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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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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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
43 views

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??
2k views

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 ...
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 ...
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 ...
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 ...
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. ...
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 ...
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 ...
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 <...
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 ...
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 ...
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. ...
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?
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, ...
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 ...
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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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 ...
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 ...
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. ...
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 ...
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....