Showing papers by "Kenneth Steiglitz published in 1981"

Design of FIR digital phase networks

Abstract: The problem of the minimax design of FIR digital filters with prescribed phase characteristics and unit magnitude is a nonlinear optimization problem. In this paper it is approximated by a linear programming problem, and it is shown that the solution of this linear program is optimal to first order. That is, if δ 0 and e 0 are optimal deviations of magnitude and phase characteristics, then the actual deviations obtained from the linear program solution satisfy \delta \leq \delta_{0} + \epsilon\min{0}\max{2} and \epsilon \leq \epsilon_{0} (1 + \delta_{0})/(1 - \delta_{0}) . Numerical examples are given, including design results for full-band M-term chirp filters which (like linear phase filters) can be implemented with (M + 1)/2 multiplications per point.

Digital Signal Processing Applications of Systolic Algorithms

Abstract: VLSI structures and algorithms are given for bit-serial FIR filtering, IIR filtering, and convolution. We also present a bit-parallel FIR filter design. The structures are highly regular, programmable, and area-efficient. In fact, we will show that most are within log factors of asymptotic optimality. These structures are completely pipelined; that is, the throughput rate (bits/second) is independent of both word size and filter length. This is to be contrasted with algorithms designed and implemented in terms of, say, multipliers and adders whose throughput rates may depend on word length.

Some Complexity Results in the Design of Deadlock-Free Packet Switching Networks

Abstract: Deadlocks are very serious system failures and have been observed in existing packet switching networks (PSN’s). Several problems related to the design of deadlock-free PSN’s are investigated here. Polynomial-time algorithms are given for some of these problems, but most of them are shown to be NP-complete or NP-hard, and therefore polynomial-time algorithms are not likely to be found.

Synthesis of Timbral Families by Warped Linear Prediction

Abstract: A central problem in the production of music by computer is how to generate sounds with similar but different timbres; that is, how to synthesize a "family" of instruments that are perceived as distinguishable but similar in timbre. This paper describes a method for synthesizing a family of string-like instruments that proceeds as follows: First, a few actual violin notes are analyzed using linear prediction. Second, a bilinear transformation is applied to the linear prediction model on synthesis, using a recently described algorithm. This yields a computationally efficient way to generate a virtual string orchestra, with violin-, viola-, violoncello-, and bass-like timbres. A realization of a 4.7-minute piece composed by P. Lansky will be played.

A Note on the Complexity of the Star-Star Concentrator Problem

Abstract: The star-star concentrator problem (SSCP) arises in computer network design. The complexity of this problem is studied, and polynomially solvable and (strongly) NP-complete cases are presented.

Synthesis of timbral families by warped linear prediction

Abstract: A central problem in the production of music by computer is how to generate sounds with similar but different timbres; that is, how to synthesize a "family" of instruments that are perceived as distinguishable but similar in timbre. This paper describes a method for synthesizing a family of string-like instruments that proceeds as follows: First, a few actual violin notes are analyzed using linear prediction. Second, a bilinear transformation is applied to the linear prediction model on synthesis, using a recently described algorithm. This yields a computationally efficient way to generate a virtual string orchestra, with violin-, viola-, violoncello-, and bass-like timbres. A realization of a 4.7-minute piece composed by P. Lansky will be played.

Some intractable problems in digital signal processing

Abstract: Over the past decade a large class of problems, called NP-complete[1], have been shown to be equivalent in the sense that if a fast algorithm can be found for one, fast algorithms can be found for all. At the same time, despite much effort, no fast algorithms have been found for any, and these problems are widely regarded as intractable. This class includes such notoriously difficult problems as the traveling salesman problem, graph coloring, and satisfiability of Boolean expressions. This paper describes some problems in digital signal processing which are NP-complete. These include: (1) Minimize the number of registers required to implement a signal flow graph; (2) Minimize the time to perform the additions (multiplications) of a signal flow graph using P adders (multipliers); (3) Minimize the computational cost for multiplication by a fixed matrix. Large-scale instances of such problems may become important with the use of VLSI technology to implement signal processing.