Is it possible to make one IIR filter from various cascading IIR filters of different orders?

I know it is possible to do it from filters of the same order, but what about filters with different orders?


You certainly can. In theory you can cascade any type of linear time invariant filter (FIR, IIR, overlap-add, warped allpass, etc.) of any filter order in any sequence and happily mix them up. The transfer function of the cascade is simply the product of all the individual transfer functions.

In practice, especially for fixed point systems, you need to watch gain, stability and noise, so depending on your application there may be some practical constraints.

The most common IIR implementation is cascaded biquad filters (also known as second order sections) since they are the easiest to manage in terms of noise, gain and stability.


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