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عنوان فارسی مقاله:
توزیع دامنه و فاز برای توزیع دو متغیره
عنوان انگلیسی مقاله:
Distributions of amplitude and phase for bivariate distributions
سال انتشار : 2016
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مقدمه انگلیسی مقاله:
1. Introduction
Let ðX; YÞ be a random vector defined on the real space ð1; þ1Þ ð1; þ1Þ. Let R ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X2 þ Y2 p and H ¼ arctan ð Þ Y=X . The distributions of R and H arise in many areas of the IEEE literature: radar communications, positioning related applications, fading channels, etc. R is usually referred to as the amplitude and H the phase.Some published examples in the IEEE literature where the distributions of R and H arise directly are: analog datatransmission [7]; radiation-pattern of an offset fed paraboloidal reflector antenna [19]; microwave pulse generation [8]; photonic beamforming based on programmable phase shifters [37]; radiation characteristics of multimode concentric circular microstrip patch antennas [32]; transmission schemes for Rayleigh block fading channels [9]; broadband microwave photonic splitters [25]; performance of transmit beamforming codebooks [13]; AC-AC converters [39]; modulation of ultrawideband monocycle pulses on a silicon photonic chip [35]. Several papers have derived the distributions of R and H: Aalo et al. [1] and Dharmawansa et al. [11] derived the distributions of R and H when X and Y are correlated and non-identical normal random variables with non-zero means; Yacoub [36] derived the distributions of R and H when X and Y are independent and identical Nakagami type random variables; Coluccia [10] derived the moments of R when X and Y are uncorrelated normal random variables with zero means and unequal variances; and so on. Almost all of the known papers have supposed X and Y are normally distributed. However, non-normal distributions are becoming increasingly popular in the IEEE literature: hyperbolic distribution in network modeling [24]; Laplace distribution in signal processing [14]; Cauchy distribution in segmentation of noisy colour images [34]; Kotz type distribution for multilook polarimetric radar data [20]; Student’s t distribution in medical image segmentation [28]; logistic distribution for networked video quality assessment [38]; Gumbel distribution for peak sidelobe level for arrays of randomly placed antennas [23]; skew normal distribution for statistical static timing analysis [33]; and so on. Also, we are not aware of any paper giving expressions for moments of R when X and Y are correlated random variables. The aim of this note is to derive the distribution of R, its moments and the distribution of H for a wide range of bivariate distributions, including the correlated bivariate normal distribution. We consider thirty four flexible bivariate distributions in total. These include eleven bivariate normal distributions, eight bivariate t distributions, five bivariate Laplace distributions, two bivariate hyperbolic distributions, two bivariate Gumbel distributions and one bivariate logistic distribution. The contents of this note are organized as follows. Section 2 derives the distribution of R, its moments and the distribution of H when X and Y are correlated normal random variables with zero means and unequal variances. These results extend those given in Coluccia [10]. Section 3 derives the same when X and Y are correlated random variables following thirty three other bivariate distributions. Details of the derivations are not given. They can be obtained from the corresponding author. To the best of our knowledge, the derived expressions for the distribution of R, its moments and the distribution of H are all new and original. Section 4 discusses simulation of R and H for the bivariate distributions considered. I
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کلمات کلیدی:
Distributions of amplitude and phase for bivariate ... - Research Explorer https://www.research.manchester.ac.uk/...amplitude-and-phase-for-bivariate.../export.ht... Nadarajah S, Chu J, Jiang X. Distributions of amplitude and phase for bivariate distributions. AEU - International Journal of Electronics and Communications. Publication insights: Distributions of amplitude and phase for bivariate ... https://www.researchgate.net/.../304490979_Distributions_of_amplitude_and_phase_for... The distribution of amplitude, its moments and the distribution of phase are derived for thirty four flexible bivariate distributions, including the correlated bivariate ... Distributions of amplitude and phase for bivariate distributions - INFONA https://www.infona.pl/.../bwmeta1.element.elsevier-8f8899a6-f3b4-32c6-9a1a-0634508... by S Nadarajah - 2016 - Related articles The distribution of amplitude, its moments and the distribution of phase are derived for thirty four flexible bivariate distributions, including the correlated bivariate ... Multivariate Phase–Amplitude Cross-Frequency ... - NCBI - NIH https://www.ncbi.nlm.nih.gov › NCBI › Literature › PubMed Central (PMC) by RT Canolty - 2012 - Cited by 21 - Related articles Oct 18, 2011 - Phase–amplitude cross-frequency coupling (CFC)—where the phase of a low-frequency signal modulates the amplitude or power of a ... Unifying Amplitude and Phase Analysis: A Compositional Data ... https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4647844/ by PZ Hadjipantelis - 2015 - Cited by 12 - Related articles Jul 6, 2015 - A joint model for amplitude, phase, and duration is presented, which ... to compositional data analysis, a joint multivariate mixed effect model ... Multivariate Phase–Amplitude Cross-Frequency ... - IEEE Xplore ieeexplore.ieee.org/document/6051471/ by RT Canolty - 2012 - Cited by 21 - Related articles Phase-amplitude cross-frequency coupling (CFC)-where the phase of a ... Compared to bivariate methods, the PCE produces sparser estimates of CFC and can ... [PDF]Analysing Synchronization Phenomena from Bivariate Data by Means ... www.stat.physik.uni-potsdam.de/~mros/pdf/dresden_bivariate_data.pdf by M Rosenblum - Cited by 129 - Related articles Bivariate data are often encountered in the study of physiological systems. ... the instantaneous phase and amplitude for a signal s(t) via construction of. Multivariate Phase–Amplitude Cross-Frequency Coupling ... - Knight Lab knightlab.berkeley.edu/publications/detail/244/ Phase-amplitude cross-frequency coupling (CFC)-where the phase of a low-frequency signal modulates the amplitude or power of a high-frequency signal-is a ...
