IIRfiltere

An IIR filter, or Infinite Impulse Response filter, is a type of digital filter used in signal processing. It is characterized by its output being a function of current and past input samples, as well as past output samples. This feedback mechanism, where past outputs influence current outputs, is what gives it the "infinite impulse response" name. When an impulse is applied to an IIR filter, its response theoretically continues indefinitely, although in practice it decays to zero over time.

The design of IIR filters often involves transforming analog filter designs into their digital equivalents. This can lead to filters that achieve a desired frequency response with fewer coefficients compared to Finite Impulse Response (FIR) filters, making them computationally more efficient for certain applications. However, this efficiency comes at the cost of potential non-linear phase responses, which can be undesirable in some situations. The transfer function of an IIR filter is typically represented as a rational function, with both numerator and denominator polynomials. Common types of IIR filters include Butterworth, Chebyshev, and Elliptic filters, each offering different trade-offs between sharpness of cutoff, ripple in the passband or stopband, and phase linearity. IIR filters are widely used in audio processing, telecommunications, and control systems.