951ff2e4-3c4c-4e87-9886-9edd266c1367 22 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Dyadic Wavelets

x f2 34 / 3 x 12 / + (* + 9 x 12 / + (2^* - :

x f1 3 x 1 + (2^* :

x F x f1 x 0.5 - ≤ x f2 cases :

x G 0 x abs 1 ≥ x F x 0 ≤ x - F - cases :

Axes system x y XY x y / :

x G x f1 x f2 x F XY 4 1 sys

x j W μ j : 12 μ^sqrt / x 2 μ^/ G * 21 line :

x G x 1 W x 1 - W XY 4 1 sys

p j x T t p t x - j W * t x 2 j^- x 2 j^+ int :

t p t :

Sanity Mathcad 11 p 3 1.5 T 8.4853 -

t Ψ 23 sqrt / π 14 / -^* (1 t 2^- (* t 2^- 2 / exp * :

Morlet wavelet [Mexican hat]

x Ψ

23 sqrt / π 14 / -^* 0.8673

Frequency response

daub4 0.48296 0.8365 0.22414 0.12941 - 41 mat :

daub4hp 0.1294 - 0.2241 - 0.8365 0.483 - 41 mat :

daub8 0.2303778 0.7148465 0.6308808 0.0279838 - 0.1870348 - 0.0308414 0.0328830 0.0105974 - 81 mat :

n 14 range :

daub4hp daub4 1 - (n^* vectorize reverse : 0.1294 - 0.2241 - 0.8365 0.483 - 41 mat

Daub4 is the impulse response of the 4-point long Daubechies wavelet, Daub8 is the impulse response of the 8-point long wavelet. You may use either one of them, if you decide to use this type of wavelet.

w coeff Hdaub coeff n el i w * n * - exp * n 1 coeff rows sum :

x u 0 x ≤ (x 2 π * ≤ (& :

w daub4 magHdaub w daub4 Hdaub abs :

x daub4 magHdaub x u * x daub4hp magHdaub x u * 2 1 sys x daub8 magHdaub x u * x π + daub8 magHdaub x u * 2 1 sys