5.2 FIR and IIR Filter Implementations

The properties of a filter depend on the value distribution of its coefficients. In particular, two types of filters are of special interest: Finite Impulse Response (FIR) filters, for which a[m] = 0 when 1 ≤ m < M, and Infinite Impulse Response (IIR) filters, those such that a[0] ≠ 0 and a[m] ≠ 0 for some m in {1, ..., M}. Other classifications within the FIR and IIR filter families account for the effects that the operation induces on input data sequences.

Furthermore, even though filtering consists on solving the difference equation stated above, several implementations are available which are more efficient than direct computation of the difference equation. Also, some other implementations are designed to execute the filtering operation under the constraints imposed by fractional arithmetic.

All these considerations lead to a proliferation of filtering operations, of which a subset is provided by the DSP Library.