Wavelet Multiresolution Analysis
DWT decomposition — approximation & detail coefficients across scales
Signal & Wavelet
Signal type:
Mixed frequencies
Chirp signal
Step + noise
ECG-like
Spike + sinusoid
Wavelet type:
Haar
Daubechies-2
Daubechies-4
Coiflet
Decomposition levels:
5
Noise σ:
0.10
Decompose
Key Equations
ψ_{j,k}(t) = 2^{j/2} ψ(2^j t − k)
Wf(j,k) = ⟨f, ψ_{j,k}⟩
Mallat: H(low-pass) + G(high-pass) → A_j + D_j
MRA: V₀ ⊃ V₁ ⊃ ... Vⱼ⊕Wⱼ=Vⱼ₋₁
Haar: ψ = χ[0,½) − χ[½,1)