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Hadamard transform

About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.


Papers
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Journal ArticleDOI
TL;DR: In this article, the Hadamard renormalization of the stress-energy tensor for a massive scalar field theory defined on a general spacetime of arbitrary dimension is studied.
Abstract: We develop the Hadamard renormalization of the stress-energy tensor for a massive scalar field theory defined on a general spacetime of arbitrary dimension. Our formalism could be helpful in treating some aspects of the quantum physics of extra spatial dimensions. More precisely, for spacetime dimensions up to six, we explicitly describe the Hadamard renormalization procedure and for spacetime dimensions from 7 to 11, we provide the framework permitting the interested reader to perform this procedure explicitly in a given spacetime. We complete our study (i) by considering the ambiguities of the Hadamard renormalization of the stress-energy tensor and the corresponding ambiguities for the trace anomaly, (ii) by providing the expressions of the gravitational counterterms involved in the renormalization process, and (iii) by discussing the connections between Hadamard renormalization and renormalization in the effective action. All our results are expanded on standard bases for Riemann polynomials constructed from group theoretical considerations and thus given on irreducible forms.

137 citations

Journal ArticleDOI
TL;DR: Two hybrid coding systems utilizing a cascade of a unitary transformation and differential pulse code modulators (DPCM) systems are proposed and the performance of this system is compared to the performances of the two- dimensional DPCM and the standard two-dimensional transform encoders.
Abstract: Two hybrid coding systems utilizing a cascade of a unitary transformation and differential pulse code modulators (DPCM) systems are proposed. Both systems encode the transformed data by a bank of DPCM systems. The first system uses a one-dimensional transform of the data where the second one employs two-dimensional transformations. Theoretical results for Markov data and experimental results for a typical picture are presented for Hadamard, Fourier, cosine, slant, and the KarhunenLoeve transformations. The visual effects of channel error and also the impact of noisy channel on the performance of the hybrid system, measured in terms of the signal-to-noise ratio of the encoder, is examined and the performance of this system is compared to the performances of the two-dimensional DPCM and the standard two-dimensional transform encoders.

136 citations

Journal ArticleDOI
TL;DR: An analytical procedure is provided which leads to a system of (n − 2)2 polynomial equations whose solutions give the parametrization of the complex n × n Hadamard matrices.
Abstract: In this paper we provide an analytical procedure which leads to a system of (n − 2)2 polynomial equations whose solutions give the parametrization of the complex n × n Hadamard matrices. It is shown that in general the Hadamard matrices depend on a number of arbitrary phases and a lower bound for this number is given. The moduli equations define interesting geometrical objects whose study will shed light on the parametrization of the Hadamard matrices, as well as on some interesting geometrical varieties defined by them.

131 citations

Journal ArticleDOI
TL;DR: In this article, the authors compare the performance of Hadamard single-pixel imaging (HSI) and Fourier single pixel imaging (FSI) with theoretical analysis and experiments.
Abstract: Single-pixel imaging is an innovative imaging scheme and has received increasing attentions in recent years. It is applicable to imaging at non-visible wavelengths and imaging under low light conditions. However, single-pixel imaging has once encountered problems of low reconstruction quality and long data-acquisition time. This situation has been changed thanks to the developments of Hadamard single-pixel imaging (HSI) and Fourier single-pixel imaging (FSI). Both techniques are able to achieve high-quality and efficient imaging, remarkably improving the applicability of single-pixel imaging scheme. In this paper, we compare the performances of HSI and FSI with theoretical analysis and experiments. The results show that FSI is more efficient than HSI while HSI is more noise-robust than FSI. Our work may provide a guideline for researchers to choose suitable single-pixel imaging technique for their applications.

131 citations

Patent
02 Mar 1993
TL;DR: In this paper, the authors proposed a method for transmitting a direct sequence, spread spectrum communication system signal, which includes a forward error correction encoder and interleaver to minimize the effect of errors that arise in the propagation of the transmitted signal.
Abstract: Apparatus and a method for transmitting a direct sequence, spread spectrum communication system signal. A transmitter (10) that receives a variable data rate information bearing input signal from a digital data source (12) includes a forward error correction encoder (80) that provides redundancy and an interleaver (82) that rearranges the input data. The forward error correction encoder and interleaver minimize the effect of errors that arise in the propagation of the transmitted signal. The output of the interleaver is applied to the input of a Hadamard encoder (84), which converts data words from the interleaver into one of N orthogonal codes, producing a Hadamard signal that varies at a bit rate that changes as the data rate of the information bearing signal varies. A pseudorandom number code generator (16) produces a code signal comprising a pseudorandom sequence of chips supplied at a constant chip rate. The Hadamard signal is input to a direct sequence (DS) modulator that modulates the information bearing signal with the code signal, using an integer number (greater than one) of chips to modulate each bit of the Hadamard signal. As the data rate of the information bearing signal varies, the number of chips per bit of the Hadamard signal is varied so as to minimize variations in the chip rate of the DS modulated signal. The transmitter is preferably combined with a receiver (29) in a transceiver. The receiver demodulates a received signal, and correlates it with a code signal from a pseudorandom number code generator (40) corresponding to the pseudorandom number code generator in the transmitter. The receiver also includes a Hadamard decoder (94), deinterleaver (96), and forward error correction decoder (98). A frequency hopping capability is optionally provided.

130 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023339
2022850
2021391
2020444
2019427
2018372