FREQTRANSDESIGN Function (PV-WAVE Extreme Advantage)

Signal Processing Toolkit User Guide > Reference (A to F) > FREQTRANSDESIGN Function (PV-WAVE Extreme Advantage)

Creates the numerator polynomial of a stable all-pass filter. The resulting filter is used to perform a frequency transformation of a lowpass prototype filter into a multiple bandpass filter.

Usage

result = FREQTRANSDESIGN(phi)

Input Parameters

phi— An array of normalized cutoff frequencies (between 0 and 1).

Returned Value

result—An array of polynomial coefficients.

Keywords

Lowstop—If present and nonzero, the transformation creates a lowstop filter. The filter passed into FREQTRANS must be a highpass filter.

Discussion

The transformation generated by FREQTRANSDESIGN must be applied to a lowpass filter with a cutoff frequency of 0.5 (normalized) or the transformation won’t work correctly.

The result polynomial is passed to FREQTRANS along with a lowpass digital filter to create a multiple bandpass filter.

The algorithm used in FREQTRANSDESIGN comes from Franchitti, 1985.

note	Using this function to generate polynomials of order 13 or greater is not advised.

Example

This example creates a lowpass filter and then transforms that into a multiple bandpass filter. The results are shown in Figure 2-16: FREQTRANSDESIGN Example on page 95, which shows a plot of the original lowpass Butterworth filter and the transformed multiple bandpass filter. Reference lines indicate the cutoff frequencies used in the FREQTRANSDESIGN multiple bandpass example.

; Defines an order-15 Butterworth filter with normalized cutoff

; frequency of 0.5.

h = IIRDESIGN(15, 0.5, /Butter)

; Defines the new cutoff frequencies.

phi = [0.1, 0.4, 0.6, 0.7, 0.8]

; Set up some plotting parameters.

!X.Ticks = 7

!X.Style = 1

!P.Charsize = 1.5

!Y.Range = [0,1.2]

!X.Tickv = [phi(0), phi(1), 0.5, phi(2), phi(3), phi(4), 1.0]

; Construct the frequency transformation polynomial.

p = FREQTRANSDESIGN(phi)

; Transform filter and compute frequency response in one step.

result = ABS(FREQRESP_Z(FREQTRANS(h, p), Outfreq = f))

ticks = ['!4u!6!l1', '!4u!6!l2', '0.5', '!4u!6!l3', '!4u!6!l4', $
'!4u!6!l5', '1.0']

!X.Tickname = ticks

; Plot the frequency response of the transformed filter.

PLOT, f, result, Thick = 2

; Plot the response of the original filter.

OPLOT, f, ABS(FREQRESP_Z(h)), Thick = 2, Linestyle = 1

; Plot some lines at the cutoff frequencies.

REFLINES, phi

Figure 2-16: FREQTRANSDESIGN Example