I am trying to understand the CWT implementation in PyWavelets. As per the definition at a given scale it involves the convolution of the wavefunction at that scale with the signal. I would assume this would imply discretizing the wavefunction for a specified number of sample points to obtain the discrete time filter which is then convolved with the given signal. However the implemention in PyWavelets seems to have an extra step namely integrate the wavefunction before discretizing and convolution. Why is that?
Below is a comparison of the cmor1.5-1.0 wavefunction with its integral along with the discretized filter at scale 1 (real parts)
https://github.com/PyWavelets/pywt/blob/74b44217a66199fa2e0f8e036955fc00f5cbc21a/pywt/_cwt.py#L126
I am trying to understand the CWT implementation in PyWavelets. As per the definition at a given scale it involves the convolution of the wavefunction at that scale with the signal. I would assume this would imply discretizing the wavefunction for a specified number of sample points to obtain the discrete time filter which is then convolved with the given signal. However the implemention in PyWavelets seems to have an extra step namely integrate the wavefunction before discretizing and convolution. Why is that?
Below is a comparison of the cmor1.5-1.0 wavefunction with its integral along with the discretized filter at scale 1 (real parts)