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Circuits and Systems, IEEE Transactions on

Issue 3 • Date March 1975

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Displaying Results 1 - 19 of 19
  • Editorial

    Page(s): 161
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    Freely Available from IEEE
  • Low-sensitivity digital ladder filters

    Page(s): 168 - 176
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    A class of low-sensitivity digital ladder filters may be realized in the voltage-current domain by direct analogy with the continuous resistively terminated LC ladder filter. The problem of unrealizability that is implied by delay-free loops in the discrete signal flow graph is overcome by using transformations that correspond to LC elements that exhibit finite Cube factors. The resultant deterioration in the passband of the transfer function is determined from the Blowstein LC ladder sensitivity theory and is, thereby, shown to be low valued at high sampling frequencies. The sensitivity properties of this class of digital ladder filters are directly analogous to the LC prototype because each LC element is replaced by a digital multiplier. Consequently, if maximum power transfer is approximately maintained throughout the passband of the LC prototype, then the first-order sensitivity of the corresponding digital transfer function to multiply a coefficient quantization is necessarily low valued. View full abstract»

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  • Frequency domain criteria for the absence of zero-input limit cycles in nonlinear discrete-time systems, with applications to digital filters

    Page(s): 232 - 239
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    On the basis of a theorem of Barkin, a number of criteria are derived which give sufficient conditions for the absence of zero-input limit cycles in discrete-time and especially digital systems. These criteria are formulated in the frequency domain and provide a possibility of investigating the absence of a zero-input limit cycle of a specific lengthN. Depending on the particular characteristics of the nonlinearities and the number of nonlinearities in the system, different criteria are obtained. Application of the criteria results in most cases in a linear programming problem. The solutions to this problem for the case of a second-order digital filter with one and with two quantization nonlinearities are discussed. View full abstract»

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  • Finite-duration digital filter design by use of cubic splines

    Page(s): 204 - 207
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    Cubic natural splines have been used to design finite duration digital filters. The design is carried out in the time domain. Cubic splines can now be used to design digital filters by a mere algebraic substitution in a formula. View full abstract»

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  • Decision-directed recursive image enhancement

    Page(s): 286 - 293
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    A nonlinear method of estimating pictorial data from noisy observations is considered. The data is assumed to be composed of an object with one texture in the background. An edge detection technique using likelihood functions is used to decide if an incoming picture element is a member of the object or the background. Then, the picture element is directed to one of the two Kalman filters designed based upon the statistics of the object or the background accordingly. View full abstract»

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  • Digital image restoration under a regression model

    Page(s): 252 - 266
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    In this paper, image-restoration techniques based upon a regression model are analyzed and verified by computer simulation. A regression model is formulated to describe image blurring, additive noise, physical image sampling, and quadrature representation. Classical estimation methods utilized for image restoration are described and related to one another. Restorations obtained by these classical techniques are shown to be poor because of noise disturbances and the ill conditioning of the image-degradation regression model. Constrained restoration methods which avoid ill conditioning problems are introduced. Computer simulations demonstrate that a boundedness constraint on the brightness of a reconstructed image provides significantly improved restorations as compared to unconstrained methods. View full abstract»

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  • Limit cycle oscillations in first-order two-dimensional digital filters

    Page(s): 246 - 251
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    In first-order two-dimensional digital filters, limit cycles can occur as a result of rounding off after multiplication. Such limit cycles are discussed for the case of fixed point arithmetic. The period and bounds for the amplitude of the limit cycles existing in the rows, columns, and diagonals are obtained. It is proved here that the bound obtained is the tightest possible bound for the amplitude of the limit cycles. Several (sufficient or necessary) conditions for the existence of the limit cycles in the rows, columns, and diagonals are also given. View full abstract»

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  • Digital simulation and processing applied to coherent imaging systems

    Page(s): 293 - 303
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    A synthetic-aperture system, such as a coherent sidelooking radar, records a quasi-hologram of the scene which is illuminated by the transmitted radiation. Conventionally, the recorded pattern is converted to an image using optical processing. However, optical processing does not always provide the flexibility, dynamic range, or accuracy necessary to produce optimum images. Digital processing offers the potential for more generalized processing operations which provide large dynamic range and can correct for system aberrations and other image degrading effects. This paper presents a general method of digital processing which has been developed for synthetic aperture systems. Results are given for processing of radar, sonar, and millimeterwave recordings. View full abstract»

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  • Stability criteria for two-variable polynomials

    Page(s): 185 - 189
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    Recursive algebraic algorithms are developed for testing various stability properties of two-variable polynomials in a finite number of steps. Stability is tested with respect to either the half-plane or the unit circle applying only two times the equivalent of the Routh or Marden test, regardless of the degree of the polynomial. View full abstract»

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  • A unified analysis of multirate and periodically time-varying digital filters

    Page(s): 162 - 168
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    A unified approach to the analysis of periodically timevarying digital filters is introduced. It is shown that this method may be used to describe both time and frequency domain responses. By considering multirate filters as a special class of periodically time-varying filters we have characterized the frequency response of a general multirate filter. A time domain synthesis procedure for periodically varying difference equations is also presented. View full abstract»

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  • Restoration of motion degraded images

    Page(s): 278 - 286
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    A new recursive procedure, based on state-space techniques and the use of a Kalman-Bucy filter is presented to solve the restoration problem of images degraded by motion in one direction. Both the noisefree and the noisy cases are considered. View full abstract»

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  • Realizations of two-dimensional recursive digital filters

    Page(s): 177 - 184
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    Algorithms are derived for realization of two-dimensional recursive digital filters using direct forms and continued fraction expansions. Included is a test for continued fraction expansion which at the same time determines the expansion coefficients. Transposed structures are also discussed, and a comparison is made of the various realizations. View full abstract»

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  • Suppression of parasitic oscillations in wave digital filters

    Page(s): 239 - 246
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    Parasitic oscillations can occur in digital filters due to the granularity of the signal and to overflow. It is shown that for wave digital filters, the earlier concept of pseudopower leads to a function called stored pseudopower, from which a simple criterion guaranteeing absence of parasitic oscillations can be derived. For fixed-point two's-complement arithmetic, this criterion can be taken into account by particularly simple requirements for the adaptor output signals. A special type of calculus is developed which makes it possible to derive the corresponding simple requirements for the chopping operations at the various stages of the signal processing in the adaptors. The method is extended to cover scaling. View full abstract»

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  • An analysis of quantization error in digital filters based on interval algebras

    Page(s): 223 - 232
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    Interval algebras are introduced as media in which to simulate digital filters for the purpose of analyzing quantization effects due to finite wordlength. The theory presented forms the basis of a computer-aided analysis scheme which generates confidence interval error bounds on the time domain response of a digital filter. The techniques are applicable to filters of arbitrary order and configuration implemented in either fixed or floating-point arithmetic. Experimental data is presented for a fourth-order low-pass Butterworth filter realized with fixed-point arithmetic in the direct, canonical direct, parallel, cascade, and ladder configurations. An example of Parker and Hess is used to illustrate the bounding limit cycles with interval techniques. View full abstract»

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  • Timing jitter in digital filtering of analog signals

    Page(s): 218 - 223
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    Effects of timing jitter in digital filtering of analog signals are analyzed. Jitter may be introduced into the system when the incoming analog signal is being sampled and when the samples of the output of the digital filter are being read out for reconstruction back into an analog signal. These two jitters are called readin and readout jitters, respectively. General expressions are derived for the spectrum of the analog output in the presence of jitter and for the mean-square error introduced by the jitter. Four specific cases are then considered. They are readin jitter only, readout jitter only, independent jitter, and locked jitter. In each case, the general expression for the spectrum of the analog output is reduced to a more explicit form, and a simple upper bound on the mean-square error is derived. An example is included to illustrate the effect of high-frequency jitter and the effect of jitter due to 60-cycle pickup. View full abstract»

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  • Chebyshev approximation for two-dimensional nonrecursive digital filters

    Page(s): 208 - 218
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    The Remez exchange algorithm is extended for the design of two-dimensional nonrecursive digital filters approximating circularly symmetrical low-pass specifications according to a weighted Chebyshev error norm. Since the approximating function does not satisfy the Haar condition, the optimal solution is not necessarily unique and a straightforward extension of the one-dimensional exchange method may fail to converge. It is shown how the algorithm has to be complemented with a perturbation technique in order to force convergence under all circumstances. In the case of nonuniqueness the solution provided by the algorithm is a vertex of the polyhedron containing all optimal solutions, and a method is given which allows one to compute an adjacent vertex located on the same edge, thereby allowing the successive determination of all the vertices defining the polyhedron. For this case also, a procedure is described which selects, among all optimal solutions, the best one according to some additional criterion. Finally, the efficiency and accuracy aspects of the algorithm are considered and practical conclusions are drawn as an aid for the designer. View full abstract»

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  • Computer enhancement of scanning electron micrographs

    Page(s): 267 - 278
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    This paper deals with the digital restoration of scanning electron micrographs. The properties of the signal and noise generated when recording a micrograph are analyzed and used to develop the optimal Wiener filter for enhancing the image. The transfer function of the display device, as well as the frequency foldover produced by sampling the image are included in the model. The mean-square-error measure is used in deriving the optimal filter, and it is shown that weighting this measure to reflect the spatial frequency response of the eye is of no benefit. A number of micrographs illustrate the success of restoration at different magnifications. In the opinion of some microscopists, the computer enhancement has produced significant, although not dramatic, improvements in the quality of the images. View full abstract»

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  • Synthesis of spectrum shaping digital filters of recursive design

    Page(s): 197 - 204
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    Several techniques are presented, both iterative and noniterative, for synthesizing a' recursive digital filter whose amplitude spectrum approximates a desired shape. The synthesis is carried out by implementing known algorithms for rational function approximation of a continuous function on a finite interval. In particular, techniques for synthesizing the best rational function approximation in the Chebyshev sense and in the least squares sense are treated. Examples are given which illustrate the quality of approximation achievable through each technique. View full abstract»

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  • A new statistical approach to the coefficient word length problem for digital filters

    Page(s): 190 - 196
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    A statistical approach is proposed for estimating the necessary coefficient word length of a digital filter. With this statistical word length definition, an optimization procedure is then proposed for minimizing the statistical word length for a given filter structure and a given set of maximum error constraints. It is shown that by minimizing this statistical word length, the actual coefficient word length upon rounding of the coefficients can generally be reduced as well. Several examples are given and improvements of one to three bits in the actual coefficient word length are observed. The procedure does not necessarily lead to the actual global minimum coefficient word length. View full abstract»

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