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8 votes
Accepted

Continuous Wavelet Transform vs Discrete Wavelet Transform

On the one hand with the DWT, only a restricted choice of wavelets is available: those that implement 2-band perfect reconstruction (Daubechies, Symmlets, Coiflets, Spline). They are non-redundant, ...
Laurent Duval's user avatar
5 votes

Continuous Wavelet Transform vs Discrete Wavelet Transform

The CWT & DWT implementations differ in how they discretize the scale parameter used to stretch or shrink copies of the basic wavelet. The finer grain scale parameter in the CWT can be useful for ...
ruoho ruotsi's user avatar
  • 1,770
4 votes

Continuous Wavelet Transform vs Discrete Wavelet Transform

Fundamentally: DWT is orthogonal, CWT is redundant. Former packs the most information per sample, latter spreads out its decomposition. As will be explained: CWT yields vastly superior analysis ...
OverLordGoldDragon's user avatar
3 votes

Why are analytical wavelets said to have no negative frequency?

If it is a complex signal and if that is the reason it doesn't have any negative frequency "Analytic" is the reason why it doesn't have any negative frequencies. That's the very definition ...
Hilmar's user avatar
  • 44.8k
3 votes

Inverse of wavelet transform modulus gives poor results

Inverting CWT modulus The problem is known as phase retrieval, and for |CWT|, the transform is proven invertible to within a global phase shift, $e^{j\omega_0}$, in ...
OverLordGoldDragon's user avatar
2 votes

What does the intensity values on wavelet transform mean? Amplitude or power?

A standard continuous wavelet transformation (the one that produce a 2D scale/shift map) is a linear operator. It produces real or complex coefficients that are related to the amplitude on "how a ...
Laurent Duval's user avatar
2 votes

Practical applications of wavelets

Wavelets remain relevant. There's lots to unpack, one by one a fad, and now have more limited applications than first assumed It's the other way around. Wavelet scattering beats neural nets on small ...
OverLordGoldDragon's user avatar
2 votes

The downsampling step with discrete wavelet transform

TL' DR: When you down-sample a real signal that is sampled at $f_s$ by a factor of two, the new sampling rate will be $f_s/2$. The frequency span from $0$ to $f_s/4$ will be intact as it was ...
Dan Boschen's user avatar
  • 51.4k
2 votes

How could I do a Discrete Fourier Transform in Python if my data is non uniform?

A DFT requires equally spaced samples. However, if you just want a similar spectrum result, you can take dot products of the sample vector against a set of orthogonal in aperture sinusoids (sine and ...
hotpaw2's user avatar
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2 votes
Accepted

What exactly is meant by "translation invariant dictionaries/wavelets"?

It's rather translation equivariant: $$ \text{CWT}_{s, t}x(t - t_0) = \text{CWT}_{s, t - t_0}x(t) \tag{1} $$ and $$ \langle x(t−t_0),\psi(t) \rangle= \langle x(t), \psi(t+t_0)\rangle \tag{2} $$ That ...
OverLordGoldDragon's user avatar
1 vote

Inverse of wavelet transform modulus gives poor results

I just write a short answer, because I mostly resolved the issue. It helped me to begin my transformation with the lowest frequency, and then subtract the inverse transform of the frequency band from ...
fweth's user avatar
  • 151
1 vote

Limited cross-correlation for multiple signals

Since $r$ is so small, I think the cheapest method will be the "naive way". If $r \approx \tau$ then cross-correlation using FFT would be cheaper.
robert bristow-johnson's user avatar
1 vote
Accepted

Discrete wavelet decomposition over detail coefficients

Indeed, that will be called a wavelet packet. No, you will split the cD3 band in two equal parts: $[Fs/16,3Fs/32]$ and $[3Fs/32,Fs/8]$ as you mentioned. Warning though, the frequency bin you ...
Laurent Duval's user avatar
1 vote

How to do appcoef and detcoef using pyWavelets?

From the matlab docs https://www.mathworks.com/help/wavelet/ref/appcoef2.html the appcoef function does: "If N = NMAX, then a simple extraction is done; otherwise, appcoef2 computes iteratively ...
user2561747's user avatar
1 vote
Accepted

Should i use window with hop_size in Wavelet Transform or Discrete Wavelet Transform?

Basically, an analysis linear filter-bank is composed of several branches of convolutive filters, each branch with its own hop. The theory consists in finding under which the filter-bank is ...
Laurent Duval's user avatar
1 vote

Waveform pattern detection in time series

Suggestion. If you have some knowledge of the original waveform, you may choose a mother wavelet that resembles most the given waveform and expand data with the given wavelet. This can also be done ...
Hossain Noubari's user avatar
1 vote

PyWavelets SWT versus MODWT

The answer to your question can be found here : https://github.com/PyWavelets/pywt/issues/600
Jokerp's user avatar
  • 179
1 vote

Why discrete wavelet transforms use sampling rate 2 and need signal length to be a power of 2?

I can't comment because of reputation but if i'm not mistaken, the need for DWT to be supplied an input that is length power of 2 is independent of it's subsequent levels being downsampled by a power ...
IsmailE's user avatar
  • 61
1 vote
Accepted

Does the Fast Wavelet Transform produce the same coefficient as the Discrete Wavelet Transform?

If the discrete wavelet transform can be implemented with a FIR filter bank, with appropriate extensions, yes, up to numerical precision, coefficients will be the same. If the discrete wavelet ...
Laurent Duval's user avatar

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