Showing papers by "Kenneth Steiglitz published in 1975"

Evaluating polynomials at fixed sets of points

Abstract: We investigate the evaluation of an $(n - 1)$st degree polynomial at a sequence of n points. It is shown that such an evaluation reduces directly to a simple convolution if and only if the sequence of points is of the form $b, ba,ba^2 , \cdots ,ba^{n - 1} $ for complex numbers a and b (the so-called “chirp transform”). By more complex reductions we develop an $O(n\log n)$ evaluation algorithm for sequences of points of the form \[ b + c + d,\quad ba^2 + ca + d,\quad ba^4 + ca^2 + d, \cdots \] for complex numbers a, b, c and d. Finally we show that the evaluation of an $(n - 1)$st-degree polynomial and all its derivatives at a single point requires at most $O(n\log n)$ steps.

Exact, Approximate, and Guaranteed Accuracy Algorithms for the Flow-Shop Problem n / 2 / F / F¯

Abstract: Improved exact and approximate algorithms for the n-job two-machine mean finishing time flow-shop problem, n/2JF/P, are presented While other researchers have used a variety of approximate methods to generate suboptimal solutions and branch-and-bound algorithms to gen- erate exact solutmns to sequencing problems, thin work demonstrates the computatmnal effectiveness of couphng the two methods to generate solutmns with a guaranteed accuracy. The computational reqmrements of exact, approximate, and guaranteed accuracy algorithms are compared expem- mentally on a set of test problems ranging in size from 10 to 50 jobs The approach is readily apphca- ble to other sequencing problems

Pitch extraction by trigonometric curve fitting

Abstract: An algorithm is proposed for extracting the pitch of voiced speech. The method is based on approximating a given segment of the speech waveform in a least-squares sense by a finite Fourier series. In the approximation the fundamental frequency of the Fourier series, as well as its coefficients, is considered variable.

A note on implementation of digital filters

Abstract: A recently proposed method to implement digital filters using ROM can also be employed to implement multiplication by a constant. This note discusses alternate implementations for digital filter sections substituting memory for logic and points out the possible advantage of doing so.