iirshiftc
Shift frequency response of IIR complex filter
Syntax
[Num,Den,AllpassNum,AllpassDen] =
iirshiftc(B,A,Wo,Wc)
[Num,Den,AllpassNum,AllpassDen] =
iirshiftc(B,A,0,0.5)
[Num,Den,AllpassNum,AllpassDen] =
iirshiftc(B,A,0,-0.5)
Description
[Num,Den,AllpassNum,AllpassDen] =
iirshiftc(B,A,Wo,Wc)
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 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 the numerator
specified by B
and the denominator specified by A
.
[Num,Den,AllpassNum,AllpassDen] =
iirshiftc(B,A,0,0.5)
calculates the allpass filter for
doing the Hilbert transformation, i.e. a 90 degree counterclockwise
rotation of an original filter in the frequency domain.
[Num,Den,AllpassNum,AllpassDen] =
iirshiftc(B,A,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.
Examples
Design a prototype real IIR halfband filter using a standard elliptic approach:
[b, a] = ellip(3, 0.1, 30, 0.409);
Rotate all features of the prototype filter in the frequency
domain by the same amount by specifying where the selected feature
of an original filter, W
o=
0.5
, should appear in the target filter, W
t=
0.25
:
[num, den] = iirshiftc(b, a, 0.5, 0.25);
Verify the result by comparing the prototype filter with the target filter:
fvtool(b, a, num, den);
After applying the shift, the selected feature from the original
filter is just where it should be, at W
t =
0.25
.
Arguments
Variable | Description |
---|---|
B | Numerator of the prototype lowpass filter |
A | Denominator of the prototype lowpass filter |
Wo | Frequency value to be transformed from the prototype filter |
Wt | Desired frequency location in the transformed target filter |
Num | Numerator of the target filter |
Den | Denominator of the target filter |
AllpassNum | 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