Documentation |
Shift frequency response of IIR filter
[Num,Den,AllpassNum,AllpassDen] =
iirshift(B,A,Wo,Wt)
[Num,Den,AllpassNum,AllpassDen] = iirshift(B,A,Wo,Wt) returns the numerator and denominator vectors, Num and Den respectively, of the target filter transformed from the real lowpass prototype by applying a second-order real shift frequency mapping.
It also returns the numerator, AllpassNum, and the denominator of the allpass mapping filter, AllpassDen. The prototype lowpass filter is given with the numerator specified by B and the denominator specified by A.
This transformation places one selected feature of an original filter located at frequency W_{o} to the required target frequency location, W_{t}. This transformation implements the "DC Mobility," which means that the Nyquist feature stays at Nyquist, but the DC feature moves to a location dependent on the selection of W_{o} and W_{t}.
Relative positions of other features of an original filter do not change in the target filter. This means that it is possible to select two features of an original filter, F_{1} and F_{2}, with F_{1} preceding F_{2}. Feature F_{1} will still precede F_{2} after the transformation. However, the distance between F_{1} and F_{2} will not be the same before and after the transformation.
Choice of the feature subject to the real shift transformation is not restricted to the cutoff frequency of an original lowpass filter. In general it is possible to select any feature; e.g., the stopband edge, the DC, the deep minimum in the stopband, or other ones.
This transformation can also be used for transforming other types of filters; e.g., notch filters or resonators can change their position in a simple way without designing them from the beginning.
Design a prototype real IIR halfband filter using a standard elliptic approach:
[b, a] = ellip(3, 0.1, 30, 0.409);
Perform the real frequency shift by defining where the selected feature of the prototype filter, originally at W_{o}=0.5, should be placed in the target filter, W_{t}=0.75:
Wo = 0.5; Wt = 0.75; [num, den] = iirshift(b, a, Wo, Wt);
Verify the result by comparing the prototype filter with the target filter:
fvtool(b, a, num, den);
Shifting the specified feature from the prototype to the target generates the response shown in the figure.
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 0 and 1, with 1 corresponding to half the sample rate.