Fast wavelet transform (original) (raw)
Die schnelle Wavelet-Transformation, englisch fast wavelet transform, ist ein effizientes Verfahren zur Berechnung einer diskreten Wavelet-Transformation. Sie kann mit der Anwendung der schnellen Fourier-Transformation zur Berechnung der Koeffizienten einer Fourier-Reihe verglichen werden.
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| dbo:abstract | Die schnelle Wavelet-Transformation, englisch fast wavelet transform, ist ein effizientes Verfahren zur Berechnung einer diskreten Wavelet-Transformation. Sie kann mit der Anwendung der schnellen Fourier-Transformation zur Berechnung der Koeffizienten einer Fourier-Reihe verglichen werden. (de) The fast wavelet transform is a mathematical algorithm designed to turn a waveform or signal in the time domain into a sequence of coefficients based on an orthogonal basis of small finite waves, or wavelets. The transform can be easily extended to multidimensional signals, such as images, where the time domain is replaced with the space domain. This algorithm was introduced in 1989 by Stéphane Mallat. It has as theoretical foundation the device of a finitely generated, orthogonal multiresolution analysis (MRA). In the terms given there, one selects a sampling scale J with sampling rate of 2J per unit interval, and projects the given signal f onto the space ; in theory by computing the scalar products where is the scaling function of the chosen wavelet transform; in practice by any suitable sampling procedure under the condition that the signal is highly oversampled, so is the orthogonal projection or at least some good approximation of the original signal in . The MRA is characterised by its scaling sequence or, as Z-transform, and its wavelet sequence or (some coefficients might be zero). Those allow to compute the wavelet coefficients , at least some range k=M,...,J-1, without having to approximate the integrals in the corresponding scalar products. Instead, one can directly, with the help of convolution and decimation operators, compute those coefficients from the first approximation . (en) 快速小波轉換（英語：Fast wavelet transform）是利用數學的演算法則用來轉換在時域的波形或信號變成一系列的以構成的小而有限的波、小波。當然，快速小波轉換本身可以很輕易地擴增它的維度以符合各種不同的需求，例如影像處理、壓縮、去除雜訊…等 (zh) |
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| rdfs:comment | Die schnelle Wavelet-Transformation, englisch fast wavelet transform, ist ein effizientes Verfahren zur Berechnung einer diskreten Wavelet-Transformation. Sie kann mit der Anwendung der schnellen Fourier-Transformation zur Berechnung der Koeffizienten einer Fourier-Reihe verglichen werden. (de) 快速小波轉換（英語：Fast wavelet transform）是利用數學的演算法則用來轉換在時域的波形或信號變成一系列的以構成的小而有限的波、小波。當然，快速小波轉換本身可以很輕易地擴增它的維度以符合各種不同的需求，例如影像處理、壓縮、去除雜訊…等 (zh) The fast wavelet transform is a mathematical algorithm designed to turn a waveform or signal in the time domain into a sequence of coefficients based on an orthogonal basis of small finite waves, or wavelets. The transform can be easily extended to multidimensional signals, such as images, where the time domain is replaced with the space domain. This algorithm was introduced in 1989 by Stéphane Mallat. where is the scaling function of the chosen wavelet transform; in practice by any suitable sampling procedure under the condition that the signal is highly oversampled, so or, as Z-transform, or (en) |
| rdfs:label | Schnelle Wavelet-Transformation (de) Fast wavelet transform (en) 快速小波轉換 (zh) |
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