Wavelet Transform & Scalogram
Continuous wavelet transform — time-frequency signal decomposition
Signal Composition
Freq 1:
5
Hz
Freq 2:
15
Hz
Chirp start:
2
Hz
Signal type:
Multi-frequency sine
Chirp (freq sweep)
Burst + transient
Amplitude modulated
Wavelet Parameters
Wavelet type:
Morlet (ψ = e^(iωt)·e^(-t²/2σ²))
Mexican Hat (ψ = (1-t²)e^(-t²/2))
Paul wavelet
Morlet ω₀:
6
Noise level:
0.05
Display
Color map:
Plasma
Viridis
Hot
Log scale power:
CWT:
W(a,b) = ∫ x(t) ψ*((t-b)/a) dt/√a
a = scale (∝1/freq), b = time
High power (bright) = signal energy at that scale/time.
Morlet wavelet gives best time-frequency trade-off.