Filter design refers to the calculation of FIR or IIR coefficients $a_n$ and $b_n$ based on certain desing criteria. If we want to control a digital filter, this should be in terms of meaningful parameters like cutoff-frequency and roll-off, not by changing the coefficients directly:
For certain designs, this also includes less disirable properties like the level of ripples in pass-band or stop-band. There are several different methods to design both finite and infinite response filters.
FIR Design¶
Design methods for FIR filters are intuitive, due to the convolution theorem: Since FIR filters can be applied by convolution, a discrete-time version of a desired continuous-time impulse response (or frequency response) has to be generated. This can be performed in both the time- and frequency domain.
Some FIR design methods are:
- Impulse response windowing
- Frequency sampling
- Least squares
IIR Design¶
Digitizing Analog Filters¶
The most common approach to designin IIR filters is to start from an analog - or a continuous-time filter - and convert it to a discrete-time digital system. This can also happen in the time domain or in the frequency domain.
Examples for analog-to-digital IIR design methods:
- Bilinear Transform
- Impulse Invariance
- Matched z-transform
Direct (Digital) Design¶
- Pole-zero placement