IIR filter order prediction

how to decide on the order requirement for the IIR filter??

my main goal was to check how far could an IIR filter get fewer coefficients and approximate the time reversed Channel Impulse Response of a wireless channel.. ?? what would be minimum required order of the IIR filter if the length of the CIR was around 5000?? being able to reconstruct to some extent close to the original one is good enough with lower number of coefficients of IIR filter..

could i have some suggestions on how to go about his?? thanks in advance...

Clearly the answer depends on the type of impulse response. To represent an arbitrary impulse response, you would need a
respective number of FIR coefficients. Some classes of responses may be reproducable with a rather short IIR structure,
others not at all. Generally, the advantage of IIR shows with representing time-continuous filters (defined e.g. in pole-zero form),
but not with arbitrary impulse responses.

CIR represented by IIR? I'm not too sure how math would fit in. Which signal is going to be fed-back to the channel?

Modeling it would be quite complex, at least I think so. I would love to see the method with which you model it.

But neodgreat, why do you need to create a CIR of 5000 coeffs? Just use a worst case scenario if you can

@ FvM
I am uploading the impulse responses that i have with me..

the impulse response from expr data is in pic :


the impulse response from IEEE model is in this pic :


i have a idea that if represented to IIR filter coefficients, then they require less coeff.. but the point is how stable will that be.?? I am having tough job to represent them to lower number of coefficients of IIR filter.. and which section of the original response is to be selected for finding the coefficients.. appreciate on any suggestions.. thank you..

Added after 8 minutes:

@ Communications_Engineer

i had attached the impulse response i am using in the thread.. since IIR can generate infinite impulses, my idea is that some information of orginal impulse response must be enough to generate the near approximate of the original channel response.. the CIR gets estimated and followed onto to approximation module.. i am stuck here.. i am not able to approximate to atleast 25% satisfactory level.. I would appreciate your help, if you could let me know whether any method that could reduce the computational complexity of system by approximating the channel response to your knowledge..

From,
neodgreat

I agree with Communications_Engineer, I can't see a simple design method to fit an IIR filter to the presented data. At first
look, it seems rather to belong to the class of arbitrary impulse responses, that are not suited for an IIR representation. It's more
random-like than showing any periodical behaviour.

@ FvM

Is it that what u are telling is that only the ones with the repeating nature could be implemented using IIR..

which other way is there to approximate this kind of impuplse reponse.?? can u suggest me some methods.??

wouldn't we be able to approximate the arbitrary time reversed channel impulse repsonse using IIR filter.????