Can you run cwt with complex Morlet function?
I have an application that I must use a complex Morlet wavelet function ( cmorfb-fc ), I can run CWT (continuous wavelet transform) and it’s fine, but I want to run DWT (Discrete wavelet transform) with this complex Morlet ( cmorfb-fc) function too. then I want to compare the DWT and CWT results.
Is the complex Morlet redundant for real signals?
Until the inception of the Meyer wavelet, and the subsequent ones (Daubechies, Symmlets, Coiflets, etc.). Their somewhat weird shapes is the sign that not every wavelet shape is possible. This is even truer as the complex Morlet is complex, hence somewhat already twice redundant for real signals.
Which is an example of a complex Morlet function?
However, multi-band filter banks are an option to build orthogonal counterparts of “Morlet”-like design. Malvar wavelets, Modulated complex lapped transforms or Lapped orthogonal transforms are instances (see a Panorama of wavelets for references), and their can be further decomposed across scales as M -band wavelets.
Can a complex Morlet be critically discretized with 2-band?
Their somewhat weird shapes is the sign that not every wavelet shape is possible. This is even truer as the complex Morlet is complex, hence somewhat already twice redundant for real signals. So, Morlet cannot be critically discretized with 2-band (dyadic), as you already guessed, as you wanted to compare CWT and DWT.
How is the complex Morlet wavelet defined?
The complex Morlet wavelet is a complex sinusoid modulated by a Gaussian envelope defined by: (6.36)ψ(t) = 1 4√πe jωcte − t2 2 where ωc = 2 πfc is the central frequency of the wavelet and determines the number of oscillations of the complex sinusoid inside the Gaussian envelope.
What is the FB of a complex Morlet?
One wavelet has an Fb value of 0.5 and the other wavelet has a value of 8. The Fb bandwidth parameter for the complex Morlet wavelet is the inverse of the variance in frequency. Therefore, increasing Fb results in a narrower concentration of energy around the center frequency.