Signal Processing Stack Exchange
Signal Processing Stack Exchange

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.

A wavelet can typically be visualized as a "brief oscillation" like one might see recorded by a seismograph or heart monitor. Generally, wavelets are purposefully crafted to have specific properties that make them useful for signal processing. Wavelets can be combined, using a "revert, shift, multiply and sum" technique called convolution, with portions of an unknown signal to extract information from the unknown signal.

Source: Wikipedia.

References

  1. Bultheel A., "Wavelets, with applications in signal and image processing"

  2. S. Allen Broughton, Kurt Bryan, "Discrete Fourier analysis and wavelets: applications to signal and image processing"

  3. Barbara Burke Hubbard, "The World According to Wavelets: The Story of a Mathematical Technique in the Making, Second Edition"

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Why Wavelet developed when we already had Short-time Fourier transform

If we already had Short-time Fourier transform for better analysis of a signal than Discrete Fourier Transform, then what was the need that leads to development of Wavelet Transform ?
Sufiyan Ghori
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Reading the Wavelet transform plot

I am having trouble understanding on how to read the plot plotted by a wavelet transform, here is my simple Matlab code, load noissin; % c is a 48-by-1000 matrix, each row % of which corresponds to a single scale. c =…
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What is the normalization factor for the quincunx lattice wavelet transform, and how do you find it?

On pages 57-60 (preview was available last I checked, images here in case), there is a quincunx lattice transform described. Lattice: o • o • o • o • • o • o • o • o o • o • o • o • • o • o • o • o o • o • o • o • • o • o • o • o o • o • o • o • • o…
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Which mother wavelet for a scalogram?

I'm attempting to create a real-time scalogram (from a 1 dimensional signal) in the style of a spectrogram; Looking through various papers+books; the Gabor wavelet, or complex Morlet seems to be favoured for keeping a close relation to…
daurnimator
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Difference between a wavelet transform and a wavelet decomposition

I'm confused about the difference between a wavelet transform and a wavelet decomposition is. For example load woman [cA1,cH1,cV1,cD1] = dwt2(X,'db1'); [c,s] = wavedec2(X,2,'db1'); What's the difference between these two matlab commands, and when…
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How to turn Morlet wavelet into second generation wavelet?

I have a very specific application which requires to use the complex Morlet wavelet (or Gabor wavelet, if that's the name you use). I currently use the convolution theorem to compute wavelets transforms, but I'm reading everywhere that direct…
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Vanishing Moments

I am reading a book titled "Two Dimensional Wavelets and their relatives" by Antoine et al. and it talks about vanishing moments. I have trouble understanding the exact significance of it. Can anybody give an idea on vanishing moments?
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What is the scaling function and wavelet function at wavelet analysis?

I'm trying to looking the meaning and functionality about scaling function and wavelet function at wavelet analysis. I have googling already. But I can't find and understand the meaning. What does those affect to analysis? Does anyone help me to…
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Intuition behind the Continuous Wavelet Transform?

I was thinking sometime back about how to explain the Continuous Wavelet Transform ELI5. So this is what I came across. The correlation of two exact signals is 1. So if I have an input signal $f(x)$ made up of an array of frequencies, how can I find…
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Implementing Wavelet Transform using Equations

I want to implement Wavelet Transform from the scratch, that mean breaking the wavelet transform into its equations to implement in any Programming language. Matlab Comes with built-in functions to implement Wavelet Transform but It is really hard…
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Why Low Frequency called Approximation and High Frequency Detail?

While we are decomposing a signal using Wavelets into levels why do we call our high frequency components as Detail and Low Frequency Components as Approximation ?
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wavelet analysis normalized to have unit energy

I am analyzing some time series of sea surface water temperature and am using wavelet analysis to do so. I am computing the continuous wavelet transform and then removing some specific frequencies and then converting the series back from the…
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Wavelet thresholding

What is the difference between soft thresholding and hard thresholding. Where we use soft and hard thresholding in image for denoising. I understand that in hard thresholding, the coefficients below threshold value are set to zero and the value…
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Any Open Source Fast Wavelet transform libraries?

I am in need of an open source library for computing Fast wavelet transforms (FWT) and Inverse fast wavelet transforms (IFWT) - this is to be part of a bigger code I am currently writing. The things I am looking for in the library: 1) Contains a…
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Scalogram (Wavelet)

Using a signal of three joined sinus of equal length at different frequencies (40 Hz, 50 Hz, 80 Hz) I calculate a scalogram of it (scale vertical, time horizontal, The steps of variing the scale parameter are equidistant): Plot of the Scalogram:…
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