IntermediateTopic 36 of 101Signals, Control & Comms
Adaptive filters
Coefficients update to track changing signals, as in echo cancellation.
In depth
Adaptive filters adjust coefficients to minimise error using LMS, NLMS or RLS algorithms: w[n+1]=w[n]+μe[n]x[n]. Applications: echo cancellation, noise cancellation, equalisation and system identification. Step size trades convergence speed against misadjustment.
Key points
- Mean-square error
- Convergence conditions
- Structures: transversal
ExampleHeadphones with active noise cancelling adapt to cancel engine noise.
Adaptive filters track changing signals and noise, which is essential in echo cancellation, noise cancellation and channel equalisation.
What is Adaptive filters?
Coefficients update to track changing signals, as in echo cancellation.
Why is it important to understand adaptive filters?
Adaptive filters track changing signals and noise, which is essential in echo cancellation, noise cancellation and channel equalisation.
What does an adaptive filter do?
It updates its coefficients on each sample to minimise an error signal, so it follows changes in the environment.
What is the LMS algorithm?
A simple adaptive method that moves the coefficients in the direction that reduces the squared error, using a small step size.
How is Adaptive filters used in practice?
Typical applications include removing the echo of your voice from a speakerphone call, cancelling engine noise in a headset microphone and equalising a radio channel that changes with the weather.
What should I learn before Adaptive filters?
Study "Multirate processing" first (topic 35 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Adaptive filters?
Mean-square error. Convergence conditions. Structures: transversal.
Can you give an example of Adaptive filters?
Headphones with active noise cancelling adapt to cancel engine noise.
What comes after Adaptive filters?
The next topic is "Spectral estimation", which builds directly on this one.
How difficult is Adaptive filters?
It is classed as Intermediate in Signals, Control & Comms (topic 36 of 101). It is an intermediate topic. Work through the beginner topics in Signals, Control & Comms first.