6,328 research outputs found
Optimized Quality Factor of Fractional Order Analog Filters with Band-Pass and Band-Stop Characteristics
Fractional order (FO) filters have been investigated in this paper, with
band-pass (BP) and band-stop (BS) characteristics, which can not be achieved
with conventional integer order filters with orders lesser then two. The
quality factors for symmetric and asymmetric magnitude response have been
optimized using real coded Genetic Algorithm (GA) for a user specified center
frequency. Parametric influence of the FO filters on the magnitude response is
also illustrated with credible numerical simulations.Comment: 6 pages, 13 figures; 2012 Third International Conference on
Computing, Communication and Networking Technologies (ICCCNT'12), July 2012,
Coimbator
Fractional Spectral Moments for Digital Simulation of Multivariate Wind Velocity Fields
In this paper, a method for the digital simulation of wind velocity fields by
Fractional Spectral Moment function is proposed. It is shown that by
constructing a digital filter whose coefficients are the fractional spectral
moments, it is possible to simulate samples of the target process as
superposition of Riesz fractional derivatives of a Gaussian white noise
processes. The key of this simulation technique is the generalized Taylor
expansion proposed by the authors. The method is extended to multivariate
processes and practical issues on the implementation of the method are
reported.Comment: 12 pages, 2 figure
The fractional orthogonal derivative
This paper builds on the notion of the so-called orthogonal derivative, where
an n-th order derivative is approximated by an integral involving an orthogonal
polynomial of degree n. This notion was reviewed in great detail in a paper in
J. Approx. Theory (2012) by the author and Koornwinder. Here an approximation
of the Weyl or Riemann-Liouville fractional derivative is considered by
replacing the n-th derivative by its approximation in the formula for the
fractional derivative. In the case of, for instance, Jacobi polynomials an
explicit formula for the kernel of this approximate fractional derivative can
be given. Next we consider the fractional derivative as a filter and compute
the transfer function in the continuous case for the Jacobi polynomials and in
the discrete case for the Hahn polynomials. The transfer function in the Jacobi
case is a confluent hypergeometric function. A different approach is discussed
which starts with this explicit transfer function and then obtains the
approximate fractional derivative by taking the inverse Fourier transform. The
theory is finally illustrated with an application of a fractional
differentiating filter. In particular, graphs are presented of the absolute
value of the modulus of the transfer function. These make clear that for a good
insight in the behavior of a fractional differentiating filter one has to look
for the modulus of its transfer function in a log-log plot, rather than for
plots in the time domain.Comment: 32 pages, 7 figures. The section between formula (4.15) and (4.20) is
correcte
Fractional biorthogonal partners in channel equalization and signal interpolation
The concept of biorthogonal partners has been introduced recently by the authors. The work presented here is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers, hence, the name fractional biorthogonal partners. The conditions for the existence of stable and of finite impulse response (FIR) fractional biorthogonal partners are derived. It is also shown that the FIR solutions (when they exist) are not unique. This property is further explored in one of the applications of fractional biorthogonal partners, namely, the fractionally spaced equalization in digital communications. The goal is to construct zero-forcing equalizers (ZFEs) that also combat the channel noise. The performance of these equalizers is assessed through computer simulations. Another application considered is the all-FIR interpolation technique with the minimum amount of oversampling required in the input signal. We also consider the extension of the least squares approximation problem to the setting of fractional biorthogonal partners
- …