Topic
Hadamard transform
About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.
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23 Aug 1994TL;DR: The quadtree code as discussed by the authors is a two dimensional data structure represented by quadtree codes with embedded Walsh transform coefficients, which permits both variable block size inherent in quadtrees, and the calculational simplicity of Walsh transform descriptions of nearly uniform blocks of data.
Abstract: Two dimensional data structures are represented by quadtree codes with embedded Walsh transform coefficients. The quadtree code permits both variable block size inherent in quadtrees, and the calculational simplicity of Walsh transform descriptions of nearly uniform blocks of data. Construction of the quadtree is calculationally simple for implementation in a digital system which does a bottom-up determination of the quadtree because Walsh transform coefficients and a measure of the distortion can be recursively calculated using only Walsh transform coefficients from the previous level in the quadtree. Uniform step size quantization, which is optimal for variable length coding and generalized gaussian distributions, permits fast encoding and decoding of quadtree code.
61 citations
TL;DR: All the possible nonisomorphic additive Hadamard codes are characterized and the rank and the dimension of the kernel are computed for each one.
Abstract: All the possible nonisomorphic additive (/spl Zopf//sub 4/-linear and non-/spl Zopf//sub 4/-linear) Hadamard codes are characterized and the rank and the dimension of the kernel are computed for each one.
61 citations
TL;DR: A Hadamard-Walsh code-based MC-CDMA system that achieves zero MAI over a frequency-selective fading channel and every user can enjoy a channel diversity gain of order L to improve the bit error performance.
Abstract: It is known that multicarrier code-division multiple-access (MC-CDMA) systems suffer from multiaccess interference (MAI) when the channel is frequency-selective fading. In this paper, we propose a Hadamard-Walsh code-based MC-CDMA system that achieves zero MAI over a frequency-selective fading channel. In particular, we will use appropriately chosen subsets of Hadamard-Walsh code as codewords. For a multipath channel of length L, we partition a Hadamard-Walsh code of size N into G subsets, where G is a power of two with GgesL. We will show that the N/G codewords in any of the G subsets yields an MAI-free system. That is, the number of MAI-free users for each codeword subset is N/G. Furthermore, the system has the additional advantage that it is robust to carrier frequency offset (CFO) in a multipath environment. It is also shown that the MAI-free property allows us to estimate the channel of each user separately and the system can perform channel estimation much more easily. Owing to the MAI-free property, every user can enjoy a channel diversity gain of order L to improve the bit error performance. Finally, we discuss a code priority scheme for a heavily loaded system. Simulation results are given to demonstrate the advantages of the proposed code and code priority schemes
61 citations
01 Jan 2000
TL;DR: In this paper, the authors proposed a set of efficient simultaneous diagonalization algorithms based on Hadamard's inequality to make the source separation feasible in the frequency domain, where the Frobenius norm is minimized.
Abstract: Reverberant signals recorded by multiple microphones can be described as sums of sources convolved with different parameters. Blind source separation of this unknown linear system can be transformed to a set of instantaneous mixtures for every frequency band. In each frequency band, we may use the simultaneous diagonalization algorithms to separate the sources. In addition to our previous simultaneous diagonalization to minimize the Frobenius norm, we now propose another set of efficient simultaneous diagonalization algorithms based on Hadamard’s inequality to make the source separation feasible in the frequency domain.
61 citations
TL;DR: Using the sparse matrix factorization, the fast and efficient algorithm to compute the SCHT transform is developed, and its computation load is described.
Abstract: In this paper, the generation of sequency-ordered complex Hadamard transform (SCHT) based on the complex Rademacher matrices is presented. The exponential form of SCHT is also derived, and the proof for the unitary property of SCHT is given. Using the sparse matrix factorization, the fast and efficient algorithm to compute the SCHT transform is developed, and its computation load is described. Certain properties of the SCHT matrices are derived and analyzed with the discussion of SCHT applications in spectrum analysis and image watermarking. Relations of SCHT with fast Fourier transform (FFT) and unified complex Hadamard transform (UCHT) are discussed.
61 citations