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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103 views

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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83 views

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 ...
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25 views

Wavelet smoothing or regression with scattered data

Suppose we have a data set $\{x_i, y_i\}_i$ where $x_i$ is a multi-dimensional tuple and scattered (not on a equally spaced regular lattice). How does one regress or smooth such a scattered data set ...
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208 views

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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666 views

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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44 views

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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656 views

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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125 views

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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569 views

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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63 views

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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37 views

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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596 views

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 can be ...
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160 views

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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110 views

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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2k views

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 ...
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289 views

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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258 views

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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79 views

Computing directly comparable wavelet features on variable-length training examples

Consider a classification problem in which the raw data are snippets of a larger 1-D time series signal. In my application, the signal is the response of a motion sensor as a function of time (the raw ...
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815 views

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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4k views

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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1answer
117 views

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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2answers
2k views

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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254 views

Classification of signals, and Wavelet Transform based denoising

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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1answer
2k views

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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1answer
353 views

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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2answers
3k views

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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393 views

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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988 views

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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1answer
1k views

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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2answers
1k views

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.
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1answer
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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273 views

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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289 views

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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553 views

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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889 views

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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189 views

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 $\tilde{V}_{i,t}$ can ...
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1answer
1k views

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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3answers
10k views

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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2k views

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). ...