Wavelet Multiresolution
Haar/Daubechies DWT · scale-space decomposition
Original Signal
Approximation (low-pass)
Detail level 1 (finest)
Detail level 2
Detail level 3
Detail level 4
Reconstructed (thresholded)
Scalogram (time-frequency)
Signal type
Frequency mix
Chirp
Step function
Sparse spikes
Noisy sine
1/f noise
Wavelet
Haar
Daubechies-4
Daubechies-6
Threshold
0.05
Noise σ
0.0
Levels
4
Generate
Animate
Multiresolution analysis
(Mallat 1989): decompose a signal into orthogonal scales.
Each level splits into approximation (scaling coefficients) and detail (wavelet coefficients).
DWT filter bank:
cA[k] = Σ h[n-2k] x[n]
cD[k] = Σ g[n-2k] x[n]
Thresholding detail coefficients = denoising.