Morlet Wavelet (CWT)

This interactive simulator explores Morlet Wavelet (CWT) in Визуализация математики. 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.

Для кого: For learners comfortable with heavier math or second-level detail. Typical context: Визуализация математики.

Ключевые понятия

morlet
wavelet
cwt
wavelet morlet
math

Как это работает

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.

Основные формулы

W(s, τ) = (1/√s) ∫ x(t) ψ*((t − τ)/s) dt

ψ(η) = π⁻¹ᐟ⁴ e^{iω₀η} e^{−η²/2}, f_pseudo ≈ ω₀ f_s / (2π s)

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Morlet Wavelet (CWT)

Как это работает

Основные формулы

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Как это работает

Основные формулы