Why are IIR and FIR filters called so?

Question

Hi, some geek on Digital signal processing help me out..

I do understand that one has feed back and another hasn't....in other words IIR filter response has the form Numerator/Denominator whereas FIR response has the form Numerator alone..all this is fine..but how can you call the responses finite or infinite?...

Answer 1

Infinite impulse response
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IIR (infinite impulse response) is a property of signal processing systems. Systems with that property are known as IIR systems or if we are dealing with electronic filter systems IIR filters. They have an impulse response function which 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.

Recursive filters are signal processing filters which re-use one or more output(s) of the filter as inputs. This feedback results in an unending impulse response characterized by either exponentially growing, decaying, or sinusoidal signal output components.

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 dependant on that of their analog counterparts which is 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, mostly, if a digital IIR filter is going to be implemented, first, an analog filter (e.g. Chebyshev filter, Butterworth filter, Elliptic filter) is designed and then it is converted to digital by applying discretization techniques such as Bilinear transform or Impulse invariance.

In practice, electrical engineers find IIR filters to be fast and cheap, but with poorer bandpass filtering and stability characteristics than FIR filters.

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

In the following subsections we focus on discrete time IIR filters which can be implemented in Digital Signal Processors.


A finite impulse response (FIR) filter is a type of a digital filter. It is 'finite' because its response to an impulse ultimately settles to zero. This is in contrast to infinite impulse response filters which have internal feedback and may continue to respond indefinitely.

Answer 2

Both filters as you know simply operate on input signals, look at different samples and combine them together using aritmetic on each sample to create the output signal.

In the FIR, the only terms combined to make the output are the input samples. Once the train of input signals stops, there is no output.

In the IIR, some of the output is actually fed back into the arithmetic units that implement the filter so give the correct math functions, even with the train of input signals stopped, the feedback from the output back in may keep the output going for an infinite time.

Answer 3

INFINITE IMPULSE RESPONSE FINITE IMPULSE RESPONSE 1.) Depends on previous input and output samples. 1.) Depends on previous input samples. 2.) Does not have linear phase characteristics. 2.) Has linear phase characteristics. 3.) 3.) Good delay characteristics and can achieve fractional constant delay; require more memory. 4.) Has zeros and poles; so has both 4.) Has only zeros; so has only numerator. numerator and denominator. 5.) Complex to implement. 5.) Easier to implement. 6.) Difficult to control and these are unstable. 6.) Stable and feedback is not involved. 7.) Has limited cycles. 7.) No limited cycles. 8.) Derived from analog. 8.) No analog history. 9.) Makes poly-phase implementation possible. 10.) Needs more multiplications and additions. 10.) FIR is of higher order when compared with IIR and requires less multiplications and additions. 11.) Recursive filters. 12.) Better for lower order tapping. 12.) Better for higher order tapping. 13.) 13.) Can be implemented with integer math.

Answer 4

Hunh? One is infinite impulse response, the other is finite impluse response. They're called that because that's the properties the exibit. One has an Infinite Impluse response, the other doest. It's just a different type of filter that is used for different purposes.