double, double)
LinearSystems Class  LinearSystems Members  Dew.Signal.Units Namespace  LowpassToBandpassZ Method
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Apply frequency band transformation from lowpass to bandpass in the z-domain.

Syntax
C#
Visual Basic
public static void LowpassToBandpassZ([In] TVec Num, [In] TVec Den, double Freq, double BW, double PrototypeFreq);
Remarks

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):

-a2 + a1*z^(-1) - z^(-2) z^(-1) ---> --------------------------- 1 - a1*z^(-1) + a2*z^(-2) cos((w2 + w1)/2) Beta = ------------------- cos((w2 - w1)/2) k = 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

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