Questions tagged [wavelet]

A wavelet denotes a wave-like, generally localized, oscillating function, equipped with certain relationships across scales. A wavelet transformation describes a representation of data, decomposed onto a set of different wavelet functions, often forming a basis or a frame.

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A Comparison of pywt for Python and wavelets for R: Discrete Wavelet Transform

Let us consider a signal assumed as in the paper by Rosso et al., i.e. given by the sampled values $S=\left\{s_0(n), n=1, \ldots, M\right\}$, corresponding to a uniform time grid with sampling time $...
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Can you decompose a wave approximately?

I have data which looks like composition of sine waves. I need to decompose it to fewest possible sine waves that would give me tolerable error. The picture is of a half-period. Each half-period ...
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Is it possible to define the wavelet phase difference for only one signal?

The wavelet phase difference between two signals $x(t)$ and $y(t)$ is derived using the real and the imaginary part of cross wavelet transform $W_{x,y}$. (Let us consider e.g. the Morlet wavelet as ...
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Discrete wavelet transform - DWT (beginner)

I recently stumbled upon this article. In the paper they use DWT and I am having trouble understanding how to construct them. Does anyone have a guide on where to start learning wavelets and slowly ...
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Why is coherence of this wavelet transform almost always near 1?

I'm trying to understand the different aspects of a wavelet transform. Wavelet power has made enough sense to me as an analogy of the covariance. However, the wavelet coherence does not make sense to ...
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How to use discrete wavelet transformation to decompose non-time series data

I want to decompose x from the ames housing data using discrete wavelet transform (dwt) and integrate it to a linear regression model lm() to predict the sale price Here is the code I used ...
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Why does the residual 1x1 conv in wavenet not have an activation?

I have been trying to implement a wavenet. From the papers and designs I have looked at on github I have come up with the following... ...
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How to get a measure for the average "frequency" for wave-like data that changes frequency constantly over time?

Sure I can measure the average amplitude, but I'm interested in trying to get a measure for the frequency given the list of amplitude values within a certain time frame. Any ideas? Maybe not even ...
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Are haar bases eigenfunctions for any kernel?

Are haar wavelet bases eigenfunctions for any kernel? If so, what Kernel is it, and how would we find the eigenvalues?
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Application of Wavelet Transform and Differencing on Time Series Data (to denoise and remove seasonal adjustment and other trends)

I am working on an LSTM model to predict time series data (stock prices) and I would like an opinion whether to denoise my data or not before feeding it into the model. According to Investopedia, ...
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Why is the Wavelet Transform not affected by non-stationarity of time series?

Here we read: Wavelet analysis overcomes the problems of non-stationarity in time series by performing a local time-scale decomposition of the signal, i.e., the estimation of its spectral ...
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I have brain wave data for different subects aka voltages recorded every X sec. How do I deal with different wave frequency between subjects?

Brain wave data is really just voltages recorded every certain number of seconds; this becomes a wave with a certain frequency. I want to use the voltages recorded every, say, 10s in a model; this is ...
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Fourier analysis to retrieve components of individual spectra

I have a basic, simple question, I am a physics student, and searching internet gives me a lot of signal processing theory but couldn't find this basic answer, which I plan to implement in my speech ...
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Estimating When A Time Series with Random Spikes Crosses a Threshold for the First Time

tl;dr Is there a way to estimate when a random spike in a time series would cross a threshold for the first time? The following is data of my performance in the game Super Hexagon, whose goal is to ...
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Techniques to apply Discrete Wavelet Transform (DWT) to denoise and predict time series

I just started playing with wavelets and have been using this library (https://github.com/rafat/wavelib) to further my understanding and see if 'denoising' the series at all possible levels is ...
GreekFire's user avatar
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Denoising technique for signal with beforehand known shape (linear and exponential)

I have a noisy signal which is linear and then exponential. I know the type (Gaussian additive noise) and degree (0.01) of noise. Part of the challenge is determining when the signal changed from ...
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How to use the data that you get from a Discrete Wavelet Transform pwyt?

Im using the pywt (PyWavelets) python library to remove the Gaussian Noise from a timeseries dataset. b is a python list of timeseries values like this, [33.33, 34.23, 35.65...] (cA, cD) = pywt.dwt(...
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Comparing wavelets with unequal lengths

I have a bunch of time varying data stored as arrays with 0 and 1 in them, like this: ...
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Get the amplitude of the components of a periodic signal from Fourier (FFT)/Wavelets analysis

I have a signal looking approximatively as the one in the first subplot below (*), and I would like to: extract the periods of the main components of the signal; associate an amplitude to these ...
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Why is the Haar wavelet providing better frequency discrimination than alternatives?

I'm using PyWavelets (aka "pywt") to understand the discrete wavelet transform, and I'm trying to construct a crude power spectrum of a sinusoidal time series with frequency components of 1/8 and 1/32....
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Difference between scale-space transform and wavelet transform

What is actual difference between scale-space and wavelet transform? It seems that wavelets require an orthonormal basis of kernels, whereas scale-space does not. Is it the only difference? Can scale-...
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Wavelet transform in the discrete domain

I quote a part of the 5.9.1 section from "The Elements of Statistical Learning" book as the following: "Notice that since these spaces are orthogonal, all the basis function are orthonormal. In ...
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Discrete wavelet transform to detect saturation point of start and end

can someone help me to detect the saturation point using wavelet transform which contain 2 waveform signal. I don't know the correct step to detect the saturation point of distorted waveform and I ...
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Wavelet-domain Gaussian processes: what is the covariance?

I've been reading Maraun et al, "Nonstationary Gaussian processes in wavelet domain: Synthesis, estimation, and significant testing" (2007) which defines a class of non-stationary GPs that ...
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Phase shifting a signal [closed]

I have a signal of the form $s(t)=A(t) \sum cos(\omega_i(t)t +\phi_0) + n(t)$, where $n$ is gaussian noise. Now I want to phase shift this to $A(t) \sum cos(\omega_i(t)t)$ and I am at a loss on how ...
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Interpretation of diagonal detail for a 2D (Haar) Wavelet Transform

I am a statistics grad student, and I have just began exploring the topic of wavelet regression (specifically, Haar wavelets for discrete functions). I understand the generalization from a one ...
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time-series analysis Vs statistical signal processing

Is there a way to identify when to use time series analysis or signal processing. Time series data analysis can be divided to signal processing and normal time series analysis. In signal processing ...
swapna sourav rout's user avatar
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Quantifying Change in a Histogram Valued Timeseries

I'm attempting to do binary classification where my raw features are collections of histograms that are recorded in a time series. These histograms are scaled to sum to 1. To be more precise and ...
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Creating classification features from wavelet transformed time series

I'm interested in using a wavelet transform, Haar for example, to create classification variables from time series data to use in logistic regression. Simple example. Let's say I'm trying to predict ...
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Detection of periodic patterns using DWT

Is it possible to detect a periodic pattern in a time series using discrete Wavelet Transform? Is there any package in R to do this job?
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time series dimensionality reduction

I have a call center data (such as one below) that has call data collected every 15 minutes. For a day the periodicity is 96 and for a week the periodicity is (7 x 96 = 672). If I would like to ...
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2 votes
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Finding similarities using Wavelet transform

I have a time serie and I want to find similarities in it. For the first step I have calculated Haar-wavelet coefficients for this time serie, and now I don't know exactly how should I continue ...
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2 answers
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Detrending & cross-correlation function

I am looking for some help with my time-series data. What is the best method of detrending/transformation of these two variables, so I do not violate assumptions of stationarity when applying a cross ...
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Classification of signals, and Wavelet Transform based denoising [closed]

Stationary Wavelet Transform based denoising methods are considered the best because of their translational invariance. On the other hand, Matlab promises SWT based denoising but in the ddencmp ...
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2 votes
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Wavelets and machine learning

I am trying to learn features from a signal using Wavelet transform and then apply ML techniques on it to classify a signal. The problem I am facing is that, at each of level of decomposition, my ...
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3 votes
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Unbalanced Haar Wavelets and R package unbalhaar

I have found the article by Fryzlewicz (2007) and his R package unbalhaar. I do not understand well the outputs of his functions and in particular of the ...
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Clustering time series with wavelets in R

Can discrete wavelet trasform be used for feature extraction from time series in order to cluster them? Any R code how to do this will be appreciated.
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On the use of the periodogram of a time series

I have a time series of hourly measurements for a duration of one year: time <- 1:(365*24)/24 set.seed(1) x <- rnorm(length(time)) The measurements are ...
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5 votes
1 answer
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Finding the instantaneous period of a signal (or calculating period degradation)

I have a signal, of varying amplitude, and after a certain point in time, I expect to see the period of this signal lengthen. I am looking for a way to measure the lengthening of this period. Is this ...
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Wavelet smoothing at different scales

I would like to perform wavelet smoothing at different scales in R. I got the idea from this figure (panel A) were they measure the density/intensity of a particular signal at different scales. Here ...
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3 votes
2 answers
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Compressing data using wavelets with R

I'm trying to compress data using wavelets and I wanted to do it with R. Could anyone tell me if there is such a tool? Thanks in advance.
Bernardo Mendoza's user avatar
2 votes
1 answer
1k views

Frequency range of wavelet packets decomposition at each level

I measured turbulent velocity in 1Hz sampling rate. To remove fluctuations with T>900 sec I decompose the time series by wavelet packets, problem is that I don't know which levels should be kept and ...
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1 answer
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Frequency of a wavelet filter

Assume that I have decomposed a data set using Symlet Wavelet with six levels. How can I estimate the approximate frequency interval of each level? That would be great if you consider your answer in ...
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How to denoise a "Poissonous" time series

I have $N$ time series each of which can be modeled as $$y_{kt}=Ax_{kt}+b+\varepsilon_{kt}\quad(1\le k\le N,1\le t\le T),$$ where $x_{kt}\sim\text{Pois}(\lambda\Delta t)$ and $\varepsilon_{kt}\sim N(0,...
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3 votes
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Wavelet analysis of EEG

I want to do a time-frequency analysis of an EEG signal. I found the GSL wavelet function for computing wavelet coefficients. How can I extract actual frequency bands (e.g. 8 - 12 Hz) from that ...
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9 votes
1 answer
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Boundary effect in a wavelet multi resolution analysis

What are the methods to minimize the effect of boundaries in a wavelet decomposition? I use R and the package waveslim. I have found for instance the function ...
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4 votes
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Wavelet analysis, scaling filter: where does the square root of 2 go to?

In their great book "Wavelet methods for time series analysis" (2006), Percival & Walden state on p. 83 that the first-round pyramid algorithm scaling filter coefficients $\tilde{V}_{i,t}...
Alexander's user avatar
2 votes
1 answer
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Wavelet auto correlation

I have a time serie that I want to analyse through a wavelet decomposition. I am using the R package WaveThres. I am interested in the wavelet autocorrelation, but I struggle to understand what ...
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27 votes
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Application of wavelets to time-series-based anomaly detection algorithms

I've been beginning to work my way through Statistical Data Mining Tutorials by Andrew Moore (highly recommended for anyone else first venturing into this field). I started by reading this extremely ...
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What is the difference between functional data analysis and high dimensional data analysis

There are a lot of references in the statistic literature to "functional data" (i.e. data that are curves), and in parallel, to "high dimensional data" (i.e. when data are high dimensional vectors). ...
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