<title>Wavelet transforms and filter banks in digital communications</title>

The theorems giving the conditions for discrete wavelet transforms (DWTs) to achieve perfect translation invariance (PTI) have already been proven, and based on these theorems, the dual-tree complex DWT and the complex wavelet packet transform, achieving PTI, have already been proposed. However, there is not so much flexibility in their wavelet density. In the frequency domain, the wavelet density is fixed by octave filter banks, and in the time domain, each wavelet is arrayed on a fixed coordinate, and the wavelet packet density in the frequency domain can be only designed by dividing an octave frequency band equally in linear scale, and its density in the time domain is constrained by the division number of an octave frequency band. In this paper, a novel complex DWT is proposed to create variable wavelet density in the frequency and time domains, that is, an octave frequency band can be divided into N filter banks in logarithmic scale, where N is an integer larger than or equal to 3, and in the time domain, a distance between wavelets can be varied in each level, and its transform achieves PTI.

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Iterated filter banks with rational rate changes connection with discrete wavelet transforms

IEEE Transactions on Signal Processing ◽

10.1109/78.258070 ◽

1993 ◽

Vol 41 (12) ◽

pp. 3232-3244 ◽

Cited By ~ 43

Author(s):

T. Blu

Keyword(s):

Wavelet Transforms ◽

Filter Banks ◽

Discrete Wavelet ◽

Discrete Wavelet Transforms

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Filter banks in digital communications

IEEE Circuits and Systems Magazine ◽

10.1109/mcas.2001.939098 ◽

2001 ◽

Vol 1 (2) ◽

pp. 4-25 ◽

Cited By ~ 1

Author(s):

P.P. Vaidyanathan

Keyword(s):

Filter Banks ◽

Digital Communications

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Lossy to lossless image coding based on wavelets using a complex allpass filter

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691314600029 ◽

2014 ◽

Vol 12 (04) ◽

pp. 1460002 ◽

Cited By ~ 1

Author(s):

Xi Zhang ◽

Noriaki Fukuda

Keyword(s):

Image Coding ◽

Wavelet Transforms ◽

Filter Banks ◽

Wavelet Filter ◽

Biorthogonal Wavelets ◽

Jpeg 2000 ◽

Effective Implementation ◽

Lossless Coding ◽

Integer Wavelet ◽

Allpass Filter

Wavelet-based image coding has been adopted in the international standard JPEG 2000 for its efficiency. It is well-known that the orthogonality and symmetry of wavelets are two important properties for many applications of signal processing and image processing. Both can be simultaneously realized by the wavelet filter banks composed of a complex allpass filter, thus, it is expected to get a better coding performance than the conventional biorthogonal wavelets. This paper proposes an effective implementation of orthonormal symmetric wavelet filter banks composed of a complex allpass filter for lossy to lossless image compression. First, irreversible real-to-real wavelet transforms are realized by implementing a complex allpass filter for lossy image coding. Next, reversible integer-to-integer wavelet transforms are proposed by incorporating the rounding operation into the filtering processing to obtain an invertible complex allpass filter for lossless image coding. Finally, the coding performance of the proposed orthonormal symmetric wavelets is evaluated and compared with the D-9/7 and D-5/3 biorthogonal wavelets. It is shown from the experimental results that the proposed allpass-based orthonormal symmetric wavelets can achieve a better coding performance than the conventional D-9/7 and D-5/3 biorthogonal wavelets both in lossy and lossless coding.

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