Wavelets

#Math
Nice Animation
Allows you to produce spectrograms by corresponding the intensity of a certain frequency at a certain time to the magnitude of the complex convolution of a small wavelet curve on the sample of interest.

$\displaystyle T(a,b)= \int_{-\infty}^{\infty} y(t)\Psi\left( \frac{t-b}{a} \right) , \mathrm{d}t$

• $\displaystyle T(a,b)$ is the intensity of the wave at a time $\displaystyle b$ and scaling (opposite of frequency) $\displaystyle a$ and is found as the convolution of the sample and wavelet
• $\displaystyle y(t)$ is the sample
• $\displaystyle \Psi$ is the wavelet and may be
• $\displaystyle t$ is time
• $\displaystyle b$ is the