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#Summary, Part II

(v) The wavelet transform

`\[w(t,s) =\int_{-\infty}^\infty \frac{1}{s} \psi^*\left(\frac{\tau-t}{s}\right) z(\tau) d\tau=\frac{1}{2\pi} \int_{-\infty}^\infty  \Psi^*(s\omega) Z(\omega) e^{i\omega t} d\omega\]`

*The right hand side of (v) follows from reflection formula; then (v) gives wavelet transform of delta and sinusoid*

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#Important Extensions

Wavelet analysis is great for visualizing the variability co