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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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
$$
\begin{align}
\sigma_{ts}^2 &= \int_{-\infty}^{\infty} (t - u)^2 |\psi_{u, s}(t)|^2 dt
= s^2 \sigma_t^...
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1answer
59 views
Energy normalization across wavelet subbands
According to the following reference: A Really Friendly Guide to Wavelets, © C. Valens, 1999
Equation 3, the wavelets are generated from the mother wavelet by scaling and translation. S is the scaling ...
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27 views
Coefficient meaning in DWT
I understand that approximate and detail coefficient represent the different signal bands. But what do the values mean and how are they used?
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14 views
How to compute inner product of Wavelet transform convoluted with signal
I have two datasets $X_1$ and $X_2$ in a sparse wavelet basis, and I have two filters $f_1$ and $f_2$. I’d like to compute the inner product of the convolutions $$\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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20 views
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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2answers
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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1answer
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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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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1answer
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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1answer
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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1answer
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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1answer
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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1answer
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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1answer
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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3answers
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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2answers
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
$$
\...
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2answers
81 views
Multiple peaks in a same signal?
I am working on peak detection in different signals, the signal plot looks like this:
After applying peak detection algorithm and tuning it for each signal, final output looks like this:
As you can ...
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1answer
78 views
CWT at low scales: PyWavelets vs Scipy
Low scales are arguably the most challenging to implement due to limitations in discretized representations. Detailed comparison here; the principal difference is in how the two handle wavelets at ...
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39 views
Wavelet denoising. Simple explanation
I am studying wavelet transform. In the matlab in the "wavemenu" package, I use "SWT denoising 1-D". I loaded my signal, performed a Haar 5 wavelet squelch. I got a good result.
I ...
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1answer
68 views
How to test wavelet transforms?
One pertinent attribute is normalization, which measures performance in describing signal spectral amplitude and energy, like here. Others are robustness to noise, time vs frequency resolution. ...
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1answer
174 views
PyWavelets CWT: normalization? Vs Scipy?
Related. The equation being implemented normalizes by sqrt(1 / scale):
$$
C_{a, b} = \frac{1}{\sqrt{a}} \sum_k s(k)\left( \int_{-\infty}^{k+1} \overline{\psi \left(\...
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1answer
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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1answer
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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17 views
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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27 views
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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1answer
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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3answers
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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35 views
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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14 views
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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28 views
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 ...
