BeginnerTopic 33 of 101Signals, Control & Comms
Filter design methods
Windowing, bilinear transform and optimisation produce coefficients.
In depth
FIR: window method, frequency sampling, least squares, Parks-McClellan. IIR: impulse invariance and bilinear transform of analog designs with frequency prewarping. Specify passband edge, stopband edge, ripples; compute minimum order; verify response and quantisation effects.
Key points
- Prewarping
- Filter order estimation
- Tools: MATLAB, SciPy
Examplescipy.signal.butter(4,0.2) returns coefficients for a 4th-order low-pass.
What is Filter design methods?
Windowing, bilinear transform and optimisation produce coefficients.
Why is it important to understand filter design methods?
Filter design methods turn a required response into coefficients, so each method suits a different specification and implementation.
What is the bilinear transform?
A mapping that converts an analogue filter design into a digital one without aliasing, though it warps the frequency scale.
Which method should I choose?
Use windowed FIR for linear phase, bilinear IIR for classic shapes with few coefficients, and optimisation for tight specifications.
How is Filter design methods used in practice?
Typical applications include designing a low-pass FIR with a window method for an audio channel, converting an analogue Butterworth prototype into a digital IIR filter with the bilinear transform and optimising the coefficients of an equiripple filter for a tight specification.
What should I learn before Filter design methods?
Study "IIR filters" first (topic 32 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Filter design methods?
Prewarping. Filter order estimation. Tools: MATLAB, SciPy.
Can you give an example of Filter design methods?
scipy.signal.butter(4,0.2) returns coefficients for a 4th-order low-pass.
What comes after Filter design methods?
The next topic is "Butterworth, Chebyshev and elliptic filters", which builds directly on this one.
How difficult is Filter design methods?
It is classed as Beginner in Signals, Control & Comms (topic 33 of 101). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.