I want to design an IIR notch filter with linear phase. It is pretty straight forward to design the IIR notch filter but I am not sure how to design the phase compensator(all pass IIR filter) that makes the overall phase of the system linear phase. Can someone throw a few pointers on this design? Many thanks

# IIR phase compensator

Started by ●June 18, 2008

Reply by ●June 18, 20082008-06-18

itsh11 wrote:> I want to design an IIR notch filter with linear phase. It is pretty > straight forward to design the IIR notch filter but I am not sure how to > design the phase compensator(all pass IIR filter) that makes the overall > phase of the system linear phase. Can someone throw a few pointers on this > design? Many thanksIt depends how linear the phase response has to be. There are approximative rational transfer function phase-equalizers (IIR and FIR), but stability and accuracy is usually a problem. One approach is forwards-backwards filtering. This squares the amplitude response and cancels the phase response of the filter. It is particularly simple to implement for offline filtering applications. For an online implementation search for the Powell / Chau algorithm. You will need lots of memory because notch filters typically have long impulse responses. At this point you might consider the FIR alternative, with about equal memory constraints, higher computational cost but much lower algorithm complexity (a DSP one liner :-). Regards, Andor

Reply by ●June 18, 20082008-06-18

On 18 Jun, 14:34, "itsh11" <its...@yahoo.com> wrote:> I want to design an IIR notch filter with linear phase.Can't be done.> It is pretty > straight forward to design the IIR notch filter but I am not sure how to > design the phase compensator(all pass IIR filter) that makes the overall > phase of the system linear phase.That's no surprise, because it can't be done. For a filter to be linear phase, the impulse response has to be symmetric. Since your notch filter is IIR, it measn that you will need an IIR anticausal component of the impulse response. The best you can do with your aproach, is to make an allpass filter which corrects for the phase 'sufficiently well' but which does *not* give an exactly linear phase. Another option is to make FIR notch filter. It can be made linear phase, but you will not have much control over the shape of the notch. Rune

Reply by ●June 18, 20082008-06-18

itsh11 wrote:> I want to design an IIR notch filter with linear phase. It is pretty > straight forward to design the IIR notch filter but I am not sure how to > design the phase compensator(all pass IIR filter) that makes the overall > phase of the system linear phase. Can someone throw a few pointers on this > design? Many thanksYou can at best approximate what you want. Sharp notch filters have steep phase characteristics. How wide a useful band do you need? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������