caa a22 4500 606204911 CHVBK 20210128101005.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00034-014-9932-0 doi (NATIONALLICENCE)springer-10.1007/s00034-014-9932-0 Stochastic Formulation of (a,b,c,d)-Bandlimited Signal Reconstruction [Elektronische Daten] [Daiping Song, Hui Zhao] Many reconstruction algorithms for bandlimited signals associated with linear canonical transform have been proposed. However, these reconstruction algorithms have assumed a deterministic signal with no noise. This assumption is almost never satisfied in real applications. Deterministic formulations do not accurately describe the random nature of the reconstruction problem when the signal is best considered as a random process, possibly corrupted by noise. In this paper, we formulate the reconstruction problem of bandlimited signal associated with linear canonical transform within a stochastic framework. A stochastic, minimum mean squared error reconstruction algorithm from noisy observations is proposed, from which four commonly used reconstruction algorithms for different stochastic models are derived. By the derived algorithms, the relationship between the theories for the stochastic and deterministic cases is clarified. The relationship between the theories for the noise-free and noisy cases is also clarified. Springer Science+Business Media New York, 2014 Reconstruction nationallicence Minimum mean squared error nationallicence Stochastic processes nationallicence $$(a, b, c, d)$$ ( a , b , c , d ) -Bandlimited signal nationallicence Song Daiping The State Key Laboratory of Mechanical Transmission, Chongqing University, 40044, Chongqing, China aut Zhao Hui School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, 400065, Chongqing, China aut Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/6(2015-06-01), 2053-2064 0278-081X 34:6<2053 2015 34 34 https://doi.org/10.1007/s00034-014-9932-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00034-014-9932-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Song Daiping The State Key Laboratory of Mechanical Transmission, Chongqing University, 40044, Chongqing, China aut NATIONALLICENCE 700 1- Zhao Hui School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, 400065, Chongqing, China aut NATIONALLICENCE 773 0- Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/6(2015-06-01), 2053-2064 0278-081X 34:6<2053 2015 34 34