Electronic – Is a IIR digital filter with a0=1 effectively a FIR digital filter


I have been experimenting with several digital filters for my thesis recently, and while learning about the FIR and IIR kind, they seem to have similar output expressions.

While using a Java class I found online to design a Butterworth IIR Filter's coefficients, I realized that the 'a0' value turns out to be 1 and, consequentially, that the resulting expression looks like a FIR filter.

Is this the case? Or is the fact that the 'y[n-i]' terms are present on the final implementation enough to warrant it not being FIR and definitely IIR?

Best Answer

It's unlikely to be true. IIR filters use feed-back paths and recirculate a fraction of the output (ever-diminishing hopefully). Hence they have the name Infinite Impulse Response meaning that an impulse on the input would cause an output that continues to decay to infinite.

FIR filter do not have feedback paths and hence the name Finite Impulse Response because the output following an inputted impulse changes and then restores to "normality" after a finite length of time.

The resulting expression may look like an IIR expression but if it contains y[n-i] then it can't be FIR