33,443 research outputs found
Order bound for the realization of a combination of positive filters
In a problem on the realization of digital ¯lters, initiated by Gersho and Gopinath [8], we extend and
complete a remarkable result of Benvenuti, Farina and Anderson [4] on decomposing the transfer function
t(z) of an arbitrary linear, asymptotically stable, discrete, time-invariant SISO system as a di®erence
t(z) = t1(z) ¡ t2(z) of two positive, asymptotically stable linear systems. We give an easy-to-compute
algorithm to handle the general problem, in particular, also the case of transfer functions t(z) with multiple
poles, which was left open in [4]. One of the appearing positive, asymptotically stable systems is always
1-dimensional, while the other has dimension depending on the order and, in the case of nonreal poles,
also on the location of the poles of t(z). The appearing dimension is seen to be minimal in some cases
and it can always be calculated before carrying out the realization
An efficient algorithm for positive realizations
We observe that successive applications of known results from the theory of
positive systems lead to an {\it efficient general algorithm} for positive
realizations of transfer functions. We give two examples to illustrate the
algorithm, one of which complements an earlier result of \cite{large}. Finally,
we improve a lower-bound of \cite{mn2} to indicate that the algorithm is indeed
efficient in general
Positive decomposition of transfer functions with multiple poles
We present new results on decomposing the transfer function t(z) of a linear, asymptotically stable, discrete-time SISO system as a difference t(z) = t(1)(z) - t(2)(z) of two positive linear systems. We extend the results of [4] to a class of transfer functions t(z) with multiple poles. One of the appearing positive systems is always 1-dimensional, while the other has dimension corresponding to the location and order of the poles of t(z). Recently, in [11], a universal approach was found, providing a decomposition for any asymptotically stable t(z). Our approach here gives lower dimensions than [11] in certain cases but, unfortunately, at present it can only be applied to a relatively small class of transfer functions, and it does not yield a general algorithm
Low passband sensitivity digital filters: A generalized viewpoint and synthesis procedures
The concepts of losslessness and maximum available power are basic to the low-sensitivity properties of doubly terminated lossless networks of the continuous-time domain. Based on similar concepts, we develop a new theory for low-sensitivity discrete-time filter structures. The mathematical setup for the development is the bounded-real property of transfer functions and matrices. Starting from this property, we derive procedures for the synthesis of any stable digital filter transfer function by means of a low-sensitivity structure. Most of the structures generated by this approach are interconnections of a basic building block called digital "two-pair," and each two-pair is characterized by a lossless bounded-real (LBR) transfer matrix. The theory and synthesis procedures also cover special cases such as wave digital filters, which are derived from continuous-time networks, and digital lattice structures, which are closely related to unit elements of distributed network theory
Computation Alignment: Capacity Approximation without Noise Accumulation
Consider several source nodes communicating across a wireless network to a
destination node with the help of several layers of relay nodes. Recent work by
Avestimehr et al. has approximated the capacity of this network up to an
additive gap. The communication scheme achieving this capacity approximation is
based on compress-and-forward, resulting in noise accumulation as the messages
traverse the network. As a consequence, the approximation gap increases
linearly with the network depth.
This paper develops a computation alignment strategy that can approach the
capacity of a class of layered, time-varying wireless relay networks up to an
approximation gap that is independent of the network depth. This strategy is
based on the compute-and-forward framework, which enables relays to decode
deterministic functions of the transmitted messages. Alone, compute-and-forward
is insufficient to approach the capacity as it incurs a penalty for
approximating the wireless channel with complex-valued coefficients by a
channel with integer coefficients. Here, this penalty is circumvented by
carefully matching channel realizations across time slots to create
integer-valued effective channels that are well-suited to compute-and-forward.
Unlike prior constant gap results, the approximation gap obtained in this paper
also depends closely on the fading statistics, which are assumed to be i.i.d.
Rayleigh.Comment: 36 pages, to appear in IEEE Transactions on Information Theor
Quantum mechanical which-way experiment with an internal degree of freedom
For a particle travelling through an interferometer, the trade-off between
the available which-way information and the interference visibility provides a
lucid manifestation of the quantum mechanical wave-particle duality. Here we
analyze this relation for a particle possessing an internal degree of freedom
such as spin. We quantify the trade-off with a general inequality that paints
an unexpectedly intricate picture of wave-particle duality when internal states
are involved. Strikingly, in some instances which-way information becomes
erased by introducing classical uncertainty in the internal degree of freedom.
Furthermore, even imperfect interference visibility measured for a suitable set
of spin preparations can be sufficient to infer absence of which-way
information. General results are illustrated with a proof-of-principle single
photon experiment.Comment: 8 pages, 3 figure
Improved Upper Bounds to the Causal Quadratic Rate-Distortion Function for Gaussian Stationary Sources
We improve the existing achievable rate regions for causal and for zero-delay
source coding of stationary Gaussian sources under an average mean squared
error (MSE) distortion measure. To begin with, we find a closed-form expression
for the information-theoretic causal rate-distortion function (RDF) under such
distortion measure, denoted by , for first-order Gauss-Markov
processes. Rc^{it}(D) is a lower bound to the optimal performance theoretically
attainable (OPTA) by any causal source code, namely Rc^{op}(D). We show that,
for Gaussian sources, the latter can also be upper bounded as Rc^{op}(D)\leq
Rc^{it}(D) + 0.5 log_{2}(2\pi e) bits/sample. In order to analyze
for arbitrary zero-mean Gaussian stationary sources, we
introduce \bar{Rc^{it}}(D), the information-theoretic causal RDF when the
reconstruction error is jointly stationary with the source. Based upon
\bar{Rc^{it}}(D), we derive three closed-form upper bounds to the additive rate
loss defined as \bar{Rc^{it}}(D) - R(D), where R(D) denotes Shannon's RDF. Two
of these bounds are strictly smaller than 0.5 bits/sample at all rates. These
bounds differ from one another in their tightness and ease of evaluation; the
tighter the bound, the more involved its evaluation. We then show that, for any
source spectral density and any positive distortion D\leq \sigma_{x}^{2},
\bar{Rc^{it}}(D) can be realized by an AWGN channel surrounded by a unique set
of causal pre-, post-, and feedback filters. We show that finding such filters
constitutes a convex optimization problem. In order to solve the latter, we
propose an iterative optimization procedure that yields the optimal filters and
is guaranteed to converge to \bar{Rc^{it}}(D). Finally, by establishing a
connection to feedback quantization we design a causal and a zero-delay coding
scheme which, for Gaussian sources, achieves...Comment: 47 pages, revised version submitted to IEEE Trans. Information Theor
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