Showing papers by "Kenneth Steiglitz published in 1965"

A technique for the identification of linear systems

Abstract: An iterative technique is proposed to identify a linear system from samples of its input and output in the presence of noise by minimizing the mean-square error between system and model outputs. The model chosen has a transfer function which is a ratio of polynomials in z-1. Although the regression equations for the optimal set of coefficients are highly nonlinear and intractable, it is shown that the problem can be reduced to the repeated solution of a related linear problem. Computer simulation of a number of typical discrete systems is used to demonstrate the considerable improvement over the Kalman estimate which can be obtained in a few iterations. The procedure is found to be effective at signal-to-noise ratios less than unity, and with as few as 200 samples of the input and output records.

The Equivalence of Digital and Analog Signal Processing

Abstract: A specific isomorphism is constructed via the transform domains between the analog signal space L2 (−∞, ∞) and the digital signal space l2. It is then shown that the class of linear time-invariant realizable filters is invariant under this isomorphism, thus demonstrating that the theories of processing signals with such filters are identical in the digital and analog cases. This means that optimization problems involving linear time-invariant realizable filters and quadratic cost functions are equivalent in the discrete-time and the continuous-time cases, for both deterministic and random signals. Finally, applications to the approximation problem for digital filters are discussed.

Rational transform approximation via the Laguerre spectrum

Abstract: A method is presented for determination of an n th order rational transform approximation for a time function, given at least n + 1 of its Laguerre coefficients. The method is based on approximating the discrete set of Laguerre coefficients with a rational generating function. The method does not require predetermination of the poles; and allows the use of as many Laguerre coefficients as are available, without increasing the complexity of the model. Applications to time domain synthesis and transfer function identification are discussed.

Application of the Maximum Principle to the Design of Minimum Bandwidth Pulses

Abstract: The minimum bandwidth pulse for a given rms value and peak amplitude is found using the Pontryagin Maximum Principle for bounded phase space. The solution is obtained by actually solving the equations of the maximum principle rather than by a verification of a solution arrived at by other means. The resulting optimal pulse shape can be used for comparisons with more easily generated pulses, and may be considered to be the optimal modification of a rectangular pulse from the point of view of minimum bandwidth. Pulses of this sort are useful in pulse communication systems.

Comments on the statistical design of linear sampled-data feedback systems

Abstract: constraint on the estimated state x-ector p which has been overlooked. Because the first hr elements of p(a) are the output, at R successive sampling instants, of a dynamic system described by a K t h order difference equation [fl) of the original paper], each is completely determined by the values of the K preceding outputs, the K preceding inputs, and the current input. These 2K+1 values for each of the output variables in g l J are contained in p(a-lj and the last K elements of Y (~ J. Therefore, while pI1! can be selected arbitrarily to minimize the criterion D , oitly the last K eIements of ~ (~ 1 (5 + 1 j can be so chosen. But the procedure described by Koop-mans2 require? that p'\": be constrained o d y bq' the equation Hence. (1) of the paper, Koopmans' result of minimization with respect to % (a) , is inap-plicable; the vectors a;*: and the corresponding D are not correct unless the uncon-strained minimum of (4) happens to coincide with the constrained minimum. The additional constraint can, of course, be ignored if the nono\\-erlapping observation sets 3.'\"' are chosen to be so widely separated that LCa' is independent of 3.Ce-lj. However, this choice nleans a much longer period of obserx-ation to obtain an estimate with a given x~ariance, and implies a n a priori assumption about the effective settling time of the system. The proposed estimate, while apparently not optimal! may still be useful if the uncon-strained minimum is close to the constrained (true) minimum. One way of checking this possibility for a particular set of observations would be to compute Koopmans' optimal state wctor after finding the estimate ?. These vectors ai*' specif\\-a n estimated set of inputs and outputs c (i) and i(i) which can be substituted into (1) along with the a's and ,a's specified by T. I t is correct, as L. E. hIcBride, Jr. observes , that in Section I\\-of the paper referred to,l the maximum likelihood estimates were determined xithout taking into account the linear constraints bettveen elements of adjacent vectors. This was not overlooked by the author, but apparently the discussions of this point in Sections IY and \\:I1 require amplification. The estimates of Section TI-utilize only a part of the information available from the .v(?t) and y (a) sequences to estimate the pulse transfer function coefficient 1-ector y, …

Optimal time-domain synthesis by iterative methods,

Abstract: : An iterative procedure is presented which permits the determination of a rational transfer function in the Laplace transform variable s which is optimal with respect to given input and output time-functions. The optimal system of a particular order is defined as the one whose output when subjected to the known input function is nearest in the time integral square sense to the desired output function. The method is thus applicable to a number of problems involving the minimization of an integral square error. (Author)

Adaptive signal reconstruction

Abstract: An adaptive filter which reconstructs a continuous signal from its samples is described This filter is based on the minimum mean-square-error reconstruction filter, assuming an all-pole model for the sampled spectral density of the input signal The use of this model leads to two important simplifications First, simple linear regression can be used to identify the unknown parameters of the signal spectral density Second, the resulting filter has an impulse response which is of finite duration These simplifications lead to an adaptive filter which is at the same time both generally applicable and easily implemented on a digital or hybrid computer Experiments with both deterministic and random inputs are described which show that the adaptive filter yields significant improvement over a linear point connector or other commonly used reconstructors with relatively low order models and with relatively short identification times