BILINTRANS Function (PV-WAVE Extreme Advantage)

Computes the bilinear transform of an analog transfer function.

Usage

result = BILINTRANS(h [, k])

Input Parameters

h—A valid analog filter structure defined as the ratio of two polynomials in positive powers of s.

k—(optional) A multiplier constant. (Default: k = 1)

Returned Value

result—A digital filter structure containing the transfer function made of a ratio of polynomials in negative powers of z.

Keywords

Newname—A scalar string specifying a name for the new filter structure. If not used, the new filter structure has the same name as the old one.

Discussion

For a given analog transfer function of the form:

where Ba and Aa are polynomials in positive powers of s, BILINTRANS performs a bilinear transformation:

to obtain a digital rational transfer function Hd(z) in negative powers of z.

Example

In this example we call BILINTRANS with a simple lowpass filter and plot the frequency response of both the analog and digital form of the filter.

b = [0.1]

a = [–0.1, 1.0]

; Define a simple analog lowpass filter H(s) = 0.1/(s – 0.1).

h= FILTSTR(b, a)

omega = FINDGEN(100)/50.0

; Plot the frequency response of the analog transfer function.

; See 
    Frequency Response of Analog and Digital Filter (a).

PLOT, omega, ABS(FREQRESP_S(h, COMPLEX(FLTARR(100), omega))), $
Title = 'Analog'

; Transform the analog transfer function to digital.

hd = BILINTRANS(h)

hdresp = FREQRESP_Z(hd, Outfreq = f)

; Plot result.

PLOT, f, ABS(hdresp), Title = 'Digital'

; See 
    Frequency Response of Analog and Digital Filter (b).

Figure 2-1: Frequency Response of Analog and Digital Filter