escaling parameter or *scale*.

Compare the wavelet transform definition with the convolution
`\[ (f\ast g)(t)\equiv  \int_{-\infty}^{\infty} f(\tau) g(t-\tau) d\tau.\]`
What are the differences?


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(i) In the wavelet transform, the output depends upon our choice of scale `$s$`, (ii) the wavlet transform has a conjugation, and (iii) the wavelet transform has `$\tau-t$` rather than `$t-\tau$`.

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#The Cross-Correlation

In fact the wavelet transform is based o