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Circuit Theory, IEEE Transactions on

Issue 4 • Date July 1973

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Displaying Results 1 - 25 of 29
  • Numerical inversion of the z-transform

    Publication Year: 1973 , Page(s): 419 - 420
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    A numerical method is developed for determining a sequence h[k] in terms of the values H(z_n) of its z -transform H(z) at a set of points z_n along the real z -axis. In the analysis, a new class of orthogonal sequences is introduced. View full abstract»

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  • Author's reply to 'Comment on 'General solution to the Spanning Tree Enumeration problem in Multigraph Wheels''

    Publication Year: 1973 , Page(s): 454 - 455
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  • Comment on "General Solution to the Spanning Tree Enumeration Problem in Multigraph Wheels

    Publication Year: 1973 , Page(s): 454
    Cited by:  Papers (2)
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  • A general analysis for the time-invariant multirate digital filter

    Publication Year: 1973 , Page(s): 450 - 452
    Cited by:  Papers (1)
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    An analysis is presented for obtaining a general transfer function for a digital filter, with a number of shift sequences in each pulse-repetition interval, as initially described by Fjällbrant. This type of filter has been given the term "multirate filter." The analysis results in a complex convolution integral which is evaluated to produce the transfer function resulting from the multirate processing. Some examples of the use of this technique in certain quantization problems are given. View full abstract»

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  • A modified moment method for the approximate evaluation of convolution

    Publication Year: 1973 , Page(s): 452 - 454
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    The response g(t) of a linear system is approximated by the sum c_{1}f(t - t_{1}) +\cdots + c_{n}f(t - t_{n}) involving delays of the input f(t) . The constants c_i and t_i are determined in terms of the moments of the impulse response h(t) . The resulting frequency fit equals 2n . View full abstract»

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  • Computation of bounds for digital filter quantization errors

    Publication Year: 1973 , Page(s): 391 - 396
    Cited by:  Papers (19)
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    Spectral theory of operators is used to determine a general procedure for determining bounds on the difference between the states and outputs of a finite precision fixed-point digital filter and its infinite precision ideal counterpart. The results bound quantization errors for transients as well as limit cycles and apply when input signals are present. The procedure is extended to digital filters associated with difference equations, including the important special case of the basic second-order section. View full abstract»

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  • An approach to the sensitivity and statistical variability of biquadratic filters

    Publication Year: 1973 , Page(s): 382 - 390
    Cited by:  Papers (20)
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    In attempting to predict the behavior of a filter during and at the end of its life, one is led to the study of sensitivity and then one must compare worst-case and expected results. This paper shows that sensitivity can be expressed as a sum of terms, where each term is the product of two sensitivity functions. One is the frequency-dependent sensitivity of the gain to the transfer function coefficients (the gain-to-coefficient sensitivity) and the other is the well-known coefficient-to-component sensitivity. The gain-to-coefficient sensitivity clearly shows that the gain of a biquadratic function is far more sensitive to changes in the resonant frequency f_0 than to changes in Q only near the 3-dB frequencies. The gain is actually less sensitive to changes in f_0 near f_0 . It is also shown that coefficient-to-component sensitivities for resistors and capacitors have no effect on the mean value of the change in the gain, but have marked effects on the standard deviation. View full abstract»

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  • Topological considerations on minimal sets of variables describing an LCR network

    Publication Year: 1973 , Page(s): 335 - 340
    Cited by:  Papers (3)
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    In a linear resistive network, a maximal set, called a basis, of variables that are linearly independent with respect to coefficients that are rational functions in edge admittances is determined. It is shown that the basis is an important concept in linear network analysis in the sense that any network equation can uniquely and minimally be expressible in terms of the elements in a basis. In order to characterize the algebraic structure of the variables in connection with the basis, existence theorems on mappings from given variables to all the source currents and voltages are presented. View full abstract»

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  • Topological formulas for networks with ideal transformers

    Publication Year: 1973 , Page(s): 425 - 426
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  • Exponential approximation via closed-form Gauss-Newton method

    Publication Year: 1973 , Page(s): 361 - 369
    Cited by:  Papers (4)
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    A convergent gradient descent technique is provided for the approximation of functions of time from their Laplace transforms. The approximation is composed of a finite series of exponential functions. Both the complex coefficients and exponents of the exponential terms are adjusted to reduce the integral squared error at each iteration. The novel feature of the present method is that all parameters are adjusted through the use of explicit formulas. This overcomes the usual numerical difficulties associated with the inversion of ill-conditioned matrices. Finally, the utility of the proposed method is demonstrated by its performance on certain examples chosen to allow comparison with previously developed methods. View full abstract»

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  • A simple all-pass network with complex poles and zeros

    Publication Year: 1973 , Page(s): 445 - 446
    Cited by:  Papers (2)
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    A modified Wien bridge circuit capable of realizing the second-order all-pass function with complex poles and zeros is presented. The effect of the limited frequency response of the amplifier is examined and a method for compensation is given along with a design example. View full abstract»

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  • An analysis of distortion in bipolar transistors using integral charge control model and Volterra series

    Publication Year: 1973 , Page(s): 341 - 351
    Cited by:  Papers (24)
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    A new analysis approach to understand and minimize nonlinear distortion in bipolar transistors is presented. It employs a recently developed nonlinear device model, known as the integral charge control model, and a powerful analysis tool: the Volterra series representation. The salient analytical features of this paper are: a simple representation of the Volterra transfer functions of the transistor, compact expressions for frequency-dependent distortion coefficients, and physically meaningful asymptotic low- and high-frequency distortion coefficients. The analytical results have been experimentally verified. Finally, specific design examples are furnished to illustrate the powerful nature of the above analytical expressions. View full abstract»

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  • Open-circuit voltage transfer-function synthesis using the generalized positive impedance converter

    Publication Year: 1973 , Page(s): 432 - 434
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    An open-circuit voltage transfer-function synthesis procedure is presented that realizes any arbitrary real rational function in the complex variable s. The procedure makes use of an active device referred to as the generalized positive impedance converter (GPIC). The synthesis procedure yields a network realization that 1) requires the minimum number of capacitors necessary for the synthesis, 2) is compatible with integrated-circuit fabrication techniques, and 3) has low sensitivity. View full abstract»

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  • A theory of algebraic n-ports

    Publication Year: 1973 , Page(s): 370 - 382
    Cited by:  Papers (13)
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    The foundational aspects of an important subclass of timeinvariant nonlinear n -ports are dealt with; namely, the class of algebraic n -ports that includes, among other things, resistors, inductors, capacitors, and memristors as special cases. Sufficient conditions that guarantee an algebraic n -port to admit all 2^n hybrid representations are given. Both global and local characterizations are considered in detail. In particular, certain global properties are shown to be invariants relative to the various modes of hybrid representation. The concept of reciprocity is explored in depth and shown to play an important role in determining such global properties as losslessness and passivity. Several generalized potential functions are defined for reciprocal algebraic n -ports. These functions are then used to derive a number of interesting circuit theoretic properties for nonlinear n -ports. View full abstract»

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  • Fault isolation with insufficient measurements

    Publication Year: 1973 , Page(s): 416 - 417
    Cited by:  Papers (7)
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    A technique is given for approximating the "most likely" values of the internal components of a system when insufficient measurements have made their exact determination impossible. It is limited to linear systems, all of whose measurements are made at a single frequency and whose connections can be represented by sets of linear algebraic equations. The technique is based on the Moore-Penrose generalized inverse of a linear approximation of the system function and is formulated in terms of the component-connection model of a largescale dynamical system. View full abstract»

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  • A new technique for symbolic active network analysis by computer

    Publication Year: 1973 , Page(s): 426 - 429
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    Topological formulas are obtained for networks containing voltage-dependent current sources, current-dependent voltage sources, voltage-dependent voltage sources, and current-dependent current sources. The formulas are expressed entirely in terms of trees of a single simply obtained graph. Each tree is multiplied by the appropriate product of transmittances, and the sign associated with a term is given. A simple example is provided. View full abstract»

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  • Writing state equations for an improper network without having to invert matrices

    Publication Year: 1973 , Page(s): 420 - 422
    Cited by:  Papers (1)
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    A method for writing state equations for an improper network without having to invert matrices is presented. The method employs substitution theorem as well as superposition principle. View full abstract»

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  • Analog and digital filtering in multiplex communication systems

    Publication Year: 1973 , Page(s): 408 - 415
    Cited by:  Papers (6)  |  Patents (1)
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    The design and realization of filters in communication systems have been influenced by various technologies over the past years. Beyond the traditional LC-filter technology, a sophisticated crystal-filter and, more recently, a mechanical-filter technology have been developed. Each filter technology is applied in multiplex communication systems according to its inherent technical and economical advantages. With the economical acceptability of integrated circuits, two more filter technologies begin to compete with the established filter concepts. Active filters in thin-film realization show promising aspects for certain applications and for mass production. Digital-filter techniques seem to be, understood well enough that it is worth looking for their application in multiplex systems. The various filter techniques, new and old, are set into the perspective of their economical use in multiplex communication systems. View full abstract»

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  • Topological equivalence of inductorless ladder structures using integrators

    Publication Year: 1973 , Page(s): 434 - 437
    Cited by:  Papers (7)
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    The leapfrog ladder synthesis technique is shown to be topologically equivalent to gyrator-simulated inductance methods of simulating ladder filters. The topological equivalence employs nullors to show that the leapfrog structure is equivalent to embedding a grounded negative element between two matched negative immittance inverters. Low-pass and bandpass ladder networks may be obtained as interconnected biquads by inspection of the low-pass prototype LC ladder. View full abstract»

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  • Hilbert transforms of periodic functions

    Publication Year: 1973 , Page(s): 454
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  • On sequential refinement schemes for recursive digital filter design

    Publication Year: 1973 , Page(s): 396 - 401
    Cited by:  Papers (1)
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    A linear synthesis technique is developed for a recursive digital filter which approximates the desired discrete impulse response. Sequential schemes which can be used to refine the preliminary filter design are developed for three distinct cases in which the output sequence number, the filter order, and the number of the numerator coefficients of the transfer function are allowed to vary separately. By use of matrix inversion lemmas, the new sets of filter coefficients are obtained sequentially based on the old estimates and the new data without having to repeat the entire design procedure. View full abstract»

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  • The predictability of certain optimum finite-impulse-response digital filters

    Publication Year: 1973 , Page(s): 401 - 408
    Cited by:  Papers (5)
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    Some of the properties of optimal solutions to the finite-impulse-response low-pass filter design problem are discussed. These solutions are optimum in the sense of discrete Chebyshev approximation over a union of closed compact sets, i.e., the error of approximation exhibits at least (N + 3)/2 alternations (of equal amplitude) over the frequency ranges of interest, where N is the duration of the filter impulse response in samples. It has been shown that, in certain special cases, the solution can exhibit (N + 5)/2 alternations of equal amplitude. These solutions have been called extraripple filters because of the extra alternation that is present. How these extraripple solutions can, within bounds, be scaled to yield additional solutions, which are still optimal over new frequency ranges, is shown.' Thus an infinite number of optimal low-pass filters may be obtained directly from a finite number of extraripple solutions. An interpretation of the various types of optimal filters, in terms of locations of the zeros of the z - transform polynomial, is also given. View full abstract»

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  • Redundant filters

    Publication Year: 1973 , Page(s): 446 - 450
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    The problem of interconnecting several identical filters so as to obtain a filter which is both nominally closer to ideal and has lower sensitivity than the original filter is studied. A feedforward design for such a redundant filter is given which is applicable to filters having any specified passband, and the results of simulations illustrating the improvement in nominal behavior and sensitivity resulting from redundancy are presented. View full abstract»

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  • A new approach to the synthesis of stiffly stable linear multistep formulas

    Publication Year: 1973 , Page(s): 352 - 360
    Cited by:  Papers (6)
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    The analysis of the linear multistep integration formulas is shown to be considerably simplified by associating to each formula a special function termed the canonical fraction. In particular, the canonical fraction approach provides a decoupling of the problem of stability from the problem of accuracy and allows the derivation of most of the properties of A -stable and stiffly stable formulas as simple restatements of elementary electrical network theorems. Results obtained tend to show that linear multistep formulas, which are much more efficient than the ones commonly used today, exist. View full abstract»

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  • Design of active RC filters with zero gain-sensitivity product

    Publication Year: 1973 , Page(s): 441 - 445
    Cited by:  Papers (5)
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    A root locus with respect to the active parameter for any second-order active RC filter is circular with center on the real axis. It is shown that for any pole pair Q and pole frequency \omega _0 , the circular root locus centered at -2Q \omega _0 on the real axis and of radius \omega _{0}\sqrt {4Q^{2}-1} exhibits zero Q -sensitivity and zero gain-sensitivity product (GSP) with respect to the active parameter. Furthermore, realization techniques to achieve zero Q -sensitivity and zero GSP for prescribed Q and \omega _0 are outlined. Experimental results agree closely with the theoretical expectations. View full abstract»

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