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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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1answer
786 views

Bandpass filter using wavelet transform

I'm working on a speech recognition project. The first step of this project is to find phoneme in the speech signal. To do that, I found this paper that discusses about it. In the paper, wavelets are ...
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1answer
249 views

Haar Wavelets vs STFT for graceful audio quality degradation (newbie question)

I'm playing around with FFT (using Naudio library) and with Wavelets (using TarsosDSP library) trying to get better understanding of both of them. I've noticed that when I zero out FFT/Wavelet ...
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1answer
78 views

Energy Preserving Laplacian Pyramid

Both Discrete Wavelet Transform (DWT) and Undecimated DWT possess an important property of energy preservation: on each level $$\sum_i W_i^2 + \sum_j V_j^2 = \sum_k X_k^2$$ where $W$ and $V$ are ...
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1answer
285 views

Difference(relation?) between filter banks and wavelet decomposition

I'm implementing multirate system and met concepts of filter banks and polyphase decomposition of filters. While trying to understand them, I've found that they look very similar to wavelet ...
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1answer
707 views

Why do Dyadic filterbanks downsample the high pass signal portions?

I'm currently programming a dyadic filter bank and have a question. I notice in all of the visual representations: (from here (Dyadic Analysis Filter Bank)), the high pass filtered output for each ...
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1answer
35 views

How can I change parameters into a text string in MATLAB? [closed]

I am trying to compute the Morlet wavelet transform (cmor) of a signal, but I have to do it several times with different parameters Fb and Fc. Is there a way to automate it? For example, I have to do ...
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1answer
43 views

How can dilation of a wavelet function lead to its sign reversal? [closed]

I am studying wavelets and it has been given that $$ \psi_{a,b} = \frac{1}{\sqrt{|a|}} \psi \left(\frac{t-b}{a}\right) $$ now the function $$ \psi(t)= \begin{cases} 1,& \text{if } 0\leq ...
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1answer
167 views

Wavelet image denoising: dual-tree versus double-density

What is the main difference between the dual-tree DWT and the double density DWT image denoising techniques? How does the combination of them improve the quality of the denoised image?
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1answer
334 views

How to extract features from nonstationary signal using SVD (singular value decomposition)?

I am trying to extract features from a nonstationary signal (frequencies and time locations). For this purpose, I computed a wavelet transform (complex morlet) of the signal in MATLAB and obtained the ...
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1answer
293 views

Reconstruction of a signal using 1D discrete wavelet

There is a signal of $50\textrm{ Hz}$ and $120\textrm{ Hz}$ corrupted with noise. The sampling rate is $1000\textrm{ Hz}$. Here I used a 3-level DWT to extract this two components of the signal ...
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352 views

Differences between $\tt wentropy$ in MATLAB and entropy definition

MATLAB offer's a Shannon entropy calculation in its wavelet package: $$ H(X) = -\sum_{i=0}^{N-1} x_i^2\log(x_i^2) $$ I'm wondering what this formula means, since it has no relation with the ...
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1answer
637 views

MATLAB: Generating and Visualizing Mother Wavelet of different scale

In MATLAB, there is a function wavefun that outputs both the scaling and wavelet functions. To generate a Daubechies, the following command can be used: ...
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1answer
740 views

Obtaining normalized matrix for the Haar Wavelet Transform

I've been reading this article: http://aix1.uottawa.ca/~jkhoury/haar.htm which explains the Haar Wavelet Transform. At a certain point, the author says: ... Since the transformation matrix $W$ is ...
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1answer
85 views

Biorthogonal Wavelet Expansion

Consider a multiresolution analysis (MRA) $\{V_j\}$ in $L^2(\mathbb R)$ generated by the scaling function $\phi(x)$ and such that for each $j\in\mathbb Z$, $V_j\subset V_{j-1}$. For a given function $...
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1answer
121 views

Find the maximum frequency in the signal section?

I'm recording the received signal after sending a 20Khz signal. I make some rotations with hand before the device and get some variations in the signal.I obtain a very noisy signal and do some pre-...
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1answer
37 views

Testing for changes in auto-covariance

I am working with uniformly-spaced time series data where I am interested in knowing whether there are changes in temporal auto-covariance. The mean can be assumed constant. Visually, there are no ...
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2answers
353 views

Whether convolution followed by down sampling equals wavelet decomposition

I know that wavelet decomposition equals convolution followed by down sampling by two.I tried to test this on mat lab on haar wavelet. I write the below code and compared with the default wavedec ...
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2answers
134 views

Perfect reconstruction: what properties must the analysis LPF satisfy

I have been reading on conjugate quadrature filters (CQF). The linked article explains that, if we have a lowpassfilter $h_0$, we can create a set of filters for a perfect reconstruction filterbank. ...
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3answers
2k views

“Fourier Transform can localize signals in frequency domain, but not in time domain.” — What does it mean in layman's terms?

I was studying the introduction to wavelets and its benefit over the frequency domain. I said that: Fourier analysis can't localize signals both in time and frequency domain. Fourier analysis can ...
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1answer
148 views

Raw signal to short for DWT

The algorithm i use to apply a discrete wavelet transform only accept raw-data with a certain number of samples (2,4,8,..128..). I have to either interpolate the raw signal or padding it with zeros (...
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1answer
1k views

Wavelet transform 3D plot for CoP

I'm trying to perform wavelet transform and make a 3D plot like : With the wavelet transform function : $$ \textrm{CWT}_x^\psi (\tau, s)=\frac{1}{\sqrt{\lvert s\rvert}}\int x(t)\psi\left(\frac{t-\...
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3answers
592 views

How Are Images Considered Non Stationary Signal When They Are Invariant to Time?

I have read Wavelets are better than Fourier in dealing with non-stationary signals such as images, but I don't understand how images are considered stationary??
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Slow Down Music Playing While Maintaining Frequency

Playing a piece of music audio at a slower speed would lower its pitch (frequency). Is there a tool and theory to slow down the song playing while keep the frequency the same? I suppose one can do ...
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1answer
394 views

Multiplication in the wavelet domain, what does it look like in real space?

Say you wavelet transform a signal, multiply by some values, and untransform. Is there anything we can say about the effect in real space? I know that it's not exactly a convolution, because the ...
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0answers
43 views

DWT initialization from nonuniform samples

Let $D\subset\mathbb R$ be compact, let $f:\mathbb R\to\mathbb R$ be a contintinuous function with support $D$. Let $\phi(x)$ be a well-defined scaling function, in the sense that it generates a ...
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1answer
436 views

How to Map CWT to Synchrosqueezed wavelet transform?

I don't understand the mapping time-scale plane to the time-frequency plane in synchrosqueezed wavelet transform, i.e. $(3)$. You can find the paper here. For the given signal of $x(t)$ and mother ...
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1answer
985 views

Adaptive Piecewise Constant Approximation (APCA) with wavelets/DWT

I am trying to approximate a vector or a time series, in order to have as little changes as possible. To do so, I pretend to apply the Adaptive piecewise constant approximation (APCA) algorithm. ...
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1answer
165 views

DWT architecture using filter bank

I am studying this paper. In one of the figures in the paper (Fig 5.b and Fig 5.c) DWT architecture is given using db2 and filter bank. I don't understand how Lo_D and Hi_D have size half of input ...
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232 views

Transfer functions from wavelet transform

So I have this problem where I need to measure the phase of a signal and correct for a delay associated with the travel time of the signal while simultaneously determining the transfer function of my ...
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1answer
901 views

Wavelet transform in MATLAB

Suppose I have a wave with $20 \textrm{ kHz}$, $100 \textrm{ kHz}$ and $300 \textrm{ kHz}$. Sampling frequency used is $1000 \textrm{ kHz}$. I apply the discrete wavelet transform on the wave like <...
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0answers
407 views

What the difference between the family of Discrete Wavelet Transform?

When I useed Mathematica,If found many Transforms in the list of Discrete Wavelet Transforms. For example: discrete wavelet transform (DWT) stationary wavelet transform (SWT) lifting wavelet ...
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1answer
56 views

Wavelet Fidelity Filter (video compression)

I have read a specification of Dirac (video compression format). A key element of this format is the use of the discrete wavelet transform. Section 15.6.3 of the specification defines individual ...
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1answer
214 views

Subsampling property of wavelet transform

One of the properties I have seen for isotropic tight wavelet frames is $$\sum_{i\in\mathbb{Z}} \left|h(2^i\omega)\right|^2 = 1$$ where $h(\omega)$ is the frequency spectrum of the original wavelet. ...
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103 views

possibility of applying ridgelet transformation on signals

After converting a 1D signal to 2D using matlab code, can the ridgelet transform be applied? Is this transformation effective compared to wavelet?
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1answer
152 views

Code for a wavelet based hilbert transform? [closed]

I normally implement the Hilbert transform using the Fourier transform. I have noise related issues I want to solve. Does anybody have an (apodized) implementation of the Hilbert transform handy, ...
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2answers
140 views

Is it required to quantize wavelet coefficients before one derives features from?

I am using wavelet coefficients for feature extraction in classification problem. As the wavelet coefficient values are real, positive and negative, is it required to quantize them before feature ...
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1answer
355 views

Wavelet transform: How to compute the initial coefficients when only samples are available?

In standard MRA we have that the space of functions at scale J can be expressed as $$V_j = V_0\oplus \left(\bigoplus_{j=0}^{J} W_j\right)$$ where $V_0$ is spanned by the orthonormal system of the ...
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0answers
41 views

Example of radial frequency functions that give scale shiftability

Simoncelli's "Shiftable multi-scale transforms" paper talks about shiftability of the parameters of a wavelet transform, in particular translation, rotation and scale. The first two are used in his ...
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0answers
116 views

Are wavelets for audio spectrograms available as a simple FIR filter?

I have read that "Debauchies Wavelet is simply a short FIR" so i am searching for a single FIR that i can make into a filterbank, a precise "bandpass filter" that detects narrow frequencies, i.e. 1Hz ...
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1answer
105 views

Expanding piecewise polynomial using Daubechies wavelet

What is the best Daubechies wavelet (i.e. the number of vanishing moment) to expand a signal $\boldsymbol{x} \in \mathbb{R}^n$? $\boldsymbol{x}$ consists of $m$ pieces of polynomial with $d$ degree. ...
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1answer
176 views

How to implement a $j$-level $M$-band wavelet transform of an image?

I want to implement an $M$-band (or multi-band) wavelet transform, to be used for feature extraction on images. Is there a built-in Matlab function available? Do I have to implement is using filter ...
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2answers
2k views

Shift invariant in wavelet

I always hear that wavelet transform is not shift invariant, and that there are other types of wavelet, like stationary wavelet and double density dual-tree wavelet transform, that are shift invariant....
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1answer
34 views

Measures that can be used to truncate linear series of functions

Say we have the following (wavelet) series representation at some location and scale in a signal: $$ f = \sum_{k=1}^{K} c_k \psi_k$$ where $c_k$ is the coefficient, in order of magnitude ($|c_k| >...
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1answer
787 views

Downsampling in DWT algorithm

I was working on wavelet signal decomposition and got confused with the downsampling part of Discrete Wavelet Transform algorithm. If we consider a signal $\{a_0[0], ... ,a_0[N-1]\}$ of length N and ...
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1answer
346 views

Discrete wavelet transform

I am unable to understand the discrete wavelet transform on images. I followed Robi Polikar's tutorial and got a brief idea about the theory. But I'm unable to understand w.r.t images. Using Matlab's ...
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1answer
98 views

Question about vanishing moments in wavelet transforms

I am reading the book Noise reduction by wavelet thresholding by Maarten Jansen. About vanishing moments, it reads To create a really sparse representation, we try to make coefficients that live ...
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3answers
3k views

What are the spike removal techniques in matlab without using filters

output from wavelet filter using daubechies 4 wavelet. Using wavelet filter this is the output obtained. The problem is elimination of the spikes at 0.023,0.043,0.063 and so on. Please note: no ...
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1answer
578 views

Daubechies wavelet transform

i have N samples obtained by sampling a signal with lot of frequency contents. How will i apply daubechies wavelet transform to obtain the frequency and its location? i need to write a program which ...
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2answers
138 views

Compression Ratio in ECG compression using Wavelet Decomposition

I have compressed and reconstructed an ECG signal using wavelet coefficients. In the compression part, many of wavelet coefficients are set to zero. For example, if in original ECG $5000$ wavelet ...
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1answer
805 views

How to do edge detection using Curvelet transform?

I wanted to use Curvelet thresholding for edge detection, that is first take discrete curvelet transform then choose coefficient which are for curve and then reconstruct back to get an edge map. ...