Revision as of 08:03, 19 September 2023 edit Rougiecorn (talk \| contribs) 2 edits No edit summary ← Previous edit		Revision as of 15:57, 19 November 2023 edit undo Luminia2001 (talk \| contribs) 30 edits m →General overview: There are examples of L¹&&L² functions that do not decay at infinity; taking such an example and making the substitution ω->1/ω now clearly gives a counterexample to "an admissible wavelet must have its Fourier transform, evaulated at 0, exactly zero". Tags: Mobile edit Mobile app edit Android app edit Next edit →
Line 25: Traditionally, this constant is called wavelet admissible constant. A wavelet whose admissible constant satisfies :<math>0<C_\psi <\infty</math> is called an admissible wavelet~~. An admissible wavelet implies that <math>\hat{\psi}(0) = 0</math>, so that an admissible wavelet must integrate to zero~~. To recover the original signal <math>x(t)</math>, the second inverse continuous wavelet transform can be exploited. :<math>x(t)=\frac{1}{2\pi\overline\hat{\psi}(1)}\int_{0}^{\infty}\int_{-\infty}^{\infty} \frac{1}{a^2}X_w(a,b)\exp\left(i\frac{t-b}{a}\right)\, db\ da</math> This inverse transform suggests that a wavelet should be defined as

Continuous wavelet transform: Difference between revisions