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iirlp2bs

Transform IIR lowpass to IIR bandstop filter

Description

example

[Num,Den,AllpassNum,AllpassDen] = iirlp2bs(B,A,Wo,Wt)transform IIR lowpass to IIR bandstop filter.

The iirlp2bs function returns the numerator and denominator vectors, Num and Den of the transformed bandstop digital filter. AllpassNum and AllpassDen are the numerator and denominator coefficients of the allpass mapping filter. The prototype lowpass filter is specified with the numerator B and a denominator A. For more details, see IIR Lowpass Filter to IIR Bandstop Filter Transformation.

Note

Frequencies must be normalized to be between 0 and 1, with 1 corresponding to half the sample rate.

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

[num,den] = iirlp2bs(b,a,0.5,[0.25 0.75]);

Compare the magnitude responses of the filters using FVTool.

fvt = fvtool(b,a,num,den);
legend(fvt,'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 must 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 must be normalized to be between 0 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

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

Data Types: single | double

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

Data Types: single | double

More About

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IIR Lowpass Filter to IIR Bandstop Filter Transformation

IIR lowpass filter to IIR bandstop filter 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. Choice of the feature subject to the lowpass to bandstop 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. It is assumed that Wt2 is greater than Wt1. Frequencies must be normalized to be between 0 and 1, with 1 corresponding to half the sample rate.

This transformation implements the "Nyquist Mobility," which means that the DC feature stays at DC, but the Nyquist feature moves to a location dependent on the selection of Wo and Wts.

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

For more details on the lowpass to bandstop frequency transformation, see Digital Frequency Transformations.

References

[1] Nowrouzian, B., and A.G. Constantinides. “Prototype Reference Transfer Function Parameters in the Discrete-Time Frequency Transformations.” In Proceedings of the 33rd Midwest Symposium on Circuits and Systems, 1078–82. Calgary, Alta., Canada: IEEE, 1991. https://doi.org/10.1109/MWSCAS.1990.140912.

[2] Nowrouzian, B., and L.T. Bruton. “Closed-Form Solutions for Discrete-Time Elliptic Transfer Functions.” In [1992] Proceedings of the 35th Midwest Symposium on Circuits and Systems , 784–87. Washington, DC, USA: IEEE, 1992. https://doi.org/10.1109/MWSCAS.1992.271206.

[3] Constantinides, A.G. “Design of Bandpass Digital Filters.” Proceedings of the IEEE 57, no. 6 (1969): 1229–31. https://doi.org/10.1109/PROC.1969.7216.

[4] Constantinides, A.G.“Spectral transformations for digital filters.” Proceedings of the IEEE, vol. 117, no. 8: 1585-1590. August 1970.

Introduced in R2011a