Scaling Function and Wavelet Function I don't understand the meaning of scaling function when I used CWT/DWT.
For me, I understand that the wavelet function (mother wavelet) is the function that we used to decompose our signal in subsignal corresponding to the frequency of the mother wavelet (for example db8). (Maybe DWT is different from wavelet decomposition ?)
For example, if I decompose my signal into 5 levels (with wavedec in MATLAB), I have :
D1, D2, D3, D4, D5 and A5, with D the detail's signal and A the approximation's signal.
But here I never used the scaling function to make the decomposition of my signal.
Can you help me on how to understand the scaling function ?
In my experience, scaling functions are not so central in the CWT. However, there are quite important on the DWT. Scaling functions act like low-pass operators, and wavelets like band-pass ones. Indeed, in the DWT, one seldom uses th wavelet and the scaling function directly, since they are hidden in the construction of the low-pass and high-pass filters that are combined in cascading filterbanks. The actual wavelet (and scaling function) are only obtained as a limiting process involving an infinite cascade of discrete filters.
A complementary discussion: Scaling Function in Wavelet Analysis