Morlet Wavelet (CWT)
This interactive simulator explores Morlet Wavelet (CWT) in Math Visualization. Continuous wavelet transform with the complex Morlet wavelet: scaleogram |W(s,t)|, log-frequency axis, cone of influence, adjustable ω₀ and scale range. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.
Who it's for: For learners comfortable with heavier math or second-level detail. Typical context: Math Visualization.
Key terms
- morlet
- wavelet
- cwt
- wavelet morlet
- math
- visualization
How it works
**Continuous Wavelet Transform** with the **complex Morlet** wavelet ψ(η) = π^(−1/4) e^{iω₀η} e^{−η²/2}. Each row of the scaleogram is the convolution of the signal with a stretched, complex sinusoid windowed by a Gaussian — small scales give sharp time + broad frequency, large scales the opposite (constant Q ≈ ω₀/√2). Compare with the STFT: the wavelet adapts its window length to the analyzed frequency, so it follows a chirp **without any window-size trade-off**, and its scaleogram has crisp edges around clicks.
Key equations
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