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iirlp2bpc

Transform IIR lowpass to complex bandpass filter

Description

example

[Num,Den,AllpassNum,AllpassDen] = iirlp2bpc(B,A,Wo,Wt)transform IIR lowpass to complex bandpass filter.

The iirlp2bpc function returns the numerator and denominator vectors, Num and Den, respectively of the target filter transformed from the real lowpass prototype by applying a first-order real lowpass to complex bandpass frequency transformation. For more details, see IIR Lowpass to Complex Bandpass 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.

Examples

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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 bandpass filter by placing the cutoff frequencies of the prototype filter at 0.25π and 0.75π.

[num,den] = iirlp2bpc(b,a,0.5,[0.25 0.75]);

Compare the magnitude responses of the filters using FVTool.

hvft = fvtool(b,a,num,den);
legend(hvft,'Prototype','Target')

Input Arguments

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

Data Types: single | double
Complex Number Support: Yes

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

Data Types: single | double
Complex Number Support: Yes

Frequency value to be transformed from the prototype filter, specified as a real scalar. Frequency Wo should be normalized to be between 0 and 1, with 1 corresponding to half the sample rate.

Data Types: single | double

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

Data Types: single | double

Output Arguments

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

Data Types: single | double
Complex Number Support: Yes

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

Data Types: single | double
Complex Number Support: Yes

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

Data Types: single | double
Complex Number Support: Yes

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

Data Types: single | double
Complex Number Support: Yes

More About

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IIR Lowpass to Complex Bandpass Transformation

IIR lowpass to complex bandpass transformation effectively places one feature of the original filter, located at frequency -Wo, at the required target frequency location, Wt1 , and the second feature, originally at +Wo, at the new location, Wt2. It is assumed that Wt2 is greater than Wt1.

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.

Choice of the feature subject to the lowpass to bandpass transformation is not restricted only to the cutoff frequency of an original lowpass filter. You can choose to transform any feature of the original filter like stopband edge, DC, deep minimum in the stopband, or others.

Lowpass to bandpass transformation can also be used to transform other types of filters, for example real notch filters or resonators can be doubled and positioned at two distinct desired frequencies at any place around the unit circle forming a pair of complex notches/resonators. This transformation can be used for designing bandpass filters for radio receivers from the high-quality prototype lowpass filter.

See Also

Functions

Introduced in R2011a