IntermediateTopic 38 of 101Signals, Control & Comms
Wavelets
Time-frequency analysis with scalable localised basis functions.
In depth
Wavelets decompose signals into scaled and shifted versions of a mother wavelet, giving time-frequency localisation: good for transients and edges. Continuous and discrete (DWT via filter banks). Uses: compression (JPEG 2000), denoising, feature extraction, ECG analysis.
Key points
- Multiresolution analysis
- Haar and Daubechies wavelets
- Scalogram
ExampleWavelet denoising removes noise while keeping sharp ECG peaks.
What is Wavelets?
Time-frequency analysis with scalable localised basis functions.
Why is it important to understand wavelets?
Wavelets analyse signals with time and frequency together, which suits signals whose frequency changes over time.
Why are wavelets better than the Fourier transform for some signals?
They localise features in time as well as frequency, so brief events and changing frequencies appear clearly.
What is multiresolution analysis?
Splitting a signal into approximation and detail components at successive scales, which gives a flexible view of its structure.
How is Wavelets used in practice?
Typical applications include detecting a transient fault in a power waveform, compressing images in a way that keeps edges sharp and finding a short burst in a vibration record that the FFT smears out.
What should I learn before Wavelets?
Study "Spectral estimation" first (topic 37 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Wavelets?
Multiresolution analysis. Haar and Daubechies wavelets. Scalogram.
Can you give an example of Wavelets?
Wavelet denoising removes noise while keeping sharp ECG peaks.
What comes after Wavelets?
The next topic is "Image processing basics", which builds directly on this one.
How difficult is Wavelets?
It is classed as Intermediate in Signals, Control & Comms (topic 38 of 101). It is an intermediate topic. Work through the beginner topics in Signals, Control & Comms first.