Questions tagged [cwt]

Continuous Wavelet Transform. Time-frequency localization method with a wavelet kernel correlating against signal across scales and translations. Is non-orthogonal and overcomplete (unlike Discrete WT), varies time & frequency resolution across scales (unlike STFT), and is invertible. Usage includes image compression, multi-resolution analysis, instantaneous frequency estimation, transient detection, feature extraction.

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1k views

Synchrosqueezing Wavelet Transform explanation?

How does Synchrosqueezing Wavelet Transform work, intuitively? What does the "synchrosqueezed" part do, and how is it different from simply the (continuous) Wavelet Transform?
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Wavelet Transform and STFT

How wavelet transform is different from STFT. I'm not able to understand what is resolution in frequency domain means?
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0answers
165 views

Why is CWT implemented with FFT convolution?

Instead of padding $x_1[n]$ and $x_2[n]$ then taking $$ \text{iDFT}(\text{DFT}(x_1[n])\cdot\text{DFT}(x_2[n])), \tag{1} $$ assuming we know $x_1(t)$ and $x_2(t)$, and their FT's, what if we do $$ \...
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2answers
106 views

How does the scale of a wavelet relate to the Fourier frequency( or period) under CWT?

I noticed that there are many ways to relate the scale factor of wavelets to some characteristic frequency, such as the peak frequency, the central instantaneous frequency, and so on(plz see section 2....
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1answer
150 views

Scalograms in python

I am reading this paper to learning basic concepts of dsp and I want to reproduce the following scalogram of a test signal (fig 4.2 of the paper): It has been produced from the discretization of the ...
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2answers
151 views

CWT Disapointing Frequency Separation

I'm attempting to perform multi-resolution analysis via Continuous-Wavelet Transform (CWT) using Pywavelets. I've heard that CWT is supposed to be superior to STFT due to varying frequency content as ...
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2answers
63 views

STFT with varying window lengths (like the continuous wavelet transform)

I was wondering if it is possible to use windows of varying lengths when making a spectrogram based on the short-time Fourier transform (STFT). That is, for higher frequencies I would use shorter ...
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2answers
345 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^...
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2answers
119 views

Why does a synchrosqueezed wavelet transform show oscillating behavior?

This question came up in the context of the ssqueezepy library. As a basic experiment I did compute the synchrosqueezed wavelet transform of three basic signals: A ...
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1answer
19 views

What scheme of padding should I choose if my 1D data satisfy the periodical boundary condition under CWT?

By CWT, I mean the continuous wavelet transform. The usual padding schemes are zero padding, periodic padding, and decay padding. If I adopt the periodic padding, can I avoid the edge effects for the ...
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1answer
39 views

Is single integral inverse CWT possible with real-valued wavelets?

Where the CWT in the title refers to the continuous wavelet transform. Torrence1998 proposed a reconstruction formula as shown below Obviously, Eq.(11) is a single integral. However, Torrence1998 ...
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2answers
91 views

How is wavelet center frequency computed?

PyWavelets (1) takes index of max DFT magnitude, (2) adds 1 to it, (3) divides by domain, which is the range of input values to the wavelet ("support"). ...
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1answer
35 views

Understanding the units of wavelet time & frequency resolution

While using a continuous wavelet transform for my research project, I came up with some questions. Having a set of equations for a Morlet wavelet, $\psi(t)=\sqrt{\frac{2}{\pi}}e^{-t^2/2}e^{i6t}$ $\...
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1answer
32 views

wavelet_transform

I have a signal $$Y=f(t),$$ which I want to show the anomalies, using the wavelets transform. I don't know if I use the CWT or the DWT and which mother wavelet could I use?
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1answer
70 views

3D (time, scale, amplitude) plot in Continuous Wavelet Transform

I will be extremely grateful if someone could please answer this basic question. How can one plot a 3D (translation, scale, amplitude) plot from the Continuous wavelet transform (CWT) coefficients? ...
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2answers
80 views

Synchrosqueezed STFT phase transform

Synchrosqueezed STFT paper, Synchrosqueezing based Recovery of Instantaneous Frequency from Nonuniform Samples, defines STFT phase transform as: $$ w(u, \xi) = \xi - \frac{\partial_tS_{g}f(u, \xi)}{j2\...
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2answers
89 views

One integral inverse CWT

MATLAB's icwt docs state inversion to be done by a single integral: $$ f(t) = 2 \Re e\left\{ \frac{1}{C_{\psi, \delta}} \int_0^\infty \left< f(t), \psi(t) \right> \frac{da}{a} \tag{1} \...
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1answer
239 views

CWT at low scales: PyWavelets vs Scipy

Low scales are arguably the most challenging to implement due to limitations in discretized representations. Detailed comparison here; the principal difference is in how the two handle wavelets at ...
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1answer
279 views

PyWavelets CWT implementation

I seek to understand PyWavelets' implementation of the Continuous Wavelet Transform, and how it compares to the more 'basic' version I've coded and provided here. In particular: How is integrated ...
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2answers
83 views

How to test wavelet transforms?

One pertinent attribute is normalization, which measures performance in describing signal spectral amplitude and energy, like here. Others are robustness to noise, time vs frequency resolution. ...
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1answer
17 views

Define frequencies present in the time-frequency spectrum using scipy.signal.cwt

I have a very basic question, but I didn't find a definite answer elsewhere. When we use scipy.signal.cwt we specify only one parameter ...
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1answer
37 views

Pywavelets CWT returning 0 after scale 64

I am running continuous wavelet transform in mexican hat wavelet basis on a data set (with millions of samples) using pywavelets. The command used is ...
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1answer
168 views

Inverse Continuous Wavelet Transform derivation?

Wiki writes iCWT as $$ f(t) = C_{\psi}^{-1} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} W_f(a,b) \frac{1}{|a|^{1/2}} \tilde\psi \left(\frac{t - b}{a}\right) db \frac{da}{a^2}, \tag{1} $$ where $\...
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1answer
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PyWavelets CWT: resampling vs recomputing wavelet

Related. The implementation pre-integrates a wavelet once, and resamples it at each scale, finally differencing to implement ...