# 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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### 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 ...
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### What's the difference between the Gabor-Morlet wavelet transform and the constant-Q transform?

At a glance, the constant-Q fourier transform and the complex Gabor-Morlet wavelet transform seem the same. Both are time-frequency representations, based on constant-Q filters, windowed sinusoids, ...
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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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### Audio time stretching, without pitch shifting

This might be a Sound Design question, or a StackOverflow question since I am attempting to do this with Java. I would like to play back a sound at the same pitch, but stretched out in time. My ...
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### Additive White Gaussian Noise (AWGN) and Undecimated DWT

One of the benefits of DWT is that it is an orthonormal transform. There are statements that the energy of noise component mainly concentrates on the high-frequency (detail) part and distributes ...
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### Implementing Continuous Wavelet Transform

I need to implement the discretized continuous wavelet transform from scratch. Could someone please point me to useful papers and references available online for this?
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### Fourier Transform of Morlet wavelet Function?

One definition of the Morlet wavelet function is given by: $$\frac{1}{\sqrt{\pi f_b}}e^{\frac{-t^2}{f_b}}e^{j2\pi f_c t}$$ The Fourier transform of this equation is: $e^{-\pi^2 f_b(f-f_c)^2}$ (is it ...
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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 ...
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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, ...
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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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### 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 ...
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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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### Explanation on Haarlets

Would someone be able to give me some info or a link etc ... regarding haarlets aka Haar wavelet-like features. I'm reading several papers for my master dissertation and several of these papers ...
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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 ...
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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 ...
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### Feature extraction/reduction using DWT

For a given time series which is n timestamps in length, we can take Discrete Wavelet Transform (using 'Haar' wavelets), then we get (for an example, in Python) - ...
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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) ...
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### What does the normalization step of the Haar wavelet transform represent?

When you perform the Haar wavelet transform, you take the sums and differences, then at each stage, you multiply the entire signal by $\small\sqrt2$. When taking the inverse transform, you multiply ...
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I need some information about Stockwell transform (also known as the S-transform): How can I implement it in MATLAB? *Does it give you the damping ratio $\zeta$ of a signal like the complex Morlet ...
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### Comparison between 2 images in Frequency domain

As you can see there are 2 images from the Tom and Jerry cartoon program. In the 1st image both Tom and Jerry are present. But in the 2nd one,only Tom is present.Now,we can clearly see this ...
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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 ...
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### Morlet wavelet time and frequency resolution

I want to calculate Morlet time and frequency resolution. the Morlet wavelet function is define as : $\psi(t)=\frac{1}{\sqrt{\pi f_b}}e^{j2\pi f_c}e^{-t^2/f_b}$ Note: I know the answers, but I don't ...
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### Noise rejection / feature extraction

I'm hoping someone could point me in the direction of some signal processing methods to clean up my data. I'm collecting physiological data from human muscle (lower leg; gastrocnemius) during walking/...