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Infinite Impulse Response::::::::::::::::::::::::

Infinite impulse response (IIR) is a property of signal processing systems. Systems with this property are known as IIR systems or, when dealing with filter systems, as IIR filters. IIR systems have an impulse response function that is non-zero over an infinite length of time. This is in contrast to finite impulse response filters (FIR), which have fixed-duration impulse responses. The simplest analog IIR filter is an RC filter made up of a single resistor (R) feeding into a node shared with a single capacitor (C). This filter has an exponential impulse response characterized by an RC time constant.

IIR filters may be implemented as either analog or digital filters. In digital IIR filters, the output feedback is immediately apparent in the equations defining the output. Note that unlike with FIR filters, in designing IIR filters it is necessary to carefully consider "time zero" case in which the outputs of the filter have not yet been clearly defined.

Design of digital IIR filters is heavily dependent on that of their analog counterparts because there are plenty of resources, works and straightforward design methods concerning analog feedback filter design while there are hardly any for digital IIR filters. As a result, usually, when a digital IIR filter is going to be implemented, an analog filter (e.g. Chebyshev filter, Butterworth filter, Elliptic filter) is first designed and then is converted to a digital filter by applying discretization techniques such as Bilinear transform or Impulse invariance.

Example IIR filters include the Chebyshev filter, Butterworth filter, and the Bessel filter.





Finite Impulse Response:::::::::::::::::::::::::

A finite impulse response (FIR) filter is a type of a discrete-time filter. The impulse response, the filter's response to a Kronecker delta input, is finite because it settles to zero in a finite number of sample intervals. This is in contrast to infinite impulse response (IIR) filters, which have internal feedback and may continue to respond indefinitely. The impulse response of an Nth-order FIR filter lasts for N+1 samples, and then dies to zero.

An FIR filter has a number of useful properties which sometimes make it preferable to an infinite impulse response (IIR) filter. FIR filters:

Are inherently stable. This is due to the fact that all the poles are located at the origin and thus are located within the unit circle. 

Require no feedback. This means that any rounding errors are not compounded by summed iterations. The same relative error occurs in each calculation. This also makes implementation simpler. 

They can easily be designed to be linear phase by making the coefficient sequence symmetric; linear phase, or phase change proportional to frequency, corresponds to equal delay at all frequencies. This property is sometimes desired for phase-sensitive applications, for example crossover filters, and mastering. 

The main disadvantage of FIR filters is that considerably more computation power is required compared to an IIR filter with similar sharpness or selectivity, especially when low frequencies (relative to the sample rate) cutoffs are needed.