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mathematical functions that break up a signal into different frequency components so that they are studied at different resolutions or scales

The wavelets are mathematical functions that break up a signal into different frequency components so that they are studied at different resolutions or scales.

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wave-like oscillations with amplitudes that start at zero

Wavelets are wave-like oscillations with amplitudes that start at zero, then increase, then decrease back to zero.

mathematical functions that give a time-scale representation of the time series and their relationships to analyze time series that contain non-stationarities

Wavelets are mathematical functions that give a time-scale representation of the time series and their relationships to analyze time series that contain non-stationarities.

mathematical functions which use principles of Fourier analysis (a method of evaluating a waveform using trigonometry)

Wavelets are simply mathematical functions which use principles of Fourier analysis (a method of evaluating a waveform using trigonometry).

mathematical functions used in processing digital signals and shrinking digital photos and movies

Wavelets are mathematical functions used in processing digital signals and shrinking digital photos and movies.

on small waves,

The transform is based on small waves, called wavelets, of varying frequency and limited duration.

functions that satisfy certain mathematical requirements and are used in representing data or other functions

Wavelets are functions that satisfy certain mathematical requirements and are used in representing data or other functions.

mathematical functions that cut wave data, such as the sound waves of a musical recording, into different components

Wavelets are mathematical functions that cut wave data, such as the sound waves of a musical recording, into different components.

mathematical functions of finite duration with an average value of zero that are useful in representing data or other functions

Very simply wavelets are mathematical functions of finite duration with an average value of zero that are useful in representing data or other functions.

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a mathematical tool

Since wavelets are a mathematical tool, Cookies have been used in a number of application in different fields of science and technology to extract information from and/or denoise many different kinds of data, including – but certainly not limited to – audio signals, images, optical spectra, time series.

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a waveform of limited duration that has an average value of zero

A wavelet is a waveform of limited duration that has an average value of zero.

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mathematical functions that have become increasingly important to researchers because of their ability to analyze data sets that are difficult to understand using traditional techniques such as Fast Fourier Transform

Wavelets are mathematical functions that have become increasingly important to researchers because of their ability to analyze data sets that are difficult to understand using traditional techniques such as Fast Fourier Transform.

a threaded conversation that is spawned from a wave (including the initial conversation)

A wavelet is a threaded conversation that is spawned from a wave (including the initial conversation).

a relatively new class of mathematical functions

Wavelets are a relatively new class of mathematical functions and I will describe how they can be used as a basis set in density functional electronic structure calculations.

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