zpkshiftc
Zero-pole-gain complex shift frequency transformation
Syntax
[Z2,P2,K2,AllpassNum,AllpassDen]
= zpkshiftc(Z,P,K,Wo,Wt)
[Num,Den,AllpassNum,AllpassDen] =
zpkshiftc(Z,P,K,0,0.5)
[Num,Den,AllpassNum,AllpassDen] =
zpkshiftc(Z,P,K,0,-0.5)
Description
[Z2,P2,K2,AllpassNum,AllpassDen]
= zpkshiftc(Z,P,K,Wo,Wt)
returns zeros, Z
2,
poles, P
2, and gain factor, K
2,
of the target filter transformed from the real lowpass prototype by
applying a first-order complex frequency shift transformation. This
transformation rotates all the features of an original filter by the
same amount specified by the location of the selected feature of the
prototype filter, originally at Wo, placed
at Wt in the target filter.
It also returns the numerator, AllpassNum
,
and the denominator, AllpassDen
, of the allpass
mapping filter. The prototype lowpass filter is given with zeros, Z
,
poles, P
, and the gain factor, K
.
[Num,Den,AllpassNum,AllpassDen] =
zpkshiftc(Z,P,K,0,0.5)
performs the Hilbert transformation,
i.e. a 90 degree counterclockwise rotation of an original filter in
the frequency domain.
[Num,Den,AllpassNum,AllpassDen] =
zpkshiftc(Z,P,K,0,-0.5)
performs the inverse Hilbert transformation,
i.e. a 90 degree clockwise rotation of an original filter in the frequency
domain.
Examples
Arguments
Variable | Description |
---|---|
Z | Zeros of the prototype lowpass filter |
P | Poles of the prototype lowpass filter |
K | Gain factor of the prototype lowpass filter |
Wo | Frequency value to be transformed from the prototype filter |
Wt | Desired frequency location in the transformed target filter |
Z2 | Zeros of the target filter |
P2 | Poles of the target filter |
K2 | Gain factor of the target filter |
AllpassDen | Numerator of the mapping filter |
AllpassDen | Denominator of the mapping filter |
Frequencies must be normalized to be between -1 and 1, with 1 corresponding to half the sample rate.
References
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.
Version History
Introduced in R2011a