Advantage of 5 Bandwidth over 60 in CWT?

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Anaga Ajoy 2022-3-1

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回答： Sudarsanan A K 2023-10-18

I want to understand the difference between bandwidths on the continuous wavelet transform. For example, what would the advantages and disadvantages be over 60 vs. 5?

Here is my code that I am using.

[cfsX, frqX] = cwt(allTrials(i).Fx,'morse',1000, 'TimeBandwidth', 5); %default is 60

[cfsY, frqY] = cwt(allTrials(i).Fy,'morse',1000, 'TimeBandwidth', 5);

Thank you!

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Answer 1

Sudarsanan A K 2023-10-18

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Hello Anaga,

I note that you are trying to understand the relevance of the property "TimeBandwidth" of the continuous-time wavelet transform function "cwt()" in MATLAB.

Here are some points regarding the "TimeBandwidth" property in "cwt()" function:

The "TimeBandwidth" indicates the time-bandwidth product for the "Morse" wavelet. This is specified as a positive scalar greater than or equal to 3 and less than or equal to 120.
The time-bandwidth product controls the time-frequency characteristics of the wavelet.
The time-bandwidth product determines the trade-off between time and frequency resolution. For Morse wavelets, a larger time-bandwidth product results in a more spread-out wavelet in time and a narrower wavelet in frequency. In other words, increasing the time-bandwidth product makes the wavelet better localized in frequency but more spread out in time. In the notation of Morse wavelet, "TimeBandwidth" is .
The square root of the time-bandwidth product, P, is proportional to the wavelet duration in time. For convenience, the Morse wavelets in "cwt()" and "cwtfilterbank()" are parameterized using the time-bandwidth product and gamma (symmetry).

Note that this property is only valid when wavelet is "Morse" (default) and is ignored for the "amor" and "bump" wavelets.

For more information regarding the choice of the time-bandwidth product depending on specific requirements of the analysis and the characteristics of the signal, you can additionally refer to the MathWorks documentations of Mores Wavelets and "cwt()" function in the links:

https://mathworks.com/help/wavelet/ug/morse-wavelets.html

https://mathworks.com/help/wavelet/ref/cwt.html#bvaytl3-TimeBandwidth

I hope this helps.