In this Digital Signal Processing course, we will be studying various methods of designing two types of filters – Infinite Impulse Response (IIR) filters, and Finite Impulse Response (FIR) filters. Let’s try to understand the difference between them to better structure our understanding as we proceed through the course.
Infinite Impulse Response Filters (IIR) 
Finite Impulse Response Filters (FIR) 
All the infinite samples of the impulse response are considered in the designing of IIR filters.  Only N samples of the impulse response are considered in the designing of FIR filters. 
The construction of an IIR filter involves designing an analog filter first for the desired specifications and then converting it into a digital IIR filter.  The construction of an FIR filter with the desired specifications can be done directly using certain methods (like windowing). 
Thus we can say that IIR filters have an analog equivalent.  Thus we can say that FIR filters don’t have an analog equivalent. 
The IIR filter requires past output samples in addition to current and past inputs to obtain its current outputs.  The FIR filter requires only past and current inputs to obtain its current output. They don’t care about past outputs. 
An IIR filter’s design specifications only specify the desired characteristics of its magnitude response.  An FIR filter’s design specifications specify both, the magnitude as well as the phase response. 
Physically realizable infinite impulse response filters don’t have linear phase characteristics.  Physically realizable FIR filters can be designed with linear phase characteristics easily. 
IIR filters are recursive  FIR filters are nonrecursive. However, it is possible to design recursive FIR filters too. 
The transfer functions of infinite impulse response filters have both poles and zeros.  The transfer functions of finite impulse response have only zeros. 
IIR filters are/have LESS:

FIR filters have/are MORE:

IIR filters are/have MORE:

FIR filters have/are LESS:

IIR filters are used in Band Stop and Band Pass filters.  FIR filters are used in Antialiasing, low pass, and baseband filters. 
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