Editing Infinite impulse response (section)

==Implementation and design==
Although almost all [[analog filter|analog]] electronic filters are IIR, digital filters may be either IIR or FIR. The presence of feedback in the topology of a discrete-time filter (such as the block diagram shown below) generally creates an IIR response. The [[Z-transform|z domain]] [[transfer function]] of an IIR filter contains a non-trivial denominator, describing those feedback terms. The transfer function of an FIR filter, on the other hand, has only a numerator as expressed in the general form derived below. All of the <math>a_i</math> coefficients with <math>i > 0</math> (feedback terms) are zero and the filter has no finite [[Pole–zero plot|poles]].

The transfer functions pertaining to IIR analog electronic filters have been extensively studied and optimized for their amplitude and phase characteristics. These continuous-time filter functions are described in the [[Laplace domain]]. Desired solutions can be transferred to the case of discrete-time filters whose transfer functions are expressed in the z domain, through the use of certain mathematical techniques such as the [[bilinear transform]], [[impulse invariance]], or [[pole–zero matching method]].  Thus digital IIR filters can be based on well-known solutions for analog filters such as the [[Chebyshev filter]], [[Butterworth filter]], and [[elliptic filter]], inheriting the characteristics of those solutions.