252 research outputs found
Augmented Slepians: Bandlimited Functions that Counterbalance Energy in Selected Intervals
Slepian functions provide a solution to the optimization problem of joint
time-frequency localization. Here, this concept is extended by using a
generalized optimization criterion that favors energy concentration in one
interval while penalizing energy in another interval, leading to the
"augmented" Slepian functions. Mathematical foundations together with examples
are presented in order to illustrate the most interesting properties that these
generalized Slepian functions show. Also the relevance of this novel
energy-concentration criterion is discussed along with some of its
applications
Fast Algorithms for the computation of Fourier Extensions of arbitrary length
Fourier series of smooth, non-periodic functions on are known to
exhibit the Gibbs phenomenon, and exhibit overall slow convergence. One way of
overcoming these problems is by using a Fourier series on a larger domain, say
with , a technique called Fourier extension or Fourier
continuation. When constructed as the discrete least squares minimizer in
equidistant points, the Fourier extension has been shown shown to converge
geometrically in the truncation parameter . A fast algorithm has been described to compute Fourier extensions for the case
where , compared to for solving the dense discrete
least squares problem. We present two algorithms for
the computation of these approximations for the case of general , made
possible by exploiting the connection between Fourier extensions and Prolate
Spheroidal Wave theory. The first algorithm is based on the explicit
computation of so-called periodic discrete prolate spheroidal sequences, while
the second algorithm is purely algebraic and only implicitly based on the
theory
Noise Effects on a Proposed Algorithm for Signal Reconstruction and Bandwidth Optimization
The development of wireless technology in recent years has increased the demand for channel resources within a limited spectrum. The system\u27s performance can be improved through bandwidth optimization, as the spectrum is a scarce resource. To reconstruct the signal, given incomplete knowledge about the original signal, signal reconstruction algorithms are needed. In this paper, we propose a new scheme for reducing the effect of adding additive white Gaussian noise (AWGN) using a noise reject filter (NRF) on a previously discussed algorithm for baseband signal transmission and reconstruction that can reconstruct most of the signal’s energy without any need to send most of the signal’s concentrated power like the conventional methods, thus achieving bandwidth optimization. The proposed scheme for noise reduction was tested for a pulse signal and stream of pulses with different rates (2, 4, 6, and 8 Mbps) and showed good reconstruction performance in terms of the normalized mean squared error (NMSE) and achieved an average enhancement of around 48%. The proposed schemes for signal reconstruction and noise reduction can be applied to different applications, such as ultra-wideband (UWB) communications, radio frequency identification (RFID) systems, mobile communication networks, and radar systems
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