On vector transformation

Li, W.

doi:10.1109/78.257241

Cited by 26 publications

(12 citation statements)

References 14 publications

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“…Although the VT was advanced in [9][10][11] FVT is generally computationally more complex than an FFT, it is should be noted that the FFT always requires complex arithmetic, while if the input to the VT is real (for example obtained as a result of BPSK modulation) and if the VT kernel is real, then the FVT requires only real arithmetic. In this case, assuming that M=2, the number of multiplications and additions for the FVT (4Nlog2 N and 6N log2 N) is actually lower than for the FFT ( 8N log2 (2N) and 8N log2 (2N) ).…”

Section: Fast Vector Transformmentioning

confidence: 99%

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Vector transform-based OFDM

Cooklev

Siohan

2006

2006 Fortieth Asilomar Conference on Signals, Systems and Computers

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In this paper we propose a new type of a system for multicarrier modulation. The modulation and demodulation in the proposed system are performed by an inverse and forward vector transforms. The properties of the vector transform allow fast vector transform algorithms to be derived in a manner similar to the FFT. Real-valued vector transforms are also possible. Appropriate vector transforms are designed. Simulation results are presented, which show that in multipath channels compared with conventional OFDM systems the proposed vector-transform-based system achieves lower bit error rate.

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Section: Fast Vector Transformmentioning

confidence: 99%

“…VECTOR TRANSFORM The vector transform was advanced in [9][10][11]. The transform pair (7) where x[n] and X[k] are sequences of vectors of dimension Mxl1 constitute forward and inverse vector transform if the matrix kernel W of dimension MxM satisfies two conditions.…”

Section: Introductionmentioning

confidence: 99%

Vector transform-based OFDM

Cooklev

Siohan

2006

2006 Fortieth Asilomar Conference on Signals, Systems and Computers

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“…In this technique, it was realized that the root of the problem lies in that the vector [1, 1] T is not generally an eigenvector of the two-scale matrix symbols H(z) and H(z) of (21) when z = 1 (corresponding to a zero-frequency, or constant source). To rectify this situation, a similarity transformation was proposed in order to "redesign" the H n and H n matrices such that [1,1] T is an eigenvector. This approach was called multiwavelet balancing [5] due to the fact that it tends to "balance" out the treatment of the vector components by the filter bank.…”

Section: A Scalar Balancingmentioning

confidence: 99%

“…Specifically, in our formulation of analysis and synthesis, (15)- (17), the conditions imposed by scalar balancing are that we want a constant scalar signal to pass through the lowpass analysis filter unchanged (up to a constant gain); that is, regarding (15), we want n H n [1,1]…”

Section: A Scalar Balancingmentioning

confidence: 99%

“…The concept of a vector transform has existed for some time [1], and a comprehensive multiresolution-analysis theory for VWTs, which closely parallels theory for scalar-wavelet expansion, was outlined by Xia and Suter [2]. Although Xia and Suter focused on the theoretical infrastructure for VWTs rather than the design of coefficient matrices for vector filter banks, they recognized that multiwavelets present a natural construction for VWTs.…”

Section: Introductionmentioning

confidence: 99%

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Wavelet transforms for vector fields using omnidirectionally balanced multiwavelets

Fowler

2002

IEEE Trans. Signal Process.

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Vector wavelet transforms for vector-valued fields can be implemented directly from multiwavelets; however, existing multiwavelets offer surprisingly poor performance for transforms in vector-valued signalprocessing applications. In this paper, the reason for this performance failure is identified, and a remedy is proposed. A multiwavelet design criterion, omnidirectional balancing, is introduced to extend to vector transforms the balancing philosophy previously proposed for multiwavelet-based scalarsignal expansion. It is shown that the straightforward implementation of a vector wavelet transform, namely the application of a scalar transform to each vector component independently, is a special case of an omnidirectionally balanced vector wavelet transform in which filter-coefficient matrices are constrained to be diagonal. Additionally, a family of symmetricantisymmetric multiwavelets is designed according to the omnidirectionalbalancing criterion. In empirical results for a vector-field compression system, it is observed that the performance of vector wavelet transforms derived from these omnidirectionally-balanced symmetric-antisymmetric multiwavelets is far superior to that of transforms implemented via other multiwavelets and can exceed that of diagonal transforms derived from popular scalar wavelets.

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Image and Video Coding

Li²

2003

Wiley Encyclopedia of Telecommunications

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On vector transformation

Cited by 26 publications

References 14 publications

Vector transform-based OFDM

Vector transform-based OFDM

Wavelet transforms for vector fields using omnidirectionally balanced multiwavelets

Image and Video Coding

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