MENTAL MODEL · M9154

Wavelet Analysis Chart

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Updated 2026-08-15

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INTRODUCTION

English translation pending.

CORE DEFINITION

A wavelet is a short oscillating function localised in time, and the wavelet transform decomposes a signal into components at different scales and positions. The resulting scalogram displays energy against time and frequency simultaneously, unlike the Fourier transform, which reports frequency content without saying when it occurred. The qualification is that the result depends on the choice of mother wavelet and that edge effects distort the estimate near the ends of the record.

SCAFFOLDING EFFECT

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- Use Transient Location: identify when a brief event occurs, not merely that its frequency is present. - Use Scale Selection: inspect several scales so features at different durations are not missed.

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Fourier analysis assumes the signal's frequency content is stationary over the whole record, so a brief burst is averaged into the overall spectrum. Localising the basis function in time means each coefficient describes a short window, which preserves the timing of transient features.

MINIMUM ACTION

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Practice this model in one real situation:

Choose a mother wavelet suited to the signal. 2. Apply the continuous or the discrete wavelet transform. 3. Plot the coefficients as a time and frequency map. 4. Inspect the map for transients and multi-scale structure. 5. Check the boundary regions of the record for edge artefacts.

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Source support: Explicit

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zh.wikipedia.orghttps://zh.wikipedia.org/wiki/%E5%B0%8F%E6%B3%A2%E5%88%86%E6%9E%90ZH · Explicit
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