# Questions tagged [wavelet]

A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero.

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### How to plot the shape of a 2D wavelet?

I often see images like this: where on the left it depicts 2D wavelets and on the right curvelets for different scales and locations. How can I visualize different 2D wavelets/curvelets in such a way ...
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### How to effectively stationarise non-periodic wave signals?

I am pre-processing a non-periodic signal for further implementation of autoregressive modelling on the signal. The signal is shown in the following figure. However, when I applied the Augmented ...
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I am trying to validate and understand Wavelet decomposition using pywt.wavedec(). Here are the steps I took: (1) For a 3 level decomposition, I added a sine component with the following frequency for ...
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### What exactly is meant by "translation invariant dictionaries/wavelets"?

I'm trying to wrap my head around the notion of translation invariance in terms of dictionaries/wavelets. For example in Lecture Notes, Page 41 its written that one starts with a family of atoms/...
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### Estimating significance in time-frequency spectrograms

I want to investigate the common input of two EMG signals using a wavelet-based approach. To this end, I chose the continuous wavelet transform to approach my research question. In addition, I would ...
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### Inverse discrete wavelet transfrom

I am trying to understand the formula of the inverse wavelet transform. Although I have looked at many papers none of them fully define the summations that appear and this is creating a lot of ...
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### How to alleviate the edging effect of the Hilbert transform?

I am trying to use Hilbert transform to extract the envelope of a residual signal. After implementing the Hilbert transform, I find that envelope jumps very high at its boundaries. May I ask the ...
137 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 ...
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### Manual DWT vs Python pywt

I am trying to understand Discrete Wavelet Transform. I am trying to do it manually to understand all the steps well. Taking as an example the wavelet function 'sym2' knowing that its low decompostion ...
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### Discrete Wavelet Transform (DWT) and wavelet family

I have just started reading about wavelets for a data compression problem that I want to perform. I am reading about Discrete Wavelet Transform (DWT) but I can't understand where the wavelet family ...
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### Alternatives to Meyer Windows as Curvelets?

I am looking for alternative to Meyer window functions (Section 4.1) from which one can define a curvelet system. Are there any similar window functions which would be as easy to implement?
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### 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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### how does wavelet transform detect pulses from a signal

I am learning wavelet transform, below image is an example I have that uses haar wavelet for decomposing the simple haar wavelet like signal. i know that the coefficients at each level are results of ...
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### What does the intensity values on wavelet transform mean? Amplitude or power?

So when applying wavelet transform, we get a 2d plot. Each point in that 2d plot has a color, showing intensity of something. But I cannot understand if it is an amplitude or power?
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### 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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### Understanding why we have low-pass/high-pass filters in MRA

I am new to Multiresolution analysis and I can't figure out and find something mathematically convincing of why in multiresolution decomposion the filters are low and high pass. I.e. in the ...
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### 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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### Compared with the real-valued continuous wavelet, what are the advantages of the complex-valued continuous wavelets?

I noticed that there are two types of wavelet functions, i.e. the real-valued, such as the Mexican hat wavelet, and the complex-valued, such as the Morlet wavelet. How was the complex-valued wavelet ...
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### Why does each node in the wavelet scattering transform split into multiple paths?

Why does each node in the wavelet scattering transform split into multiple paths as in this figure from https://arxiv.org/abs/1304.6763? I understand roughly what’s happening along a single path, but ...
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### How to filter out noise from non-stationary signal

I have this non-stationary signal. the mean is roughly constant but the second moment (autocorrelation) does not depend only on the time lag $tau$. Correct me if I am wrong in the above statement. ...
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### Detecting and removing interferences from a signal

I am using MATLAB in order to denoise and remove interferences on a signal. I used wdenoise to denoise my signal which works by setting a threshold (for example ...
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### Smoothing contours for contour analysis for character recognition

I am making a character recognition library using contour analysis. Contours are sequencies of complex numbers X + j*Y (in fact in contour analysis they are defined ...
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### Scaling Function and Wavelet Function

I don't understand the meaning of scaling function when I used CWT/DWT. For me, I understand that the wavelet function (mother wavelet) is the function that we used to decompose our signal in ...
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### Difference between Gabor filtering and Discrete Wavelet Transform

Both Gabor filtering and discrete wavelet transform (DWT) analyze the image in both spatial and frequency domains, unlike Fourier transform which analyzes the image only in the frequency domain. What ...
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### How do I implement a footstep recognition algorithm? One that recognizes the start and end points of each footstep?

I have some time series data captured from a person's footsteps/strides (specifically, a person on rollerblades). It came from an IMU sensor placed on a person's boot. Each data point captures ...
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### Wavelet, scaling, detail, and smooth/approximation coefficients

I was reading through the documentation for the R wavelets package and doing a little experimentation and noticed that the modwt ...
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### PyWavelets SWT versus MODWT

I'm just learning about wavelets and the PyWavelets package. I saw a reference to MODWT, which led me to the SO post here and then to this Python package: https://github.com/pistonly/modwtpy What ...
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### 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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### 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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### 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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### How does signal scaling affects stationary wavelet?

I'm currently working on some signals recorded with different sensors with different adc resolutions. I wonder how this different resolutions affect signal's stationary wavelet. Does it just changes ...
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### Are the Daubechies 4 wavelet function and scaling function dimensionless?

If the dimension of the independent variable $x$ of $f(x)$ is length, i.e. $[x]=L$, then what is the dimension of Daubechies 4 (hereafter D4) wavelet and scaling function?
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### Regarding custom wavelets and their validity

I've recently started working with wavelets, and want to focus primarily on Discrete Wavelet Transform. For experimental purposes, I use the PyWavelets library in Python. In one of my tests, I tried ...
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### Stockwell S-Transform and multitapering

I want to estimate just the spectral amplitudes at different time points using S-transform given a noisy signal. Would I benefit (in terms of noise reduction) from an approach used in multi taper ...
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### Pros/Cons to using Spectral and Diffusive Graph Wavelets

As I understand, there are two major methods of constructing wavelets on graphs. Spectral wavelets, from David K Hammond et. al, and diffusive wavelets from Coifman and Maggioni. I can't quite parse ...
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### Check vanishing moment property of db4 wavelets

I am reading the book "a primer on wavelets and their scientific applications" by James S. Walker. In chapter 3, Property I on page 46 says that if a signal $f$ is linear, then the $k$-level ...
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### energy normalization across different scales in case of discrete wavelet transform

In case of continuous wavelet transform (CWT), the wavelets are generated from the mother wavelet by scaling and translation. To achieve energy normalization and to ensure that all wavelets have the ...
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### Why the inverse discrete fourier transform of the Ricker pulse isn't the same as the Ricker pulse in time domain?

Question I'm trying to use Python's scipy library to compute the IDFT of the Ricker wavelet function and compare it with the analytical time-domain version of the same function. When I compare the ...
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### Why discrete wavelet transforms use sampling rate 2 and need signal length to be a power of 2?

I know Fourier transforms but new to wavelet transforms. I can understand Haar transform needs signal length a power of 2, since the filters have 2 taps and down-sampling and up-sampling in the ...
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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^... 1answer 88 views ### Energy normalization across wavelet subbands According to the following reference: A Really Friendly Guide to Wavelets, © C. Valens, 1999 Equation 3, the wavelets are generated from the mother wavelet by scaling and translation. S is the scaling ... 2answers 66 views ### Coefficient meaning in DWT I understand that approximate and detail coefficient represent the different signal bands. But what do the values mean and how are they used? 0answers 22 views ### How to compute inner product of Wavelet transform convoluted with signal I have two datasets X_1 and X_2 in a sparse wavelet basis, and I have two filters f_1 and f_2. I’d like to compute the inner product of the convolutions\langle X_1 \star f_1, X_2 \star f_2\...
I am wondering how and if it is possible to define a Fourier transform or Wavelet transform on DNA sequences which are basically arrays with the values $\{T,C,G,A\}$ in them. I have found a paper ...