I am doing mathematical analysis of Wavelet transform, my problem is a Single Degree of Freedom (SDOF) self excited linear vibrations (both damped and undamped cases). The following are required for doing wavelet analysis:
1. selection of mother wavelet,
2. construction of mother wavelet equation.
3. construction of real signal for the defined problem
hi
Suggest use discrete time model. Ref (Multirate Systems and Filter Banks..P.PVaidyanathan). Basically the wavelet basis are the impulse response of filters in the analysis bank.So the impulse response of proto filters will determine Father/Mother/Daughter wavelets.Father wavelet is the filter around zero frequency. All others are Mother/ Daughter wavelets. Use PR condition . Output of analysis bank gives basis coefficients. See P493-P495 of ref for formulas and figures.
Cheers
Check this.
https://elcvia.cvc.uab.es/article/view/v18-n1-sunkara
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