audioflux.type.WaveletContinueType
- class audioflux.type.WaveletContinueType(value)
Wavelet Continue Type
- MORSE:
\(\Psi_{eta, \gamma}(\omega) = U(\omega)a_{\beta,\gamma} \omega^{\beta}e^{-\omega^{\gamma}}\)
\(U(\omega)\) is the step function, \(\omega\) is the positive and negative sign, \(\omega^{eta}e^{-\omega^{\gamma}}\) is \(e^{eta\ln\omega -\omega^{\gamma} }\)
\(a_{eta,\gamma}=\omega_0^{-eta} e^{\omega_0^\gamma}=e^{-eta\ln\omega_0+\omega_0^\gamma}\), \(\omega_0\) represents the peak frequency of the center of the wavelet window, \(\omega_0=\left( \cfraceta\gamma \right)^{\frac1\gamma}\) is \(e^{\frac1\gamma(\ln\beta-\ln\gamma)}\) calculation
default: \(\gamma=3,eta=20\)
- MORLET:
\(\Psi(\omega)=\pi^{-1/4}e^{-(\omega-\omega_0)^2/\sigma}\)
default: \(\omega_0=6,\sigma=2\)
- BUMP:
\(\Psi(\omega)=e^{(1-\frac{1}{1-(\omega-\omega_0)^2/\sigma^2}) }I(\omega)\)
\(I(\omega)\) represents the \(\omega\) interval range mark, \(\| (w-\omega_0)/\sigma \| \le 1\)
default: \(\omega_0=5,\sigma=0.6\)
- PAUL:
\(\Psi(\omega)=U(\omega)\frac{2^m}{\sqrt{m(2m-1)!}}\omega^{m}e^{-\omega}\)
default: \(m=4\)
Default gamma/beta values for different wavelet_types:
morse: gamma=3 beta=20
morlet: gamma=6 beta=2
bump: gamma=5 beta=0.6
paul: gamma 4
dog: gamma 2 beta 2; must even
mexican: beta 2
hermit: gamma 5 beta 2
ricker: gamma 4
Attributes
MORSEMORLETBUMPPAULDOGMEXICANHERMITRICKER