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.

Filter by
Sorted by
Tagged with
0
votes
1answer
15 views

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 ...
0
votes
0answers
12 views

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 ...
0
votes
0answers
18 views

Difference between dynamic time warping, windowed cross-correlation and wavelet coherence?

I have video data with people talking with each other and I'm planning to analyse patterns of their head movements and facial expressions. I'm not very advanced in terms of statistics, so could you ...
0
votes
0answers
15 views

How to compare/ quantify how similarity between wave patterns

I have an idealized wave pattern, and I'm trying to come up with a measure to compare how similar other wave patterns are to it. I'm more concerned with the overall shape and timing of a wave as ...
0
votes
0answers
51 views

Calculate similarity between two time series using discrete wavelet transform cofficients

I am new to the field of signal processing but I have read that DWT can be used to find similarity between two time series, I am curious as to what kind of similarity measure do we use once we have ...
0
votes
0answers
8 views

How to understand the statistical noise level of wavelet bicoherence?

Wavelet bicoherence was given by Van Milligen1995, which used to analyze turbulence. And the normalized squared wavelet bicoherence (usually called wavelet bicoherence) is shown below. $$ WBC(a_1,a_2)=...
2
votes
1answer
97 views

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... ...
0
votes
0answers
14 views

Questions about orthogonality of wavelets and other time-frequency representations

Context After some time seeking more understanding about the properties of orthogonal wavelets, this presentation by Stéphane Mallat helped me understand the truly revolutionary breakthrough that ...
0
votes
0answers
29 views

Cross Wavelet vs Wavelet Coherence in Financial Time Series Analysis

I like to know the intuitive difference between Cross Wavelet vs Wavelet Coherence in any Financial Time Series correlation Analysis. Also, like to know what is the difference between cross-...
1
vote
1answer
23 views

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 ...
1
vote
0answers
16 views

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?
2
votes
0answers
54 views

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, ...
1
vote
2answers
272 views

Why Wavelet Transform is 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 ...
0
votes
0answers
12 views

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 ...
0
votes
1answer
24 views

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 ...
1
vote
1answer
1k 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 ...
2
votes
0answers
784 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 ...
0
votes
0answers
41 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 ...
1
vote
1answer
339 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 ...
2
votes
1answer
1k 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(...
1
vote
0answers
52 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: ...
1
vote
0answers
929 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 ...
1
vote
0answers
146 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....
2
votes
2answers
810 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-...
0
votes
1answer
73 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 ...
1
vote
0answers
47 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 ...
25
votes
1answer
904 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 ...
0
votes
1answer
172 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 ...
1
vote
0answers
165 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 ...
4
votes
1answer
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 ...
0
votes
1answer
356 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 ...
1
vote
0answers
278 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 ...
1
vote
0answers
82 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 ...
1
vote
1answer
853 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?
8
votes
2answers
9k 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 ...
2
votes
1answer
155 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 ...
2
votes
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 ...
1
vote
0answers
257 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 ...
1
vote
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 ...
2
votes
1answer
362 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 ...
1
vote
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.
1
vote
0answers
425 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 ...
5
votes
1answer
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 ...
4
votes
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 ...
3
votes
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.
2
votes
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 ...
2
votes
1answer
287 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 ...
6
votes
0answers
341 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,...
2
votes
1answer
592 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 ...
9
votes
1answer
1k 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 ...