Distortionless Condition Research Articles

Performance Limit of Fiber-Longitudinal Power Profile Estimation Methods

This paper presents analytical results on longitudinal power profile estimation (PPE) methods, which visualize signal power evolution in optical fibers at a coherent receiver. The PPE can be formulated as an inverse problem of the nonlinear Schr\"odinger equation, where the nonlinear coefficient (and thus signal power) is reconstructed from boundary conditions, i.e., transmitted and received signals. Two types of PPE methods are reviewed and analyzed, including correlation-based methods (CMs) and minimum-mean-square-error-based methods (MMSEs). The analytical expressions for their output power profiles and spatial resolution are provided, and thus the theoretical performance limits of the two PPE methods and their differences are clarified. The derived equations indicate that the estimated power profiles of CMs can be understood as the convolution of a true power profile and a smoothing function. Consequently, the spatial resolution and measurement accuracy of CMs are limited, even under noiseless and distortionless conditions. Closed-form formulas for the spatial resolution of CMs are shown to be inversely proportional to the product of a chromatic dispersion coefficient and the square of signal bandwidth. With MMSEs, such a convolution effect is canceled out and the estimated power profiles approach a true power profile under a fine spatial step size.

Distortionless condition for microlens images in light field imaging

Distortionless condition for microlens images in light field imaging

On the Distortionless Propagation in Multiconductor Transmission Lines

In this paper, we investigate the distortionless conditions for multiconductor transmission lines (MTLs) with frequency-independent per-unit-length (p.u.l.) parameters. In fact, the well-known distortionless Heaviside condition is valid only for single-conductor transmission lines. The MTL is modeled using the delayed Green’s-function-based method recently proposed by the authors. In this method, the impedance matrix is described in terms of a rational part, which accounts for the low-frequency behavior, and a hyperbolic part, which determines the high-frequency response of the MTL. We find that the hyperbolic part is already distortionless at high frequency and that this property can be used to identify the p.u.l. parameters of the distortionless lossy MTL associated with the original line. To serve this purpose, the line is decoupled using a frequency-independent modal decomposition. The Heaviside condition can be enforced in the modal domain on each of the single-conductor decoupled lines. The features of the distortionless lines in the modal domain are preserved in the physical domain as a consequence of the real-valued similarity transform. The numerical results demonstrate that the new line completely characterizes the distortionless propagation of a generic MTL with frequency-independent p.u.l. parameters. The proposed formulation could be used in the optimization design process by enforcing the distortionless condition along with other design constraints.

Stability analysis of the telegrapher’s equations with dynamic boundary condition

This paper is concerned with the stability analysis of a distributed parameter circuit with dynamic boundary condition. The distributed parameter circuit is written by the telegrapher’s equations whose boundary condition is described by an ordinary differential equation. First of all, it is shown that, for any physical parameters of the circuit, the system operator generates an exponentially stableC0-semigroup on a Hilbert space. However, it is not clear whether the decay rate of the semigroup is the most precise one. In this paper, the spectral analysis is conducted for the system satisfying the distortionless condition, and it is shown that the semigroup satisfies the spectrum determined growthcondition.

Capacity and Error Performance of Reduced-Rank Transmitter Multiuser Preprocessing Based on Minimum Power Distortionless Response

In this contribution we first derive a transmitter multiuser preprocessing (TMP) scheme for a general multiuser multiple-input-multiple-output (MIMO) system based on the minimum power distortionless response (MPDR) criterion, which minimizes the power in the context of a given downlink mobile terminal (MT) under the distortionless condition. This optimization problem results in a solution, which has the same form as the minimum mean-square error (MMSE) multiuser detection (MUD). Hence, we then extend the well-known rank-reduction techniques in MMSE-MUD to the MPDR-TMP in order to mitigate the possible implementation problems of the MPDRTMP. In our study three classes of rank-reduction algorithms are considered, which are derived, respectively, based on the eigen-analysis methods of principal components (PC) and crossspectral metrics (CSMs) as well as on the Taylor polynomial approximation (TPA) approach, which does not depend on the eigen-analysis. In this contribution both the capacity and error performance of a downlink space-division multiple-access (SDMA) system is investigated, when either the full-rank or reduced-rank MPDR-TMP is invoked. From our study and simulation results, it can be shown that the MPDR-TMP scheme is highly efficient for achieving the capacity and for suppressing the multiuser interference (MUI). The reduced-rank techniques can be employed by the MPDR-TMP, so as to reduce its implementation complexity while achieving the near full-rank performance of the full-rank MPDR-TMP.

From, Obscurity to Enigma: The Work of Oliver Heaviside, 1872–1889 by Ido Yavetz

TECHNOLOGY AND CULTURE Book Reviews 765 always “we found this” or “we did that.” Yet there is no sense of the communal work ofthe lab in these pages, and only in the faintest asides do we glimpse the all-night sprees that made the Edison labo­ ratory so unique and so productive. Faced with the enormity of their task, the editors of the Edison Papers have toned down their expectations; what began as the first full record of Edison’s life is now “a guide into the much fuller rec­ ord presented on microfilm” (p. xxviii). Will these twenty projected volumes enable us to rewrite Edison’s life story and show us new ways to understand his creativity, as was previously claimed? Volume three is too early to tell. Andre Millard Dr. Millard is professor of history at the University of Alabama at Birmingham and the author of Edison and the Business of Innovation (Baltimore: Johns Hopkins University Press, 1990). From, Obscurity to Enigma: The Work ofOliver Heaviside, 1872-1889. By Ido Yavetz. Basel and Boston, Mass.: Birkhauser Verlag, 1995. Pp. 334; figures, appendices, notes, bibliography, index. $89.00 (hard­ cover) . As the title of Yavetz’s book suggests, Oliver Heaviside is an enig­ matic figure. He is well known to us for three achievements. As an electrical engineer he first suggested the circuital condition that guarantees the distortionless transmission of messages in long-dis­ tance telephony. As a physicist, he not only reformulated Maxwell’s complicated formula into a few neat equations but proposed in 1902 the existence of an ionic layer (the so-called Heaviside-Kennelly layer) in the sky that made possible the transmission of electromag­ netic waves across the Atlantic. As a mathematician, he devised vec­ tor algebra and initiated operational calculus. These achievements in different fields were made by a man with no higher education in science or engineering. Heaviside is also a man of irony. Neither he nor the British Maxwellians nor the British electrical engineers developed his theory of distortionless transmission into a practical technology. (Michael Pupin and George Campbell in the United States first invented the practical loading coil that materialized Heaviside’s theory.) When Heaviside suggested the hypothesis of the ionic layer in 1902, he actually thought it less plausible than the hypothesis of the transmis­ sion of waves along the surface of the earth. His new mathematics was hardly understood by his contemporaries, including his Maxwel­ lian friends, and it rather made him more isolated from the scientific and engineering communities of his day. Yavetz explores in detail Heaviside’s major works between 1872 766 Book Reviews TECHNOLOGY AND CULTURE and 1889. Interesting in this story is how Heaviside moved between Maxwell’s field theory and the practical world of telegraphic and telephonic engineering. Heaviside started his career as a telegra­ phist in 1872 and worked mainly on linear circuit theory between 1872 and 1881. Working on this topic, he encountered the dynamic nature of electrical current, which led him to Maxwell’s electromag­ netic theory. From 1882 and 1885, he devoted himselfto reformulat­ ing Maxwell’s field theory by using a new mathematical tool, vector algebra. In 1885 he arrived at the radical conclusion that in a cur­ rent-carrying wire energy flows not inside the wire, but outside. This led him to a new field-theoretic understanding of the skin effect. In 1887-88, he was involved in a bitter debate with William H. Preece, a chief engineer of the Post Office, over the issue of the distor­ tionless cable. Yavetz suggests that Heaviside obtained the distor­ tionless condition by thinking concretely about the relationship be­ tween the parameters (such as resistance, capacitance, inductance, and leakance) involved in a transmission line in telegraphy and tele­ phony engineering, rather than by simply solving Maxwell’s field equations. Heaviside then presented his distortionless condition as a “royal road” by which engineers could be brought to the abstract realm of Maxwell’s field theory and electrodynamics. Heaviside was a mediator between Maxwell’s field theory and elec­ trical engineering. As a “teacher,” he wanted practical engineers to think of technological phenomena in terms of Maxwell’s dynamical fields. He also forced...

Waveform distortion and distortion power

The distortionless conditions between nonsinusoidal voltages and currents are deduced, and the definitions of distortion current, distortion voltage and distortion power are introduced. The authors discuss some current formulas for nonsinusoidal power. In general the aim of compensation is not to reduce the distortion power but to raise the power factor to one. These two objectives are not directly related. >

Synthesis of impedance transformable filter by artificial nonuniform transmission line with distortionless property

AbstractThis paper proposes a simple synthesis method of impedance matching and transforming filter. This method is based on the use of a multistage ladder network simulating a nonuniform transmission line. When the filter charactersitic functions defined in this paper satisfy the distortionless conditions of the voltage and current waveforms the artificial transmission line mentioned above almost operates as an ideal lowpass filter. As an example the characteristics of 1 ‐ 2ω transformable type lowpass filter are evaluated and the obtained results almost satisfy the conditions for the ideal filter.

Design theory of a distortionless nonreflective all‐pass impedance transformer using a nonuniform transmission line

AbstractTraditionally, the use of nonuniform transmission lines has been suggested for designing a wideband impedance transformer. However, no rigorous design method has been found. This paper proposes two rigorous methods each for designing distortionless, nonreflective all‐high‐ and low‐impedance transformers which are simple and of minimum attenuation, based on the distortionless conditions of the voltage and current waveforms in a nonuniform transmission line. The methods make only C(x) or L(x) of the primary constants of the transmission line uniform. It was found sufficient that these distributions be of square or inverse square. According to the design method, we designed a 50 to 75 ω transformer which is subsequently modeled by a 100‐stage ladder network. We performed experiments in the dc ‐ 10 MHz frequency domain as well as in the time domain. The experiment has been proceeded in accordance with the theory and the effectiveness of the proposed design method and the validity of the distortionless theory of nonuniform transmission line are proved.

Distortionless theory of one‐dimensional non‐uniform transmission lines

AbstractFor transmitting distortionless arbitrary waveforms over set‐ups with different impedances, the nonuniform lines have been used for a long time by wide‐band impedance‐transform and matching. But rigorous theory is still lacking in treating the basic problems concerning the relationship between the distortionless waveform and the nonuniform line distribution, i.e., the distortionless conditions or the impedance‐matching conditions for the nonuniform lines. This paper first investigates the voltage/current transfer‐functions over any line interval and the local propagation constant. It is then clarified that there exist on the one‐dimensional nonuniform line essentially six localized distortionless conditions for the voltage/current waveforms. Next, the distortionless wave quantities and characteristics, the finitely long line analysis, as well as method of excitation (matching) of the distortionless wave, are presented. Finally, it is shown that all‐pass impedance transformer, attenuator and phase shifter can be realized by using the distortionless line.