iirbpc2bpc

Transform IIR complex bandpass filter to IIR complex bandpass filter with different characteristics

Syntax

[Num,Den,AllpassNum,AllpassDen] = iirbpc2bpc(B,A,Wo,Wt)

Description

[Num,Den,AllpassNum,AllpassDen] = iirbpc2bpc(B,A,Wo,Wt) transform IIR complex bandpass filter to IIR complex bandpass filter with different characteristics.

The iirbpc2bpc function returns the numerator and denominator vectors, Num and Den, respectively of the target filter transformed from the complex bandpass prototype by applying a first-order complex bandpass to complex bandpass frequency transformation. For more details, see IIR Complex Bandpass Frequency Transformation.

The function also returns the numerator, AllpassNum, and the denominator, AllpassDen, of the allpass mapping filter. The prototype lowpass filter is specified with the numerator B and a denominator A.

Frequencies must be normalized to be between -1 and 1, with 1 corresponding to half the sample rate.

Examples

Shift Complex Bandpass

Design a prototype real IIR lowpass elliptic filter with a gain of about –3 dB at 0.5π rad/sample.

[b,a] = ellip(3,0.1,30,0.409);

Create a complex passband from 0.25π to 0.75π.

[bc,ac] = iirlp2bpc(b,a,0.5,[0.25 0.75]);

Move the bandpass to between –0.3π and 0.1π.

[num,den] = iirbpc2bpc(bc,ac,[0.25 0.75],[-0.3 0.1]);

Compare the three filters.

hvft = filterAnalyzer(b,a,bc,ac,num,den,...
    FrequencyRange="centered",...
    FilterNames=["Prototype","PositiveComplexBand","Target"]);

Input Arguments

B — Numerator of prototype lowpass filter

row vector

Numerator of the prototype lowpass filter, specified as a row vector.

Data Types: single | double
Complex Number Support: Yes

A — Denominator of prototype lowpass filter

row vector

Denominator of the prototype lowpass filter, specified as a row vector.

Data Types: single | double
Complex Number Support: Yes

Wo — Frequency values to be transformed from prototype filter

two-element vector

Frequency values to be transformed from the prototype filter, specified as a two-element vector. Frequencies in Wo must be normalized to be between -1 and 1, with 1 corresponding to half the sample rate.

Data Types: single | double

Wt — Desired frequency locations in transformed target filter

two-element vector

Desired frequency locations in the transformed target filter, specified as a two-element vector. Frequencies in Wt must be normalized to be between -1 and 1, with 1 corresponding to half the sample rate.

Data Types: single | double

Output Arguments

Num — Numerator of target filter

row vector

Numerator of the target filter, returned as a row vector.

Data Types: single | double
Complex Number Support: Yes

Den — Denominator of target filter

row vector

Denominator of the target filter, returned as a row vector.

Data Types: single | double
Complex Number Support: Yes

AllpassNum — Numerator of mapping filter

row vector

Numerator of the mapping filter, returned as a row vector.

Data Types: single | double
Complex Number Support: Yes

AllpassDen — Denominator of mapping filter

row vector

Denominator of the mapping filter, returned as a row vector.

Data Types: single | double

More About

IIR Complex Bandpass Frequency Transformation

IIR Complex Bandpass Frequency transformation effectively places two features of the original filter, located at frequencies W_o1 and W_o2, at the required target frequency locations, W_t1, and W_t2 respectively. It is assumed that W_t2 is greater than W_t1. In most of the cases the features selected for the transformation are the band edges of the filter passbands. In general it is possible to select any feature; e.g., the stopband edge, the DC, the deep minimum in the stopband, or other ones.

Relative positions of other features of the original filter do not change in the target filter. This means that it is possible to select two features of an original filter, F₁ and F₂, with F₁ preceding F₂. Feature F₁ will still precede F₂ after the transformation. However, the distance between F₁ and F₂ will not be the same before and after the transformation.

IIR complex bandpass frequency transformation can also be used for transforming other types of filters; e.g., complex notch filters or resonators can be repositioned at two distinct desired frequencies at any place around the unit circle for example in the adaptive system.

Version History

Introduced in R2011a