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 ?


1 Answer 1


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

  • $\begingroup$ Thank you for your answer. I also don't really understand what is the difference between wavelet decomposition, wavedec in MATLAB (which give me coefficients for each level) and MODWT in MATLAB which give me signal representation on wavelet basis. $\endgroup$
    – Mo0nKizz
    Apr 21, 2021 at 9:27
  • $\begingroup$ This is a whole topic, and cannot really be solved in a comment. Did you already pick-up a book, or are you interested in some application? $\endgroup$ Apr 21, 2021 at 9:40
  • $\begingroup$ I already read lots of articles concerning Wavelet concepts but I didn't managed to understand all the feature. I had to remove interferences from a signal. So first of all I used wdenoise from MATLAB to denoise my signal. But it only remove noise, not interference spikes in signal. So I try to identify interferences with wavelet decomposition (wavedec) in order to identify and remove those interferences. $\endgroup$
    – Mo0nKizz
    Apr 21, 2021 at 9:44
  • $\begingroup$ Even with a lot of practice, I have still discovering stuff with wavelets. Noise and spikes may require different approaches in the wavelet domain $\endgroup$ Apr 21, 2021 at 9:50
  • $\begingroup$ So what is the approach to spikes problems ? Maybe articles, books or concepts ? $\endgroup$
    – Mo0nKizz
    Apr 21, 2021 at 9:50

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