The mother wavelet function ψ(t) must satisfy the following:
+∞∫−∞|ψ(ω)|2ωdω<+∞, ψ(ω)|ω=0=0, and +∞∫−∞ψ(t) dt=0
To serve as the wavelet basis for wavelet transform γ(s,τ)=+∞∫−∞f(t) ψs,τ(t) dt
where ψs,τ(t)≜ψ(t−τs).
While I understand that the wavelet must be an oscillatory function having no frequency component at ω=0 and effectively have a band pass filter like spectrum, from the equation of wavelet series or wavelet transform can you tell me why is it that the wavelet transform is implemented as a filter bank? What is the intuition behind it? What makes it possible?
I am asking this question since the fact that practically the DWT is implemented as a filter bank means that it is not a DWT anymore, it is just a set of low pass and high pass filters. It is mind bogling.
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