difference between scaling and wavelet coefficient
Answers
Answered by
0
The scaling function ϕ(t)ϕ(t) can be regarded as a low-pass filter Φ(ω)Φ(ω), while the wavelet ψ(t)ψ(t) can be thought of as a band-pass filter Ψ(ω)Ψ(ω). Here, Φ(ω)Φ(ω) and Ψ(ω)Ψ(ω) are the Fourier transforms of the scaling function and the wavelet respectively.
We can account for successively higherfrequency bands by diadically dilating the wavelet: ψ(2t),ψ(4t),ψ(8t),…ψ(2t),ψ(4t),ψ(8t),…. Up to a normalization, the corresponding Fourier transforms are Ψ(t/2),Ψ(t/4),Ψ(t/8),…Ψ(t/2),Ψ(t/4),Ψ(t/8),… .
The plot below depicts the amplitude responses of the filters ϕ(t)ϕ(t), ψ(t)ψ(t) , ψ(2t)ψ(2t) and ψ(4t)ψ(4t) for a Daubechies-22 wavelet. I have normalized the vertical scale so that the peak amplitudes in the respective bands are one.
We can account for successively higherfrequency bands by diadically dilating the wavelet: ψ(2t),ψ(4t),ψ(8t),…ψ(2t),ψ(4t),ψ(8t),…. Up to a normalization, the corresponding Fourier transforms are Ψ(t/2),Ψ(t/4),Ψ(t/8),…Ψ(t/2),Ψ(t/4),Ψ(t/8),… .
The plot below depicts the amplitude responses of the filters ϕ(t)ϕ(t), ψ(t)ψ(t) , ψ(2t)ψ(2t) and ψ(4t)ψ(4t) for a Daubechies-22 wavelet. I have normalized the vertical scale so that the peak amplitudes in the respective bands are one.
Similar questions