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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What Properties Make Certain Wavelets "Better" Than Others In Image Compression?

I am trying to teach myself more about image compression using the wavelet transform method. My question is: What is it about certain wavelets that make them preferable when compressing images? Are they easier to compute? Do they produce smoother…
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Which time-frequency coefficients does the Wavelet transform compute?

The Fast Fourier Transform takes $\mathcal O(N \log N)$ operations, while the Fast Wavelet Transform takes $\mathcal O(N)$. But what, specifically, does the FWT compute? Although they are often compared, it seems like the FFT and FWT are apples and…
endolith
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Bag of Tricks for Denoising Signals While Maintaining Sharp Transitions

I know this is signal dependent, but when facing a new noisy signal what is your bag of tricks for trying to denoise a signal while maintaining sharp transitions (e.g. so any sort of simple averaging, i.e. convolving with a gaussian, is out). I…
John Robertson
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What's the difference between the Gabor and Morlet wavelets?

The Gabor wavelet is a kind of the Gaussian modulated sinusoidal wave (source)   Gabor wavelets are formed from two components, a complex sinusoidal carrier and a Gaussian envelope. (source) and In fact, the wavelet shown in Figure 2a…
endolith
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Using continuous verses discrete wavelet transform in digital applications

I am familiar with much of the mathematical background behind wavelets. However when implementing algorithms on a computer with wavelets I am less certain about whether I should be using continuous or discrete wavelets. In all reality everything on…
John Robertson
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What Is the Difference between Difference of Gaussian, Laplace of Gaussian, and Mexican Hat Wavelet?

There are three techniques used in CV that seem very similar to each other, but with subtle differences: Laplacian of Gaussian: $\nabla^2\left[g(x,y,t)\ast f(x,y)\right]$ Difference of Gaussians: $ \left[g_1(x,y,t)\ast f(x,y)\right] -…
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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 ?
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When can we write Heisenberg uncertainty Principle as a equality?

We know that Heisenberg uncertainty Principle states that $$\Delta f \Delta t \geq \frac{1}{4 \pi}.$$ But (in many case for Morlet wavelet) I have seen that they changed the inequality to an equality. Now my question is when are we allowed to change…
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How can I plot frequency vs magnitude of wavelet transform?

I am running Morlet continuous wavelet transform. I have got wscalogram of signal and now I want to plot freq-magnitude like the following picture., but I don't know how to do it: I've used scal2freq MATLAB function to convert scales to pseudo…
SAH
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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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Discrete Wavelet Transform - Visualizing Relation between Decomposed Detail Coefficients and Signal

I'm trying to directly visualize the relation between discrete wavelet transform (DWT) detail coefficients and the original signal/its reconstruction. The goal is to show their relation in an intuitive way. I would like to ask (see questions below):…
geekoverdose
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STFT and DWT (Wavelets)

STFT can be successfully used on sound data (with a .wav soundfile for example) in order to do some frequency-domain modifications (example : noise removal). With N=441000 (i.e. 10 seconds at sampling rate fs=44100), windowsize=4096, overlap=4, STFT…
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Comparison between Fourier transform, short-time Fourier transform and wavelets

What is the difference between the Fourier transform, short-time Fourier transform and wavelets?
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How do I get started with Wavelets

Our current project requires us to do some analysis using Wavelet Transform. Can anybody suggest me a practical book, preferably with MATLAB or C examples. I am currently reading some tutorials, but it is not giving me a feeling as I have for…
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Which transform most closely mimics the human auditory system?

The Fourier transform is commonly used for frequency analysis of sounds. However, it has some disadvantages when it comes to analyzing the human perception of sound. For example, its frequency bins are linear, whereas the human ear responds to…
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