BeginnerTopic 32 of 101Signals, Control & Comms
IIR filters
Recursive filters achieve sharp responses with fewer coefficients.
In depth
y[n]=Σb_k x[n-k]-Σa_k y[n-k] uses feedback to get sharp responses with low order, but can be unstable, has nonlinear phase and sensitivity to coefficient quantisation. Implement as cascaded second-order sections (biquads). Designed from analog prototypes by bilinear transform.
Key points
- Poles and zeros
- Direct form II transposed
- Limit cycles
ExampleA 4th-order Butterworth IIR gives a smooth low-pass using two biquads.
What is IIR filters?
Recursive filters achieve sharp responses with fewer coefficients.
Why is it important to understand IIR filters?
IIR filters give sharp responses with few coefficients, so they save computation when a steep cutoff is needed.
What is the main drawback of IIR filters?
They use feedback and can be unstable if poles are outside the unit circle, and they usually have nonlinear phase.
What is a biquad?
A second-order IIR section, widely used as a building block because it is easy to implement and to keep stable.
How is IIR filters used in practice?
Typical applications include building a low-cost digital filter for a microcontroller, implementing a notch filter to remove interference at one frequency and smoothing a control signal with a recursive filter.
What should I learn before IIR filters?
Study "FIR filters" first (topic 31 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of IIR filters?
Poles and zeros. Direct form II transposed. Limit cycles.
Can you give an example of IIR filters?
A 4th-order Butterworth IIR gives a smooth low-pass using two biquads.
What comes after IIR filters?
The next topic is "Filter design methods", which builds directly on this one.
How difficult is IIR filters?
It is classed as Beginner in Signals, Control & Comms (topic 32 of 101). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.