O que (quem) é wavelets - definição

FUNCTION FOR INTEGRAL FOURIER-LIKE TRANSFORM

Wavelets; Wavelet analysis; Father wavelets; Mother wavelet; History of wavelets; List of wavelets

Wavelet

A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation".

https://en.wikipedia.org/wiki/Wavelet

wavelet

<mathematics> A waveform that is bounded in both frequency and duration. Wavelet tranforms provide an alternative to more traditional Fourier transforms used for analysing waveforms, e.g. sound. The Fourier transform converts a signal into a continuous series of sine waves, each of which is of constant frequency and amplitude and of infinite duration. In contrast, most real-world signals (such as music or images) have a finite duration and abrupt changes in frequency. Wavelet transforms convert a signal into a series of wavelets. In theory, signals processed by the wavelet transform can be stored more efficiently than ones processed by Fourier transform. Wavelets can also be constructed with rough edges, to better approximate real-world signals. For example, the United States Federal Bureau of Investigation found that Fourier transforms proved inefficient for approximating the whorls of fingerprints but a wavelet transform resulted in crisper reconstructed images. SBG Austria (http://mat.sbg.ac.at/waveletuhl/wav.html). ["Ten Lectures on Wavelets", Ingrid Daubechies]. (1994-11-09)

wavelet

(wavelets)

Wavelets are small waves on the surface of a sea or lake. (LITERARY)

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Wikipédia

Wavelet

A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing.

For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly one tenth of a second. If this wavelet were to be convolved with a signal created from the recording of a melody, then the resulting signal would be useful for determining when the Middle C note appeared in the song. Mathematically, a wavelet correlates with a signal if a portion of the signal is similar. Correlation is at the core of many practical wavelet applications.

As a mathematical tool, wavelets can be used to extract information from many different kinds of data, including – but not limited to – audio signals and images. Sets of wavelets are needed to analyze data fully. "Complementary" wavelets decompose a signal without gaps or overlaps so that the decomposition process is mathematically reversible. Thus, sets of complementary wavelets are useful in wavelet-based compression/decompression algorithms, where it is desirable to recover the original information with minimal loss.

In formal terms, this representation is a wavelet series representation of a square-integrable function with respect to either a complete, orthonormal set of basis functions, or an overcomplete set or frame of a vector space, for the Hilbert space of square integrable functions. This is accomplished through coherent states.

In classical physics, the diffraction phenomenon is described by the Huygens–Fresnel principle that treats each point in a propagating wavefront as a collection of individual spherical wavelets. The characteristic bending pattern is most pronounced when a wave from a coherent source (such as a laser) encounters a slit/aperture that is comparable in size to its wavelength. This is due to the addition, or interference, of different points on the wavefront (or, equivalently, each wavelet) that travel by paths of different lengths to the registering surface. Multiple, closely spaced openings (e.g., a diffraction grating), can result in a complex pattern of varying intensity.

https://en.wikipedia.org/wiki/Wavelet

Exemplos do corpo de texto para wavelets

1. Computer simulations predict that those random impacts will redistribute enough of the energy imparted by the wind to prevent worrisome oscillations from building up –– ultimately dissipating that energy as imperceptible wavelets of heat.