5,375 research outputs found
Approximating Ideal Filters by Systems of Fractional Order
The contributions in this paper are in two folds. On the one hand, we propose a general approach for approximating ideal filters based on fractional calculus from the point of view of systems of fractional order. On the other hand, we suggest that the Paley and Wiener criterion might not be a necessary condition for designing physically realizable ideal filters. As an application of the present approach, we show a case in designing ideal filters for suppressing 50-Hz interference in electrocardiogram (ECG) signals
Filter bank based fractional delay filter implementation for widely accurate broadband steering vectors
Applications such as broadband angle of arrival estimation require the implementation of accurate broadband steering vectors, which generally rely on fractional delay filter designs. These designs commonly exhibit a rapidly decreasing performance as the Nyquist rate is approached. To overcome this, we propose a filter bank based approach, where standard fractional delay filters operate on a series of frequency-shifted oversampled subband signals, such that they appear in the filter's lowpass region. Simulations demonstrate the appeal of this approach
Implementation of accurate broadband steering vectors for broadband angle of arrival estimation
Motivated by accurate broadband steering vector requirements for applications such as broadband angle of arrival estimation, we review fractional delay filter designs. A common feature across these are their rapidly decreasing performance as the Nyquist rate is approached. We propose a filter bank based approach, which operates standard fractional delay filters on a series of frequency-shifted subband signals, such that they appear in the filters’ lowpass region. We demonstrate the appeal of this approach in simulations
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
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Variable domain transformation for linear PAC analysis of mixed-signal systems
This paper describes a method to perform linear AC analysis on mixed-signal systems which appear strongly nonlinear in the voltage domain but are linear in other variable domains. Common circuits like phase/delay-locked loops and duty-cycle correctors fall into this category, since they are designed to be linear with respect to phases, delays, and duty-cycles of the input and output clocks, respectively. The method uses variable domain translators to change the variables to which the AC perturbation is applied and from which the AC response is measured. By utilizing the efficient periodic AC (PAC) analysis available in commercial RF simulators, the circuit’s linear transfer function in the desired variable domain can be characterized without relying on extensive transient simulations. Furthermore, the variable domain translators enable the circuits to be macromodeled as weakly-nonlinear systems in the chosen domain and then converted to voltage-domain models, instead of being modeled as strongly-nonlinear systems directly
H^∞-Optimal Fractional Delay Filters
Fractional delay filters are digital filters to delay discrete-time signals by a fraction of the sampling period. Since the delay is fractional, the intersample behavior of the original analog signal becomes crucial. In contrast to the conventional designs based on the Shannon sampling theorem with the band-limiting hypothesis, the present paper proposes a new approach based on the modern sampled-data optimization that aims at restoring the intersample behavior beyond the Nyquist frequency. By using the lifting transform or continuous-time blocking the design problem is equivalently reduced to a discrete-time optimization, which can be effectively solved by numerical computation softwares. Moreover, a closed-form solution is obtained under an assumption on the original analog signals. Design examples are given to illustrate the advantage of the proposed method
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