Memory for FIR and IIR
In order to accomplish a particular specified filtering task, the FIR filter order will almost certainly be much higher than the IIR filter order.  For instance a low-pass filter that requires a particular "sharpness" in cutoff, the transition region between the passband (at low frequencies) and the stopband (at high frequencies).  What a 4th-order IIR filter can do might correspond to what a 20th or 25th-order FIR can do.  The 4th-order IIR requires 10 coefficients and 4 states.  the 20th-order FIR requires 21 coefficients and 20 states.

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