How does MATLAB compute the scales of wavelet automatically

As a part of my learning experience in regards to wavelet analysis using MATLAB, I see that users don't have to explicitly define the scaling parameter of the wavelet. Instead the scaling parameter is computed automatically. In fact when I check the documentation of continuous wavelet transform (cwt), I see this sentence, "The minimum and maximum scales are determined automatically based on the wavelet's energy spread in frequency and time". I am having hard time understanding this line. It will be great if someone could explain this process or point out to some references for better understanding.

[Samyuktha]

Hi Arush,

I understand that you want to know how the minimum and maximum scales are determined. Please refer to the Algorithms section in the following documentation link for information on how the scales are determined in 'cwt' command.

Continuous 1-D wavelet transform

Hope this helps!

[ARUSH SHAILENDRA]

Thank you for your help and providing the documentation link!

Answer 1

[Swaraj]

The Scaling Parameter determines the size of the wavelet. Choosing an appropriate scaling parameter can be challenging as it depends on the characteristics of the signal being analysed.

The MATLAB "cwt" function automatically establishes the minimum and maximum scales based on the wavelet's energy spread in frequency and time to handle this problem. In more detail, the function calculates the wavelet's Fourier transform and establishes the energy distribution in the frequency domain. It then adjusts the wavelet appropriately to make sure that it has a wide enough frequency range to capture the properties of the signal. To choose the proper range of scales, the function additionally considers the length and sampling rate of the incoming signal.

You can go through the following for understanding more about CWT.

Continuous Wavelet Transform and Scale-Based Analysis - MATLAB & Simulink (mathworks.com)

[ARUSH SHAILENDRA]

Thank you for the explanation!