Linked Questions

7 votes
3 answers
3k views

Continuous Wavelet Transform vs Discrete Wavelet Transform

The discrete wavelet transform is applied in many areas, such as signal compression, since it is easy to compute. I notice that, However, the continuous wavelet transform (CWT) is also applied to ...
Wang Yun's user avatar
  • 124
8 votes
4 answers
2k views

Advantage of STFT over wavelet transform

I have learned about STFT and wavelet transform recently, and wavelet transform seems better than STFT in my opinion. So, I wonder if there is any advantage of using STFT than WT, and if so, what are ...
lemoncake's user avatar
  • 103
4 votes
4 answers
1k views

Why to pad zeros at the middle of sequence instead at the end of the sequence?

One of the implementation of Bluestein algorithm as show in the below link Bluestein's Algorithm [conj(W), zeros(1, L-2*N+1), conj(W(N:-1:2)) ] padding the zeros ...
jomegaA's user avatar
  • 659
2 votes
2 answers
3k views

How is wavelet time & frequency resolution computed?

Mallat gives analytic wavelet time & frequency widths/uncertainties as $$ \begin{align} \sigma_{ts}^2 &= \int_{-\infty}^{\infty} (t - u)^2 |\psi_{u, s}(t)|^2 dt = s^2 \sigma_t^...
OverLordGoldDragon's user avatar
4 votes
1 answer
2k views

PyWavelets CWT: normalization? Vs Scipy?

Related. The equation being implemented normalizes by sqrt(1 / scale): $$ C_{a, b} = \frac{1}{\sqrt{a}} \sum_k s(k)\left( \int_{-\infty}^{k+1} \overline{\psi \left(\...
OverLordGoldDragon's user avatar
1 vote
1 answer
463 views

How to validate a wavelet filterbank (CWT)?

I've seen many different implementations of CWT, especially in generating the wavelets. Often these implementations produce significantly different outputs - e.g. ...
OverLordGoldDragon's user avatar
3 votes
1 answer
322 views

Why does a signal with constant frequency have spots that changes colors at a specific value of scale (and so frequency) in the scalogram?

I am studying the Wavelet transform and I am considering this example that I took from PyWavelets documentation. The signal in time domain has the following shape: Till the value of zero on the ...
User's user avatar
  • 55
4 votes
1 answer
261 views

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\} \...
robert bristow-johnson's user avatar
1 vote
1 answer
196 views

Weird Noise arises on the small scales: one question about the fast CWT algorithm implemented in real space

Background: I am learning an interesting Fast CWT algorithm(PPCWT) by reading this paper published in 2019. The algorithm is summarized as below. The continuous wavelet transform of a signal can be ...
Wang Yun's user avatar
  • 124
-1 votes
1 answer
265 views

Why does using a log scale ruin (warp) my scaleograms?

I'm trying to make a scaleogram of neural data using the continuous wavelet transform (with Morlet wavelets). As a starting point, I use just a simple sine wave built from two frequencies, 50 and 80 ...
neverreally's user avatar
2 votes
1 answer
187 views

What should the time-shift be when implementing a continuous wavelet transform on a computer?

I'm currently researching implementation methods of the Continuous Wavelet Transform(CWT). On paper, the CWT produces infinitely many outputs on a finite signal since the scaling and shifting ...
Izzo's user avatar
  • 803