Inverse IIR Filter - computing the inverse of a filter

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cplusruss

Newbie
Hey all,

New here. I'm trying to compute the inverse of a filter in the Z domain. Given the system transfer function H(z) = N(z)/D(z), I wish to find an inverse filter transfer function. If I put a sine wave into the forward filter H(z) and then put the output into the inverse filter, I should get the input signal back. The way I understand this is that the inverse filter transfer function is literally 1/H(z) = G(z), where G(z) is the inverse filter. I seem to be getting a large impulse for 10 ns or so and then a very, very small output. Any ideas? Anyone ever computed an inverse filter?

Regards

neodgreat

Newbie level 6
Re: Inverse IIR Filter

@ cplusruss

i am also new to filter designing.. i had been trying to approximate the arbitrary channel impulse response of the wireless channel. I didnt have any luck on creating the inverse filter...

cplusruss

Newbie
Re: Inverse IIR Filter

Thanks anyway, I'm also very new to IIR filters. It turns out from my reading of Williams and Taylor's Electronic Filter Design Handbook and a few other miscellaneous sources that inverse filtering of certain signals can be quite difficult. My filter is in the Z-Domain strictly (as IIRs somewhat are) so then it would seem that

If H(z) was my system transfer function with input X(w) being a sine wave or rectangular function then we would expect the inverse filter (in Hz) to be described by H(z)G(z)=1, such that G(z), the inverse filter transfer function, is G(z)=1/H(z). However, since the stability of the system in the time domain is affected by the choice of Z coefficients, the inverse filter might not be BIBO stable. This would mean simply that a Z-Transform could not be taken, or that the denominator will have poles which are high magnitude. In theory, if I cascaded my forward and inverse second-order IIR Lowpass filters together, my output should clearly be X(w). However, this is not the case. I decided, unless someone knows anything about inverse filtering, to simply try finding filter coefficients for the equivalent highpass filter (the inverse of the lowpass).

Filters can be tricky...

micard

Member level 3
Inverse IIR Filter

you should also be aware of minimal and non-minimal phase filters. Some of the filters are not invertible from it's principles.

bassa

Super Moderator
Staff member
Refer the attached text for example of IIR Inverse Filter (Ex 5.5: IIRinverse)

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