Maximum errors from quantization in multirate digital control systems
Upper bound determination for errors due to signal quantization in multirate digital control system through state variable or z transform formulations
Johnson, J. C.↗
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Sampled data systems and generating functions
Application of Z-transforms to sampled-data systems
Halijak, C. A.↗
Digital-computer normal shock position and restart control of a Mach 2.5 axisymmetric mixed-compression inlet
Digital computer control of a mixed-compression inlet is discussed. The inlet was terminated with a choked orifice at the compressor face station to dynamically simulate a turbojet engine. Inlet diffuser exit airflow disturbances were used. A digital version of a previously tested analog control system was used for both normal shock and restart control. Digital computer algorithms were derived using z-transform and finite difference methods. Using a sample rate of 1000 samples per second, the digital normal shock and restart controls essentially duplicated the inlet analog computer control results. At a sample rate of 100 samples per second, the control system performed adequately but was less stable.
Neiner, G. H.↗
On identifying transfer functions and state equations for linear systems.
Two methods are established for identifying constant-coefficient, C to the 2n power type of noise-free linear systems if the time response data of the input-output or of all states are known. 2n response data are required to identify an nth-order transfer function or state equation for an unknown linear system. The order of the unknown system can be identified by checking a sequence of determinants. The Z transform and its inversion are mainly used.
Shieh, L. S.↗
The use of precession modulation for nutation control in spin-stabilized spacecraft
The relations which determine the nutation effects induced in a spinning spacecraft by periodic precession thrust pulses are derived analytically. By utilizing the idea that nutation need only be observed just before each precession thrust pulse, a difficult continuous-time derivation is replaced by a simple discrete-time derivation using z-transforms. The analytic results obtained are used to develop two types of modulated precession control laws which use the precession maneuver to concurrently control nutation. Results are illustrated by digital simulation of an actual spacecraft configuration.
Taylor, J. M.↗
Uniform sampling analysis of a hybrid phase-locked loop with a sample-and-hold phase detector
Phase-locked-loop (PLL) bit synchronizers often employ integrate-and-dump type phase detectors that provide phase error information only at discrete points in time. Usually these phase detectors are followed by sample-and-hold circuits to produce a stairstep error voltage as the input to a standard analog circuit loop filter. When the loop is configured in this manner, it is referred to as a hybrid PLL. Sampled-data analysis methods (Z transforms) are used to determine the stability and transient response of this loop.
Barab, S.↗
On the time-weighted quadratic sum of linear discrete systems
A method is proposed for obtaining the time-weighted quadratic sum for linear discrete systems. The formula of the weighted quadratic sum is obtained from matrix z-transform formulation. In addition, it is shown that this quadratic sum can be derived in a recursive form for several useful weighted functions. The discussion presented parallels that of MacFarlane (1963) for weighted quadratic integral for linear continuous systems.
Jury, E. I.↗
A satellite digital controller or 'play that PID tune again, Sam'
The problem discussed is to design a digital controller for a typical satellite. The controlled plant is considered to be a rigid body acting in a plane. The controller is assumed to be a digital computer which, when combined with the proposed control algorithm, can be represented as a sampled-data system. The objective is to present a design strategy and technique for selecting numerical values for the control gains (assuming position, integral, and derivative feedback) and the sample rate. The technique is based on the parameter plane method and requires that the system be amenable to z-transform analysis.
Seltzer, S. M.↗
CCD correlation techniques
Two CCD techniques were discussed for performing an N-point sampled data correlation between an input signal and an electronically programmable reference function. The design and experimental performance of an implementation of the direct time correlator utilizing two analog CCDs and MOS multipliers on a single IC were evaluated. The performance of a CCD implementation of the chirp z transform was described, and the design of a new CCD integrated circuit for performing correlation by multiplication in the frequency domain was presented. This chip provides a discrete Fourier transform (DFT) or inverse DFT, multipliers, and complete support circuitry for the CCD CZT. The two correlation techniques are compared.
Hewes, C. R.↗
Spectral analysis using CCDs
Charge-coupled devices (CCDs) are ideally suited for performing sampled-data transversal filtering operations in the analog domain. Two algorithms have been identified for performing spectral analysis in which the bulk of the computation can be performed in a CCD transversal filter; the chirp z-transform and the prime transform. CCD implementation of both these transform algorithms is presented together with performance data and applications.
Hewes, C. R.↗
Low power, compact charge coupled device signal processing system
A variety of charged coupled devices (CCDs) for performing programmable correlation for preprocessing environmental sensor data preparatory to its transmission to the ground were developed. A total of two separate ICs were developed and a third was evaluated. The first IC was a CCD chirp z transform IC capable of performing a 32 point DFT at frequencies to 1 MHz. All on chip circuitry operated as designed with the exception of the limited dynamic range caused by a fixed pattern noise due to interactions between the digital and analog circuits. The second IC developed was a 64 stage CCD analog/analog correlator for performing time domain correlation. Multiplier errors were found to be less than 1 percent at designed signal levels and less than 0.3 percent at the measured smaller levels. A prototype IC for performing time domain correlation was also evaluated.
Bosshart, P. W.↗
The development of a power spectral density processor for C and L band airborne radar scatterometer sensor systems
A real-time signal processor was developed for the NASA/JSC L-and C-band airborne radar scatterometer sensor systems. The purpose of the effort was to reduce ground data processing costs. Conversion of two quadrature channels of data (like and cross polarized) was made to obtain Power Spectral Density (PSD) values. A chirp-z transform (CZT) approach was used to filter the Doppler return signal and improved high frequency and angular resolution was realized. The processors have been tested with record signals and excellent results were obtained. CZT filtering can be readily applied to scatterometers operating at other wavelengths by altering the sample frequency. The design of the hardware and software and the results of the performance tests are described in detail.
Harrison, D. A., III↗
Advanced acousto-optic signal processors
The basic acousto-optic signal processing architectures (spectrum analyzer, space-integrating, time-integrating, and triple product processor) systems and algorithms such as the chirp-Z transform are reviewed. New acousto-optic data processing systems and applications that utilze these basic architectures and new ones are described. These include a matched spatial filter acousto-optic processor, two new hybrid time and space-integrating systems, a triple product processor, and four new matrix-vector iterative feedback systems.
Casasent, D.↗
Performance analysis of the DSN baseband assembly (Bba) Real-Time Combiner (RTC)
The operation of the BBA Real Time Combiner (RTC) is discussed and its performance investigated in detail. It is shown that each channel of the RTC can be modelled by a simple block diagram in the z-transform domain from which all pertinent transient and steady state behavioral characteristics can be determined. In particular, the characteristic equation of the tracking loop and its equivalent noise bandwidth are found and used to evaluate the closed loop transient response and steady-state mean squared timing jitter. The impact of the totality of these loop jitter contributions on the combiner output SNR is evaluated and illustrated numerically. These results show that for parameters of interest to various space missions, the RTC is capable of providing significant SNR improvement relative to a single receiving antenna.
Simon, M. K.↗
Performance analysis of the DSN baseband assembly (Bba) Real-Time Combiner (RTC)
The operation of the BBA Real Time Combiner (RTC) is discussed and its performance investigated in detail. It is shown that each channel of the RTC can be modelled by a simple block diagram in the z-transform domain from which all pertinent transient and steady state behavioral characteristics can be determined. In particular, the characteristic equation of the tracking loop and its equivalent noise bandwidth are found and used to evaluate the closed loop transient response and steady state mean squared timing jitter. The impact of the totality of these loop jitter contributions on the combiner output SNR is evaluated and illustrated numerically. These results show that for parameters of interest to various space missions, the RTC is capable of providing significant SNR improvement relative to a single receiving antenna.
Simon, M. K.↗
Dispersion, damping and confinement of propagating pulses in large space structures
Pulse propagations in large space structures caused by repeated pulse excitations are studied analytically (by using the Z-transforms) and numerically. It is found that resonance regimes can be generated not only by periodical, but also by non-periodical repeated pulses; the conditions for such regimes are derived. Special attention is paid to the dispersion of propagating pulses due to structural irregularities, to damping of pulses due to appropriate combination of elastic and viscous properties of joints between structural members, and to the protection of certain areas of Large Space Structures (LSS) from impacts provided by a pulse trapping effect.
Zak, Michail↗
Design of QMF (Quadrature Mirror Filter) in spatial domain and edge encoding
Simoncelli and Adelson have extended the one dimensional Quadrature Mirror Filter (QMF) to two dimensions with hexagon symmetry and three dimensional spatio-temporal extensions with rhombic-duodecahedray symmetry. Jain and Crochiere presented an excellent QMF design technique in the time domain. It is proposed to extend the design of a two dimensional QMF over a rectangular lattice in the spatial domain based primarily on the extension of the idea of Jain and Crochiere. In addition, the design will investigate the use of two dimensional Z-transformations. Since this proposed QMF is intended for the applications in image processing, all the important and interesting engineering issues will be addressed throughout the development phase. The design of a two dimensional QMF is discussed. The motivation is to achieve an extremely high data compression ratio. It is entirely possible to achieve dramatic results when pattern recognition techniques are employed. The final goal is the demonstration of extremely high data compression ratios using NASA pictures.
Wang, Paul P.↗
Analysis of exhaustive limited service for token ring networks
Token ring operation is well-understood in the cases of exhaustive, gated, gated limited, and ordinary cyclic service. There is no current data, however, on queueing models for the exhaustive limited service type. This service type differs from the others in that there is a preset maximum (omega) on the number of packets which may be transmitted per token reception, and packets which arrive after token reception may still be transmitted if the preset packet limit has not been reached. Exhaustive limited service is important since it closely approximates a timed token service discipline (the approximation becomes exact if packet lengths are constant). A method for deriving the z-transforms of the distributions of the number of packets present at both token departure and token arrival for a system using exhaustive limited service is presented. This allows for the derivation of a formula for mean queueing delay and queue lengths. The method is theoretically applicable to any omega. Fortunately, as the value of omega becomes large (typically values on the order of omega = 8 are considered large), the exhaustive limited service discipline closely approximates an exhaustive service discipline.
Peden, Jeffery H.↗