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Allpass filter for complex shift transformation


[AllpassNum,AllpassDen] = allpassshiftc(Wo,Wt)
[AllpassNum,AllpassDen] = allpassshiftc(0,0.5)
[AllpassNum,AllpassDen] = allpassshiftc(0,-0.5)


[AllpassNum,AllpassDen] = allpassshiftc(Wo,Wt) returns the numerator, AllpassNum, and denominator, AllpassDen, vectors of the allpass mapping filter for performing a complex frequency shift of the frequency response of the digital filter by an arbitrary amount.

[AllpassNum,AllpassDen] = allpassshiftc(0,0.5) calculates the allpass filter for doing the Hilbert transformation, a 90 degree counterclockwise rotation of an original filter in the frequency domain.

[AllpassNum,AllpassDen] = allpassshiftc(0,-0.5) calculates the allpass filter for doing an inverse Hilbert transformation, i.e. a 90 degree clockwise rotation of an original filter in the frequency domain.


Design the allpass filter precisely rotating the whole filter by the amount defined by the location of the selected feature from an original filter, Wo=0.5, and its required position in the target filter, Wt=0.25:

Wo = 0.5; Wt = 0.25; 
[AllpassNum, AllpassDen] = allpassshiftc(Wo, Wt);

Calculate the frequency response of the mapping filter in the full range:

[h, f] = freqz(AllpassNum, AllpassDen, 'whole');



Frequency value to be transformed from the prototype filter


Desired frequency location in the transformed target filter


Numerator of the mapping filter


Denominator of the mapping filter

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


Oppenheim, A.V., R.W. Schafer and J.R. Buck, Discrete-Time Signal Processing, Prentice-Hall International Inc., 1989.

Dutta-Roy, S.C. and B. Kumar, “On Digital Differentiators, Hilbert Transformers, and Half-band Low-pass Filters,” IEEE® Transactions on Education, vol. 32, pp. 314-318, August 1989.

Introduced in R2011a

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