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Subband coding resides at the heart of the popular MP3 format (more properly known as MPEG-1 Audio Layer III), for example. Sub-band coding is used in the G.722 codec which uses sub-band adaptive differential pulse code modulation (SB-ADPCM) within a bit rate of 64 kbit/s. In the SB-ADPCM technique, the frequency band is split into two sub ...
The wavelets generated by the separable DWT procedure are highly shift variant. A small shift in the input signal changes the wavelet coefficients to a large extent. Also, these wavelets are almost equal in their magnitude in all directions and thus do not reflect the orientation or directivity that could be present in the multidimensional signal.
Originally known as optimal subband tree structuring (SB-TS), also called wavelet packet decomposition (WPD; sometimes known as just wavelet packets or subband tree), is a wavelet transform where the discrete-time (sampled) signal is passed through more filters than the discrete wavelet transform (DWT).
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.
Spectrum of the Meyer wavelet (numerically computed). The Meyer wavelet is an orthogonal wavelet proposed by Yves Meyer. [1] As a type of a continuous wavelet, it has been applied in a number of cases, such as in adaptive filters, [2] fractal random fields, [3] and multi-fault classification.
Lifting sequence consisting of two steps. The lifting scheme is a technique for both designing wavelets and performing the discrete wavelet transform (DWT). In an implementation, it is often worthwhile to merge these steps and design the wavelet filters while performing the wavelet transform.
The equation of a 1-D Gabor wavelet is a Gaussian modulated by a complex exponential, described as follows: [3] = / ()As opposed to other functions commonly used as bases in Fourier Transforms such as and , Gabor wavelets have the property that they are localized, meaning that as the distance from the center increases, the value of the function becomes exponentially suppressed.
As shown in, [1] it is better to choose a filter with a longer sloping tail in an image coding task. In certain applications, other decompositions have advantages. Although there are many such decompositions possible, here we briefly present two popular methods: Mexican hat wavelets and the steerable pyramid.