Dear all,
thank you for considering this question. Do you know any reason why Daubechies wavelet can't be used for CWT ? Matlab toolbox and Python packages don't allow for such transform, and I was wondering about theoritical rational here. Thank you
Daubechies wavelets are a family of orthogonal wavelets that are widely used in signal and image processing. They are characterized by their compact support, which means that they are nonzero only over a finite interval. This property makes them well-suited for applications where it is important to localize the signal or image in time or space.
Continuous Wavelet Transform (CWT) is a mathematical tool that decomposes a signal into a set of wavelets. The wavelets are functions that are scaled and translated versions of a mother wavelet. The CWT of a signal is a function of time and scale, and it represents the signal as a set of coefficients that measure the similarity between the signal and the wavelets at different scales.
Daubechies wavelets can be used for CWT, but they are not the most common choice. This is because Daubechies wavelets are orthogonal, which means that they are not well-suited for representing signals that have a lot of high-frequency content. In these cases, it is often better to use wavelets that are not orthogonal, such as Morlet wavelets or Gabor wavelets.
Daubechies' wavelet is created by a recurrent procedure from a few discret samples of mother and father wavelets, and so it cannot be represented as a continuous functtion.
Because they have compact support implying a low localization in frequency domain. Yannick Daviaux
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