# 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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### Understanding this Haar Wavelet Example

I'm trying to understand Wavelet Transform , I've done well enough to understand Continuous Wavelet Transform which was easy enough, where we simply stretch the wavelet and match it with the original ...
12k views

### 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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### 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 ...
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### wavelet denoising routine for environmental data series

I have a time series of water temperature, e.g. y = 1+(30-10).*rand(1,365); I have previously used the wavelet denoising routine in the wavelet toolbox by matlab ...
333 views

I've read there are two admissibility criteria for wavelets, both of which are designed to preserve total power of the signal (source: http://en.wikipedia.org/wiki/Wavelet#Mother_wavelet, as well as ...
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### What are the uses of those three types of wavelet transformations?

In my studies of wavelets, there appear to be 3 different families of them: The Continuous wavelet transform The Discrete wavelet transform The Redundant wavelet transform They are all based on the ...
439 views

### Wavelets and cryptography [closed]

What papers/articles/books are considered good for getting started with wavelets' application to cryptography? I'm primarily interested in irregular grid wavelets, but regular grid will do for ...
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### Scalogram (and related nomenclatures) for DWT?

My understanding of the scalogram is that, for a particular row, the scores of the projection of the input signal with the wavelet at a particular displacement is shown. Across rows, the same thing ...
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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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### Using Discrete Wavelet Transform in the time-frequency domain

I am creating an application that works like the Shazam service. In short, my goal is to create an audio pattern matching service. However, I would like to use DWT and not the short time Fourier ...
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### Adding noise to an ECG signal

I am doing a project on ECG arrythmia analysis using matlab. I have designed notch filter for removing 50 Hz noise but don't know how to add a 50 Hz powerline interference noise to a clean ECG signal?...
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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, ...
421 views

### Pitch detection algorithm for minsample size

I am looking for a pitch detection algorithm that uses the least number of samples. I don't care about the processing time. I hope to use this on audio signals. I have tried using the one at the ...
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### Signal matching: How to quantify the difference between two signals of varying frequency

I have two waves, and I would like to quantify the difference between them. They are exponential sine waves where the frequency decreases with time. I'm interested in the difference in decay ...
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### Number of Daubechies coefficients

I am wondering about the correlation between input size and number of coefficients given by a discrete wavelet transform. I am using Daubechies wavelets to describe a 1D function and I'm using ...
170 views

### wavelet analysis/ dimension reduction

How wavelet analysis works as a dimension reduction techniques? The approximations coefficients at higher level of decomposition are the fewer retained coefficients from the originial ?Is it correct?
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### Discrete (Inverse) Haar (2D) transform implementations

I am interested in implementations of the Haar transform, and its inverse, such that when composed always result in the identity operation. My inputs are discrete ordinals within a given range - and ...
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### Tutorial on 2nd generation wavelets (with lifting)?

For some denoising and deconvolution experiments, I'd like to apply a 2nd generation wavelet transform (using lifting steps) to images. I know that there are several implementations available, but ...
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### Generating wavelet using amplitude spectra

Equation (4) of a recent paper (An improved peak-frequency-shift method for Q estimation) shows how to generate a wavelet using a zero-phase Ricker wavelet. $|B_1(f)| = |B_0(f)|\exp(-\pi t f / Q)$ ...
288 views

### 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: ...
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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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### 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 ...
163 views

### "Normalizing" my D4 wavelet transformation at each step reduces final image quality

Original image: (Images included are .png images, so no additional distortion was added in save/upload for viewing) I have used the D4 transform from page 20 of "Ripples in mathematics", ...
307 views

### T wave analyis and extraction using discrete wavelets

I'm doing a project in T-wave extraction from ECG signal. Initially I completed the preprocessing steps like noise removal and baseline drift cancellation. Then I need to extract T wave using discrete ...
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### Apply wavelet transform to analyse EEG signal

I would like to apply The Morlet wavelet transform to analyse my EEG signals. I have many short signals each is only 1 min long. and they all recorded in 30Hz. I have Two questions: In the Morlet ...
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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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I have used both correlation and coherence as measures of correlation between signals. I was thinking that a time-frequency approach would give me the best of these worlds. My question is whether ...
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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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### 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) ...
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 ...