Here there is a coverage of the digital filter types that have been employed for different projects.It is intended as a practical pass through of different design approaches , not a theoretical filter design course. See Tools site for filter designs

FIR (Finite Impulse Response) Filter

A pure digital filter with many variants, commonly programmed into a DSP. Some DSP (see Analogue Devices, Sharc series) have hardware FIR co-processors which allow the burden of a FIR filter calculation to be off-loaded from the main DSP software flow. However all professional DSP incorporate specific commands to carry out the basic FIR filter calculation to be carried out in one clock cycle. However digital filters are non-monotonic in that the frequency response repeats at multiples of the sample frequency.

Here there is a multiplication, addition, and recovery of 2 pieces of data all in one clock cycle.

Fir Formula 3

Explain Calculation

FIR Filters

IIR (Infinite Impulse Response) Filter

A pure digital filter, commonly programmmed into a DSP. Some DSP (see Analogue Devices, Sharc series) have hardware FIR co-processors which allow the burden of a IIR filter calculation to be off-loaded from the main DSP software flow. Commonly derived from passive formats the IIR is a digital synthesis of a passive prototype.

IIR Filters