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Re: [Tftb-help] Urgent Help needed on wavelet

From: Eric Chassande-Mottin
Subject: Re: [Tftb-help] Urgent Help needed on wavelet
Date: Tue, 4 Sep 2007 10:24:23 +0200 (CEST)

W(t,a;h) = (a^-0.5) x Integrate [f(t') x h((t-t')/a)]dt' (1)

W(tau,omega) = (tau^0.5) Integrate [F(w) x H(tau(w-omega)] dw (2)

strictly speaking, Eq. (2) is not a new definition of the wavelet transform since it is equivalent to (1) by Parseval if F and H are the Fourier transforms of f and h.

i guess the question is: how to compute the wavelet transform using
the FFT of both signal and wavelet? none of the routines of the TFTB
use this kind of implementation of the continuous wavelet transform.

W(tau,omega) = (tau^-0.5) x Integrate [f(t) x h(t/tau) x exp(j*omega*tau)] dt (3)

Eq. (3) arises when the wavelet can be expressed as a modulated
window (like the Morlet wavelet where h(t) is a Gaussian window).
Eq. (3) is the variable "tfr" computed by tfrrmsc.m.

hope this helps,

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