Saturday, October 22, 2016

What is the intuitive meaning of FIR and IIR filters? What is the difference? Why do we prefer FIR over IIR? What is the physical significance?



"Impulse Response" of any system is the output you get when you apply a standard "impulse" signal at its input. An impulse response fully describes the behavior of the system.
 
As the name suggests, an FIR filter gives a finite-length output for an impulse, while if you excite an IIR filter with an impulse, it continues producing output for infinite duration. This is because an IIR filter has a "feedback" which continues to provide input to the filter implicitly, even when you have removed your external input signal.
 
Since IIR filter continues to generate output from a feedback process you can't control, the output might "feed" on itself and increase to undesired/harmful levels if the filter is not designed correctly. So, it is easier to design stable FIR filters. However, IIR filters are more "powerful" than FIR as you can make smart use of feedback to reduce total number of elements in the filter.
 
Assume you are speaking at a huge public function, with loudspeakers lining up the road for a kilometer. You speak a sharp "Hi" into the mic and the speakers relay your voice with successive (propagation) delays till the end of the road. This is like a stable FIR filter response.
 
Now assume that a speaker is placed close to the mic itself. As soon as you say "Hi", the speaker feeds it back to the mic with a larger amplitude and a slight delay. This starts a cycle till the speaker output increases uncontrollably to its maximum. This is why you sometimes hear the "screeching" in a mic+speaker system, and is analogous to an unstable IIR filter.

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