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# Questions tagged [discrete-wavelet-transform]

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141 views

### Wavelet basis orthonormality

I recently started learning about wavelet transforms, and there's something that is confusing me. My understanding was that most wavelet decompositions are simply a decomposition of a given signal in ...
36 views

### Laplace Transform and Inverse laplace Transform for 2D images python code available?

I am wondering if there is any implementation of Laplace Transform and Inverse Laplace Transform available for 2D data (i.e., images). For example, a batch of N ...
• 163
1 vote
55 views

### Correlation Matrix Problem of Three Decomposition Level of DWT

I'm trying to apply a DWT with 3 composition levels and the following question arose when calculating the composition matrix. The step I'm trying to follow is: The DWT coefficientes are obtained from ...
23 views

### Identify variation patterns in image time series

I am working on time series of 12 remote sensing images obtained at irregular intervals. The pixels of all images are of exact same region. Pixels of some areas in these images vary in time with ...
1 vote
14 views

### Avoiding latency distortion at high denoise levels with DWT

I am denoising biological signals using the DWT, and for UI reasons would prefer the smoother waveform afforded by denoise level 5. However, higher denoise levels seem to distort the latency of ...
• 133
142 views

### How to fit a rectangular wave to a signal?

I have some binary data that mostly comes under the form of a rectangular signal. In order to "idealize" my signal I would like to fit a rectangular wave that best represent my signal (Here ...
• 507
1 vote
49 views

### Does filtering by wavelet decomposition and reconstruction introduce a phase shift in the filtered signal?

I am removing low frequency noise from a signal using Matlab using the DWT and then reconstruction at a specific level: I am removing the approximation signal at level 10 which approximates the low ...
• 11
80 views

### Integrating over the translation on a DWT

I'm really a begginer at Wavelet transform and I'm starting to use the pywt module. I have some difficulties understanding the link between the following integral and the coefficients of the DWT:  W(...
1 vote
150 views

### Why are analytical wavelets said to have no negative frequency?

I have been reading about analytical wavelets and came across this definition: An analytic wavelet is a complex wavelet such that its Fourier transform is null for negative frequency. If it is a ...
38 views

### How can we prove using matlab that after each level of decomposition of a signal using DWT the frequency content is halved?

I was trying to decompose an EMG signal, which was sampled at 200 Hz, into 7 levels of decomposition using DWT. And the result is shown in the figure( only up to level 3 is shown here) However, I ...
131 views

### How to compute the frequency bands corresponding to the scale level in Discrete wavelet transform

I am using MATLAB's built-in function to compute maximal overlap discrete wavelet transform (modwt)and want to know the frequency bands at each scale level. I am ...
• 19
35 views

### Relation between discrete wavelet transform and filter banks

I have approached wavelet transformation from a projection perspective. Specifically, we can show for a certain class of functions (in the continuous setting) that they can be written in terms of a ...
163 views

### Inverse of wavelet transform modulus gives poor results

I just want to understand, why is the result of my wavelet(?) transform so bad. For $0\le i< k$, where I set $k$ to $10$, I split the signal in blocks of length $s_i:=2^{i+2}$, overlapping by $s/2$...
• 151
1 vote
28 views

### undecimated wavelet transformation

I have 20kHz sampled dc current data of 3 second (i.e signal length of 60000). I want to use undecimated wavelet transform to extract statistical features from it. But i don't know how to choose best ...
59 views

### Best 'SNR-like' detection statistic for time series signal in the wavelet domain?

What is the best way to define a detection statistic for a time series event trigger generator, which computes the wavelet transform of some time series data? I want such quantity to be similar to a ...
• 31
1 vote
184 views

### Limited cross-correlation for multiple signals

I have $N$ signals, each of length $\tau$, with $N\ll \tau$, eg. $\tau=10^8$ samples and $N=100$. I want the $r=10$ first components of all pairwise cross-correlation for the $N$ signals. The naive ...
1 vote
51 views

### Discrete Wavelet Transform With Overlaps

Maybe this is a trivial question, but I couldn't find an answer yet. Is there some discrete wavelet transformation which works with overlapping wavelets (half on half)? In other words, is there some ...
• 151
97 views

### How to get frequency axsis from pythnon CWT

I did the cwt on a chirp signal : ...
257 views

### Estimate Power spectral density using Discrete wavelet transform form pycwt

I want to estimate the Power spectral density using Discrete wavelet transform and a Morlet Wavelet. Bellow you can find the function I am using. Any comments or suggestions on wether or not the ...
• 179
258 views

### Practical applications of wavelets

I know wavelets were all the rage a few years ago, but I missed that boat and am wondering if it is worth putting significant effort into learning about them. My impression is that they were a little ...
• 1,797
75 views

### Discrete wavelet transform - DWT (beginner)

I recently stumbled upon this article: A wavelet-based multivariate multi scale approach for forecasting (PDF) In the paper they use DWT and I am having trouble understanding how to construct them. ...
• 101
85 views

### Estimation of scaling exponent in the wavelet leaders multi-fractal formalism

I am trying to extract multi-fractal features from time-series data by estimating the singularity spectrum using the wavelet leaders multi-fractal formalism (WLMF) method. Specifically, I want to be ...
• 121
53 views

### Adjust Wavelet output to CNN

I want to extract features from the signal using DWT and then feed the results into CNN, after calling the 'dwt' library function I got a runtime error. ...
• 11
1 vote
978 views

### The downsampling step with discrete wavelet transform

For one stage discrete wavelet transform (DWT), if we have a signal with 1000 samples occupying the frequency range from zero to 500 Hz, the output of the low-pass filter is a signal with frequency ...
• 349
1 vote
111 views

### Discrete wavelet decomposition over detail coefficients

per my understanding, if we take a 3-level discrete wavelet decomposition (DWT) over a 1-D signal with sampling rate $F_s$, we will get a series of detail and approximation coefficients, ex: [cA3, cD3,...
• 13
390 views

• 11
1 vote
53 views

### 1D Interpolating subdivision for wavelet lifting schemes

I am looking into wavelet lifting methods first introduced by Swelden, and explained in this paper: Build your own wavelets at home. In this paper (in chapter 2 specifically), they discuss ...
1 vote
142 views

### Polyphase Filter Implementation for oversampled (undecimated) wavelet lifting scheme?

I am learning about lifting schemes, and for my project, it seems as though it would be beneficial to use an undecimated wavelet transform (UWT). I have found a paper by Lee, Lee, and Yoo (New lifting ...
1 vote
327 views

### How to do appcoef and detcoef using pyWavelets?

I am new to signal processing and currently doing a school project in wavelet transform using Python. I want to extract all details and approximations (Example: cA2, cA1, cD2, cD1), pywt could return ...
• 11
1 vote
148 views

### Should i use window with hop_size in Wavelet Transform or Discrete Wavelet Transform?

I have a signal (audio - voice) with 1 second of duration with sample rate of 50000 Hz. It is big signal and I wish extract some features and apply pattern recognition or classification. My question ...
709 views

### How could I do a Discrete Fourier Transform in Python if my data is non uniform?

I have been trying to find a way to transform my time series data in an equivalent manner to the discrete Fourier transform. What I wish to find is something like: ...
• 21
1 vote
275 views

### 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/...
• 35
4k 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 ...
• 124
286 views

### Extract signals with certain frequenceis from a data sample using python

I did not major in signal processing, and I do not know a lot about some possibly very basic facts, so although SE has some questions related to this, I still have some confusion. I am given a data ...
• 1
809 views

### 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?
• 149
1 vote
160 views

### How to find the Wavelet measurement matrix in compressed sensing?

Assume that an image vector x = Ψs. s is a sparse vector in which the image vector x of length N x 1 is sparse in the wavelet Ψ basis. I have issue in finding the measurement matrix A= φ Ψ where φ is ...
• 61
1 vote
396 views

### Waveform pattern detection in time series

I have some IMU data which I am using to detect activity patterns - walking, running etc. In order to differentiate one activity from another I need to do pattern matching in time series. Different ...
1 vote
267 views

### 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 ...
1 vote
1k views

### 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 ...
68 views

### 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 ...
• 21
38 views

### What does the sample entropy of a digital signal mean?

What sample entropy signifies about a signal and how it used to analyse a signal?
1 vote
393 views

### 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 ...
• 11
1 vote