# 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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9 views

### Signal/Wavelet Clustering

Problem Setting In an experiment: I have 3 signal sources and 10 sensors each generating wavelets as time goes by. The distances from each source to sensors change from experiment to experiment. ...
156 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 ...
235 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 ...
28 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 ...
237 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 ...
774 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(...
46 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: ...
752 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 ...
129 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....
630 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-...
65 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 ...
42 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 ...
659 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 ...
165 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 ...
125 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 ...
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 ...
294 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 ...
262 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 ...
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 ...
834 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?
5k 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 ...
125 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 ...
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 ...
255 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 ...
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 ...
357 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 ...
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.
408 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 ...
1k 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 ...
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 ...
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.
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 ...
276 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 ...
312 views

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 ...