Browsing by Subject "Invariance"

Now showing 1 - 3 of 3

Open Access
Cumulant-based parametric multichannel FIR system identification methods
(Elsevier, 1994) Özgen, M. T.; Alshebeili, S. A.; Çetin, A. Enis; Venetsanopoulos, A. N.
In this paper, “least squares” and recursive methods for simultaneous identification of four nonminimum phase linear, time-invariant FIR systems are presented. The methods utilize the second- and fourth-order cumulants of outputs of the four FIR systems of which the common input is an independent, identically distributed (i.i.d.) non-Gaussian process. The new methods can be extended to the general problem of simultaneous identification of three or more FIR systems by choosing the order of the utilized cumulants to be equal to the number of systems. To illustrate the effectiveness of our methods, two simulation examples are included.
Open Access
Quantum stereographic projection and the homographic oscillator
(American Physical Society, 1996) Hakioǧlu T.; Arik, M.
The quantum deformation created by the stenographic mapping from S2 to C is studied. It is shown that the resulting algebra is locally isomorphic to su(2) and is an unconventional deformation of which the undeformed limit is a contraction onto the harmonic oscillator algebra. The deformation parameter is given naturally by the central invariant of the embedding su(2). The deformed algebra is identified as a member of a larger class of quartic q oscillators. We next study the deformations in the corresponding Jordan-Schwinger representation of two independent deformed oscillators and solve for the deforming transformation. The invertibility of this transformation guarantees an implicit coproduct law which is also discussed. Finally we discuss the analogy between Poincaré's geometric interpretation of the quantum Stokes parameters of polarization and the stereographic projection as an important physical application of the latter.
Open Access
Signal processing issues in diffraction and holographic 3DTV
(IEEE, 2005) Onural, Levent; Özaktaş, Haldun M.
Image capture and image display will most likely be decoupled in future 3DTV systems. For this reason, as well as the need to convert abstract representations to display driver signals, and the need to explicitly consider diffraction and propagation effects, it is expected that signal processing issues will play a fundamental role in achieving 3DTV operation. Since diffraction between two parallel planes is equivalent to a 2D linear shift-invariant system, various signal processing techniques play an important role. Diffraction between tilted planes can also be modeled as a relatively simple system, leading to efficient discrete computations. Two fundamental problems are digital computation of the optical field due to a 3D object, and finding the driver signals for a given optical device so as to generate the desired optical field in space. The discretization of optical signals leads to several interesting issues; for example, it is possible to violate the Nyquist rate while sampling, but still maintain full reconstruction. The fractional Fourier transform is another signal processing tool which finds application in optical wave propagation.