Fred J. Taylor

A comparison of DFT algorithms using a residue architecture

Abstract The Fast Fourier Transform (FFT), Good-Winograd Fourier Transform (GWFT) and Winograd Fuorier Transform (WFT) are studied using residue arithmetic. High speed, high precision arithmetic is achieved by using arithmetic architecture and a plurality of small wordlength processors running is parallel. The disadvantage of this arithmetic is overflow intolerance. To insure that register overflow will not occur, in this modular structure, scaling policies for the three DFTs are derived and compared.

A floating-point residue arithmetic unit☆

Abstract A floating-point arithmetic unit (FPAU), based on the residue number system, is reported which can perform addition, subtraction and multiplication. As a result, several classic problems associated with RNS based digital filters such as: overflow detection, sign detection and non-integer filter coefficients are overcome by virtue of thefloating-point representation of rational numbers over a large dynamic range. The FPAU has potential applications in computing, digital filtering, and implementing high speed, high precision Fast Fourier Transform (FFT) and Winograd Fourier Transform (WFTA). It will be shown that by using parallel small word-length architectures (viz. microprocessors), a high speed FPAU can be realized.

Transient response analysis of linear differential systems on minicomputers

A common problem in system simulation is producing the solution to a differential equation of the form x(t)= Ax(t) + Bu(t), where A and B are constants. In particular, simulation often requires solutions for a step, ramp, or constant-acceleration forcing function. Standard numerical integration methods may fail or be extremely slow when implemented on a mini computer because of its short wordlength. This paper presents a new deterministic integration method which will accurately and rapidly produce the solution. Some numerical experiments are shown to demonstrate the new method.

Recursive estimation of incremental cost curves

Abstract The economic scheduling of power generation among fossil fuel plants has historically been based on incremental cost curves which relate the rate of change of cost with respect to change in power delivered to the transmission system. These curves are based on steady-state measurements and are up-dated periodically, normally weekly or monthly, to reflect changes in operating conditions. Since the load of a power system is constantly changing, one or more of the generation units must be in a dynamic state at any given time. Also, changes in such quantities as ambient temperature and feedwater temperature affect the overall system efficiency. Thus the incremental cost given by a cost curve is at best only an approximation of the actual incremental cost. In this work, a superior estimation technique is used to model this economic metric. It features on-line, real-time capabilities which allow the algorithm to adaptively follow structural changes in the generating system. The practical problems of divergence and parameter initialization are also treated. The experimental results presented demonstrate that the developed real-time method is accurate and will fit in a mini-computer controller.

Large moduli multipliers

In this work we present a new table look-up storage scheme and a class of table look-up multipliers capable of working with exact (modular) numbering systems. Memory savings associated with the new look-up multiplier, when compared to contemporary methods, are shown to be on the order of 2/N where N=2^{n} , n =input wordlength. Throughput is shown to be equal to that obtained using VLSI and classic architectures.

On the Fourier transform of sequency limited signals with applications to delta modulation and medicine

Abstract It is the binary nature of the Walsh basis functions that make the Walsh transform a potentially useful signal processing tool. Unlike the FFT, which produces a database in the easily interpreted frequency domain, a Walsh data base resides in the obscure sequency domain. Using a fast Walsh algorithm, an N-point transform can, however, be computed more rapidly than a FFT using a similar computer architecture. Even though the sequency space has been shown to be useful in coding and picture processing applications, the aperiodic behaviour of its basis functions make it. unsuitable for many traditional signal-processing problems. It would be desirable, for example, to be able to relate the computationally efficient Walsh spectra to the intuitively pleasing Fourier spectra. This work will address that problem and present new results.

A new technique for WFTA input/output reordering

The Winograd Fourier transform algorithm (WFTA) is receiving intensive study. The advantage of this class of transform is its potential high throughput due to reduced multiplication count. However, both input and output reorderings have to be performed when the algorithm is implemented. In this work, a technique for the WFTA input/output reorderings is developed. This technique is flexible to the choice of the base numbers of WFTA and capable of operating at high speed in digital hardware. This technique requires no extra memory for reordering when implementing the WFTA in the residue number system if the moduli set of RNS is carefully chosen to contain the base numbers of WFTA.

Optimal trajectory transfer in the presence of large controlled gain variations

Abstract A common problem encountered in the design of an optimal linear time invariant trajectory transfer system is the maintenance of the optimal control policy in the presence of large parameter variations. In this work, the maintenance of the control policy in systems having uncertain actuator (or controller) gains is developed. Necessary and sufficient conditions are derived using linear programming techniques. The resulting analysis computes the maximal dynamic range over which a nominally optimal control policy, less a scale factor, is algebraically invariant. The scaling of the original unperturbed control policy is accomplished through the application of a derived constant coefficient linear transform. The computed maximal dynamic range of admissible parameter variations can be used as an acceptance or rejection criteria for mass produced optimized controllers. Finally, a simple example is presented which demonstrates the mechanics of the developed methodology.

New bioacoustic signal processing techniques

The engineering principles and techniques applicable to the study and eventual non-invasive detection of aneursyms are being studied at the University of Cincinnati. Reported statistics indicate the ruptures of a subarachnoid aneurysm is the cause of 2% of all sudden deaths, is 68% mortal and leaves 21% mentally deficient otherwise. Surgical survival after hemorrhage is rated at 77% and 90% if detected. Statistics indicate that a patients chances for a productive life are good if the aneursym can be detected and surgically treated. Approximately 12% of all polycystic and 15% of al migrane patients have aneurysms. These statistics are not high enough to warrant the risk of angiography for pre-bleed analysis however. Angiography, which entails patient risk and hospitalization, is the only presently available test for the above conditions.

An All Digital Automated Wind Measurement System

In addition to supplying basic meteorological information, vectored wind velocity measurements are essential to the analysis of small caliber ballistic trajectories, optical wave propagation in the lower atmosphere, and wind shears and vorticies. Conventional electromechanical methods, using velocity-to-direct current converters, are often unsatisfactory when integrated into a multisensor array over long path lengths. An all digital system capable of operating as an array over long path lengths has been developed. The system is totally automated. Using complementary metal oxidized semiconductors (CMOS) signal processing remote data acquisition stations, operated under microprocessor control, reliable and accurate asynchronous data transfer has been obtained.