All Questions
6 questions
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How to implement scale-dependent Gaussian averaging using Morlet wavelet envelope in Python?
I'm trying to reproduce the scale-dependent Gaussian averaging of a time series as described in this paper: https://arxiv.org/pdf/1706.01126.pdf
The process involves performing a continuous wavelet ...
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-1
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1
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219
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Standard deviation of Morlet wavelet's Fourier transform
MATLAB has the complex Morlet Wavelet in the following form:
$$\psi(t) = \frac{1}{\sqrt{\pi f_b}}e^{\frac{-t^2}{f_b}}e^{j2\pi f_ct}$$
I arrived at its Fourier transform as shown below (another ...
0
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1
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628
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Scaling a wavelet in continuous wavelet transform
The mexican hat wavelet, obtained from the second derivative of a Gaussian, has a functional form of
$$ \frac{2}{\sqrt{3 \sqrt{\pi} \sigma \ }} \left(1-\frac{t^2}{\sigma^2} \right) e^{-t^2/(2\sigma^...
- 666
4
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1
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310
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Does a "chirp"-like generalization of the Gabor or Morlet wavelets definitions exist in the lit somewhere?
I have asked this at the Math SE also.
Predicating this on the definition of the continuous Fourier Transform preferred by most electrical engineers:
$$ X(f) \triangleq \mathscr{F} \Big\{ x(t) \Big\} \...
- 21.4k
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160
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Transform coding gain of two channel Haar Wavelet transform (first stage)
Question
My interpretation
Work
I'm attempting to do this in MATLAB.
I know that for discrete Random Processes going into an LTI system the autocorrelation function of the output is $R_y[n] =...
5
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2
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376
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Additive White Gaussian Noise (AWGN) and Undecimated DWT
One of the benefits of DWT is that it is an orthonormal transform.
There are statements that the energy of noise component mainly concentrates on the high-frequency (detail) part and distributes ...
