Can anybody recommend a good source for material of Gaussian and Complex Gaussian wavelet? Please share the link if possible.
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1$\begingroup$ Welcome to SE.DSP. Some of us are able to do so, yet could you tell us more about why you need it, and what you have found so far? $\endgroup$ – Laurent Duval Aug 31 '19 at 13:56
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$\begingroup$ I need to prepare a presentation on these two wavelets to present in front of class.And it is also included in my syllabus so I have to study them for my end term exams. researchgate.net/publication/… I have found only this much and nothing on complex gaussian wavelet. $\endgroup$ – Mayank Singh Aug 31 '19 at 16:59
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The notion of "Gaussian wavelet", whether real or complex, is not clear from the literature. Indeed, the Gaussian has a positive average, while wavelets are (or should be) zero-mean (to satisfy the admissibility condition).
Two standard wavelets may suit your need:
- the Morlet wavelet, or Gabor wavelet, a complex exponential multiplied by a Gaussian window envelope (or its real part),
- derivatives of Gaussians (including differences of Gaussians or DoG), sometimes called Ricker wavelet in 1D in geosciences or mexican hat in 2D.
Their complex extensions, or real restrictions, are relatively natural.
answered Aug 31 '19 at 18:42
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1$\begingroup$ another generalization of Morlet is the chirplet. not calling it that, i essentially use that in this paper regarding time-scaling in a modified phase vocoder. $\endgroup$ – robert bristow-johnson Aug 31 '19 at 22:22
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$\begingroup$ Indeed, and I am glad for the flattened Hann window I haven't met before $\endgroup$ – Laurent Duval Sep 1 '19 at 10:02
