Questions tagged [wavelet]

A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero.

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31 views

Check vanishing moment property of db4 wavelets

I am reading the book "a primer on wavelets and their scientific applications" by James S. Walker. In chapter 3, Property I on page 46 says that if a signal $f$ is linear, then the $k$-level ...
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50 views

Fejer korovkin discrete wavelet transforn? what is this? [closed]

I have been searching all night about Fejer-Korovkin in wavelet decomposition and all I got just some people doing research using it, cant even finding any page, site or pdf that explain how this type ...
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32 views

energy normalization across different scales in case of discrete wavelet transform

In case of continuous wavelet transform (CWT), the wavelets are generated from the mother wavelet by scaling and translation. To achieve energy normalization and to ensure that all wavelets have the ...
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24 views

Why the inverse discrete fourier transform of the Ricker pulse isn't the same as the Ricker pulse in time domain?

Question I'm trying to use Python's scipy library to compute the IDFT of the Ricker wavelet function and compare it with the analytical time-domain version of the same function. When I compare the ...
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27 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 ...
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12 views

Plot frequency tiling wavelets/curvelets

Is there a convinient way to plot the frequency tiling of for wavelets/curvelets? For example the input would be the number of scales $j$ and the output would be something like this: Preferably in ...
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82 views

How is wavelet time & frequency resolution computed?

Mallat gives analytic wavelet time & frequency widths/uncertainties as $$ \begin{align} \sigma_{ts}^2 &= \int_{-\infty}^{\infty} (t - u)^2 |\psi_{u, s}(t)|^2 dt = s^2 \sigma_t^...
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59 views

Energy normalization across wavelet subbands

According to the following reference: A Really Friendly Guide to Wavelets, © C. Valens, 1999 Equation 3, the wavelets are generated from the mother wavelet by scaling and translation. S is the scaling ...
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27 views

Coefficient meaning in DWT

I understand that approximate and detail coefficient represent the different signal bands. But what do the values mean and how are they used?
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14 views

How to compute inner product of Wavelet transform convoluted with signal

I have two datasets $X_1$ and $X_2$ in a sparse wavelet basis, and I have two filters $f_1$ and $f_2$. I’d like to compute the inner product of the convolutions $$\langle X_1 \star f_1, X_2 \star f_2\...
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55 views

Is there a systematic method for converting an even length FIR filter to odd length?

I'm currently implementing a discrete wavelet transform (DWT) as a cascaded QMF filter bank (pictured below). I've put together a convolution function that attempts to filter an input signal in a non-...
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71 views

Is it possible to define Fourier or wavelet transforms on DNA sequences?

I am wondering how and if it is possible to define a Fourier transform or Wavelet transform on DNA sequences which are basically arrays with the values $\{T,C,G,A\}$ in them. I have found a paper ...
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How to take wavelet transform of sparse input data

I have a sparse dataset indexed by nanoseconds. Storing the dataset in a discrete fashion would take too much memory. I'd like to take a wavelet transform and I'd like it to be relatively fast. The ...
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460 views

Synchrosqueezing Wavelet Transform explanation?

How does Synchrosqueezing Wavelet Transform work, intuitively? What does the "synchrosqueezed" part do, and how is it different from simply the (continuous) Wavelet Transform?
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29 views

Does the Fast Wavelet Transform produce the same coefficient as the Discrete Wavelet Transform?

Does the Fast Wavelet Transform(FWT) produce the same coefficients as the Discrete Wavelet Transform(DWT) if configured for the same depths? Or is the the FWT just an approximation of the DWT?
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48 views

What mother wavelet should be chosen as an alternative to the STFT?

The Short Time Fourier Transform (STFT) is used to identify time localized frequency content of a signal. The STFT operates by chunking an input signal into blocks and performing FFT on the block, and ...
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26 views

One integral inverse CWT

MATLAB's icwt docs state inversion to be done by a single integral: $$ f(t) = 2 \Re e\left\{ \frac{1}{C_{\psi, \delta}} \int_0^\infty \left< f(t), \psi(t) \right> \frac{da}{a} \tag{1} \...
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42 views

What should the time-shift be when implementing a continuous wavelet transform on a computer?

I'm currently researching implementation methods of the Continuous Wavelet Transform(CWT). On paper, the CWT produces infinitely many outputs on a finite signal since the scaling and shifting ...
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52 views

Where is the mother wavelet defined in the Fast Wavelet Transform?

Referring to the Fast Wavelet Transform, this transform is implemented as a QMF filter bank. This algorithm consists of high/low pass filtering and subsampling. However, a wavelet transform is ...
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22 views

Why are the Continuous Wavelet Transforms of the same signal drastically different?

I'm currently studying wavelets and am running into confusion with regards to CWT coefficients. Ideally, I want a CWT algorithm that produces outputs similar to that of a STFT - i.e. produces ...
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28 views

Reverse biorthogonal 2.2 wavelet inverse DWT implementation

I have some image data that are - supposedly - transformed using the MATLAB’s 5/3 Le Gall integer lifting wavelet transformation. The actual Matlab code that does the inverse DWT calls the following ...
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42 views

Understanding noise removal method using wavelets

I am trying to understand how wavelet transform can be used to denoise a time series or signal and how to plot the scalogram image. My signal has a lot of fluctuations and as such I am finding it ...
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68 views

Are Fast Wavelet Transform coefficients constant if the input signal frequency coefficients are constant?

I'm currently studying the Fast Wavelet Transform. As I currently understand, the Fast Wavelet Transform is implemented as a QMF filter bank where the frequency resolution decreases as the signal is ...
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53 views

Inverse Continuous Wavelet Transform derivation?

Wiki writes iCWT as $$ f(t) = C_{\psi}^{-1} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} W_f(a,b) \frac{1}{|a|^{1/2}} \tilde\psi \left(\frac{t - b}{a}\right) db \frac{da}{a^2}, \tag{1} $$ where $\...
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29 views

Log derivative interpretation

In the origin paper on Synchrosqueezing Wavelet Transform, the phase transform, used to extract the instantaneous frequency of a signal $f(t)$, is defined as $$ \omega (a, b) = -j[W_\psi f(a, b)]^{-1} ...
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86 views

Unclear time-to-frequency integration step

From here; $\hat f=\mathcal{F}(f)$, bar = complex conjugate: Time-shift property: $x(t-b) \Leftrightarrow e^{-j\omega b}{\bf X} (\omega)$, so why is it $+$ (red)? What at all is happening? Looks like ...
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100 views

Suitable signal processing techniques for frequency response functions?

Good day everyone I have recorded experimental frequency response functions (frfs) for a loose bolt monitoring project. Please see figure 1 below for an example of the frf. Figure 1 The purpose of my ...
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57 views

How is wavelet center frequency computed?

PyWavelets (1) takes index of max DFT magnitude, (2) adds 1 to it, (3) divides by domain, which is the range of input values to the wavelet ("support"). ...
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123 views

Alternative convolution theorem?

Instead of padding $x_1[n]$ and $x_2[n]$ then taking $$ \text{iDFT}(\text{DFT}(x_1[n])\cdot\text{DFT}(x_2[n])), \tag{1} $$ assuming we know $x_1(t)$ and $x_2(t)$, and their FT's, what if we do $$ \...
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81 views

Multiple peaks in a same signal?

I am working on peak detection in different signals, the signal plot looks like this: After applying peak detection algorithm and tuning it for each signal, final output looks like this: As you can ...
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78 views

CWT at low scales: PyWavelets vs Scipy

Low scales are arguably the most challenging to implement due to limitations in discretized representations. Detailed comparison here; the principal difference is in how the two handle wavelets at ...
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Wavelet denoising. Simple explanation

I am studying wavelet transform. In the matlab in the "wavemenu" package, I use "SWT denoising 1-D". I loaded my signal, performed a Haar 5 wavelet squelch. I got a good result. I ...
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68 views

How to test wavelet transforms?

One pertinent attribute is normalization, which measures performance in describing signal spectral amplitude and energy, like here. Others are robustness to noise, time vs frequency resolution. ...
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174 views

PyWavelets CWT: normalization? Vs Scipy?

Related. The equation being implemented normalizes by sqrt(1 / scale): $$ C_{a, b} = \frac{1}{\sqrt{a}} \sum_k s(k)\left( \int_{-\infty}^{k+1} \overline{\psi \left(\...
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27 views

PyWavelets CWT: resampling vs recomputing wavelet

Related. The implementation pre-integrates a wavelet once, and resamples it at each scale, finally differencing to implement ...
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112 views

PyWavelets CWT implementation

I seek to understand PyWavelets' implementation of the Continuous Wavelet Transform, and how it compares to the more 'basic' version I've coded and provided here. In particular: How is integrated ...
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52 views

Decompose a Morlet wavelet in a sine wave to its gaussian and sine components

I have a sine wave where there is a morlet wavelet inside: Now, first I'd like to decompose my signal (func) to 2 components which are the sine wave and the wavelet. After this, I'd like to decompose ...
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How can a thresholding method in discrete wavelet transform be adaptive and denoising is performed level independent?

I am a bit confused regarding the thresholding methods and noise estimation options found in Matlab regarding Discrete Wavelet Transform. Please correct me if I am wrong. I am understanding that noise ...
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26 views

Is convolving a signal by a wavelet (in time domain) equivalent to wavelet filtering?

I am a noob in signal processing. Please help me understand if the following relation is true or not: ...
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59 views

What does voices per octave means?

I was studying the description of continuous wavelet transform in Matlab and I came across this term '**cwt uses 10 voices per octave**' ...
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22 views

Morlet wavelet: DFT vs Fourier Transform

I find what seem to be contradictions between the two. "Morlet" defined here, and its Fourier Transform (FT) below it. DFT's imaginary component zeroes with large ...
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21 views

Fbank back to wav

Here's my problem. I have some wav files. I use the wavs as input to compute the fbanks. Then I want to do some stuff with the fbanks and then I want to recreate a wav file associated to the new fbank....
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What are the wavelet packet functions and how are they different from the wavelet and scaling functions?

I understand that in the decomposition process, wavelet and scaling functions are used to split the signal to approximation and detail coefficients. Most of the time I saw the wavelet and scaling ...
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65 views

EEG signal processing with wavelet or fft?

I have confusion about signal processing related with EEG signal. I have done some of my research and that made me more confused about processing and filtering the signal. Let me jump into the problem ...
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83 views

Why does MATLAB's dualtree3 function not return the lowpass subband of the imaginary tree?

MATLAB has a function named dualtree3 which computes 3-D dual-tree complex wavelet transform. This function only retains the last low-pass coefficients/subband of ...
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Energy of coefficients of wavelet decomposition?

I have recently been working with a dataset associated with the paper Human Activity Recognition from Accelerometer Data Using a Wearable Device. In Section 3.1 - Feature Selection for Motion Data, ...
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Why should wavelet re-synthesis produce an output when the main component is suppressed and what does this mean for denoising?

I understand that aliasing occurs in DWPT if the wavelet used is of low order since the "filters" are not perfect and the combination of down sampling and overlapping between bands causes ...
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19 views

Discrete wavelet center frequency

I am understanding that mother wavelets have a center frequency. Wavelets are limited in duration and oscillate then decay, so the center frequency is the mid pulse of the wavelet or so. But my ...
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How well can discrete wavelet packet transform reduce noises that are similar to the input signal in the same frequency band?

If I had 50Hz noise coming from power line, and signals in the same frequency range (EEG for example 0.1Hz to 100Hz). If my sampling frequency is 30kHz but I downsample my signal to 937kHz and use the ...
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Best way to measure effectiveness of discrete wavelet denoising?

I am using matlab wavelet toolbox to denoise physiological signals, I am plotting the denoised signal on top of the original noisy signal and making sure spikes were not removed as a measure of ...

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