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At least 1,171 records · Page 65
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

A Parallel Genetic Algorithm for Automated Electronic Circuit Design

Parallelized versions of genetic algorithms (GAs) are popular primarily for three reasons: the GA is an inherently parallel algorithm, typical GA applications are very compute intensive, and powerful computing platforms, especially Beowulf-style computing clusters, are becoming more affordable and easier to implement. In addition, the low communication bandwidth required allows the use of inexpensive networking hardware such as standard office ethernet. In this paper we describe a parallel GA and its use in automated high-level circuit design. Genetic algorithms are a type of trial-and-error search technique that are guided by principles of Darwinian evolution. Just as the genetic material of two living organisms can intermix to produce offspring that are better adapted to their environment, GAs expose genetic material, frequently strings of 1s and Os, to the forces of artificial evolution: selection, mutation, recombination, etc. GAs start with a pool of randomly-generated candidate solutions which are then tested and scored with respect to their utility. Solutions are then bred by probabilistically selecting high quality parents and recombining their genetic representations to produce offspring solutions. Offspring are typically subjected to a small amount of random mutation. After a pool of offspring is produced, this process iterates until a satisfactory solution is found or an iteration limit is reached. Genetic algorithms have been applied to a wide variety of problems in many fields, including chemistry, biology, and many engineering disciplines. There are many styles of parallelism used in implementing parallel GAs. One such method is called the master-slave or processor farm approach. In this technique, slave nodes are used solely to compute fitness evaluations (the most time consuming part). The master processor collects fitness scores from the nodes and performs the genetic operators (selection, reproduction, variation, etc.). Because of dependency issues in the GA, it is possible to have idle processors. However, as long as the load at each processing node is similar, the processors are kept busy nearly all of the time. In applying GAs to circuit design, a suitable genetic representation 'is that of a circuit-construction program. We discuss one such circuit-construction programming language and show how evolution can generate useful analog circuit designs. This language has the desirable property that virtually all sets of combinations of primitives result in valid circuit graphs. Our system allows circuit size (number of devices), circuit topology, and device values to be evolved. Using a parallel genetic algorithm and circuit simulation software, we present experimental results as applied to three analog filter and two amplifier design tasks. For example, a figure shows an 85 dB amplifier design evolved by our system, and another figure shows the performance of that circuit (gain and frequency response). In all tasks, our system is able to generate circuits that achieve the target specifications.

Long, Jason D.↗
NASA NTRS2004

Probability Distribution Estimated From the Minimum, Maximum, and Most Likely Values: Applied to Turbine Inlet Temperature Uncertainty

Modern engineering design practices are tending more toward the treatment of design parameters as random variables as opposed to fixed, or deterministic, values. The probabilistic design approach attempts to account for the uncertainty in design parameters by representing them as a distribution of values rather than as a single value. The motivations for this effort include preventing excessive overdesign as well as assessing and assuring reliability, both of which are important for aerospace applications. However, the determination of the probability distribution is a fundamental problem in reliability analysis. A random variable is often defined by the parameters of the theoretical distribution function that gives the best fit to experimental data. In many cases the distribution must be assumed from very limited information or data. Often the types of information that are available or reasonably estimated are the minimum, maximum, and most likely values of the design parameter. For these situations the beta distribution model is very convenient because the parameters that define the distribution can be easily determined from these three pieces of information. Widely used in the field of operations research, the beta model is very flexible and is also useful for estimating the mean and standard deviation of a random variable given only the aforementioned three values. However, an assumption is required to determine the four parameters of the beta distribution from only these three pieces of information (some of the more common distributions, like the normal, lognormal, gamma, and Weibull distributions, have two or three parameters). The conventional method assumes that the standard deviation is a certain fraction of the range. The beta parameters are then determined by solving a set of equations simultaneously. A new method developed in-house at the NASA Glenn Research Center assumes a value for one of the beta shape parameters based on an analogy with the normal distribution (ref.1). This new approach allows for a very simple and direct algebraic solution without restricting the standard deviation. The beta parameters obtained by the new method are comparable to the conventional method (and identical when the distribution is symmetrical). However, the proposed method generally produces a less peaked distribution with a slightly larger standard deviation (up to 7 percent) than the conventional method in cases where the distribution is asymmetric or skewed. The beta distribution model has now been implemented into the Fast Probability Integration (FPI) module used in the NESSUS computer code for probabilistic analyses of structures (ref. 2).

Holland, Frederic A., Jr.↗
NASA NTRS1993

Space marching calculations about hypersonic configurations using a solution-adaptive mesh algorithm

A solution-adaptive marching algorithm is developed and applied to a three-dimensional parabolized Navier-Stokes equation solver. The resulting algorithm obtains accurate solutions by using a spatial-marching/adaptive grid procedure. The adaptation step redistributes grid points line by line in both crossflow directions, with grid point motion controlled by forces analogous to tensional and torsional spring forces with the tensional force proportional to the error measure or weighting functions. The solution-adaptive marching procedure is applied to the hypersonic flow about two generic aircraft configurations. The first of these is an all-body-type geometry with elliptical cross sections and is studied at angles of attack of 0.5, and 15 deg. The second geometry is a generic blended-wing-body design. Results are presented that demonstrate the improvements in flowfield resolution obtainable with the solution-adaptive marching procedure over conventional fixed grid techniques. Computed pitot pressure profiles obtained using the solution-adaptive algorithm show improved agreement with experimental data compared to predictions obtained using a fixed grid.

Harvey, Albert D.↗
NASA NTRS1982

Quantiles, parametric-select density estimation, and bi-information parameter estimators

A quantile-based approach to statistical analysis and probability modeling of data is presented which formulates statistical inference problems as functional inference problems in which the parameters to be estimated are density functions. Density estimators can be non-parametric (computed independently of model identified) or parametric-select (approximated by finite parametric models that can provide standard models whose fit can be tested). Exponential models and autoregressive models are approximating densities which can be justified as maximum entropy for respectively the entropy of a probability density and the entropy of a quantile density. Applications of these ideas are outlined to the problems of modeling: (1) univariate data; (2) bivariate data and tests for independence; and (3) two samples and likelihood ratios. It is proposed that bi-information estimation of a density function can be developed by analogy to the problem of identification of regression models.

Parzen, E.↗
NASA NTRS2012

Investigation into Cloud Computing for More Robust Automated Bulk Image Geoprocessing

Geospatial resource assessments frequently require timely geospatial data processing that involves large multivariate remote sensing data sets. In particular, for disasters, response requires rapid access to large data volumes, substantial storage space and high performance processing capability. The processing and distribution of this data into usable information products requires a processing pipeline that can efficiently manage the required storage, computing utilities, and data handling requirements. In recent years, with the availability of cloud computing technology, cloud processing platforms have made available a powerful new computing infrastructure resource that can meet this need. To assess the utility of this resource, this project investigates cloud computing platforms for bulk, automated geoprocessing capabilities with respect to data handling and application development requirements. This presentation is of work being conducted by Applied Sciences Program Office at NASA-Stennis Space Center. A prototypical set of image manipulation and transformation processes that incorporate sample Unmanned Airborne System data were developed to create value-added products and tested for implementation on the "cloud". This project outlines the steps involved in creating and testing of open source software developed process code on a local prototype platform, and then transitioning this code with associated environment requirements into an analogous, but memory and processor enhanced cloud platform. A data processing cloud was used to store both standard digital camera panchromatic and multi-band image data, which were subsequently subjected to standard image processing functions such as NDVI (Normalized Difference Vegetation Index), NDMI (Normalized Difference Moisture Index), band stacking, reprojection, and other similar type data processes. Cloud infrastructure service providers were evaluated by taking these locally tested processing functions, and then applying them to a given cloud-enabled infrastructure to assesses and compare environment setup options and enabled technologies. This project reviews findings that were observed when cloud platforms were evaluated for bulk geoprocessing capabilities based on data handling and application development requirements.

Brown, Richard B.↗
NASA NTRS2006

Three-Function Logic Gate Controlled by Analog Voltage

The figure is a schematic diagram of a complementary metal oxide/semiconductor (CMOS) electronic circuit that performs one of three different logic functions, depending on the level of an externally applied control voltage, V(sub sel). Specifically, the circuit acts as A NAND gate at V(sub sel) = 0.0 V, A wire (the output equals one of the inputs) at V(sub sel) = 1.0 V, or An AND gate at V(sub sel) = -1.8 V. [The nominal power-supply potential (VDD) and logic "1" potential of this circuit is 1.8 V.] Like other multifunctional circuits described in several prior NASA Tech Briefs articles, this circuit was synthesized following an automated evolutionary approach that is so named because it is modeled partly after the repetitive trial-and-error process of biological evolution. An evolved circuit can be tested by computational simulation and/or tested in real hardware, and the results of the test can provide guidance for refining the design through further iteration. The evolutionary synthesis of electronic circuits can now be implemented by means of a software package Genetic Algorithms for Circuit Synthesis (GACS) that was developed specifically for this purpose. GACS was used to synthesize the present trifunctional circuit. As in the cases of other multifunctional circuits described in several prior NASA Tech Briefs articles, the multiple functionality of this circuit, the use of a single control voltage to select the function, and the automated evolutionary approach to synthesis all contribute synergistically to a combination of features that are potentially advantageous for the further development of robust, multiple-function logic circuits, including, especially, field-programmable gate arrays (FPGAs). These advantages include the following: This circuit contains only 9 transistors about half the number of transistors that would be needed to obtain equivalent NAND/wire/AND functionality by use of components from a standard digital design library. If multifunctional gates like this circuit were used in the place of the configurable logic blocks of present commercial FPGAs, it would be possible to change the functions of the resulting digital systems within shorter times. For example, by changing a single control voltage, one could change the function of thousands of FPGA cells within nanoseconds. In contrast, typically, the reconfiguration in a conventional FPGA by use of bits downloaded from look-up tables via a digital bus takes microseconds.

Zebulum, Ricardo↗
NASA NTRS1977

Description of path-in-the-sky contact analog piloting display

A contact analog display called Path-In-The-Sky (PITS) integrates information on airplane attitude, airplane kinematic performance, navigation situation, and path prediction into one instrument. The pictorial format utilized in the PITS display concept was designed to reduce the required instrument scan and to simplify interpretation of informtion with the objective of reducing pilot work load. Described are the symbology of the PITS display, the coordinate systems used to generate the display, and the magnitudes of pertinent geometric characteristics selected during the display development. Also included are examples of the PITS display generated on a stand-alone graphics computer.

Knox, C. E.↗
NASA NTRS2008

Integrated Software Systems for Crew Management During Extravehicular Activity in Planetary Terrain Exploration

Initial planetary explorations with the Apollo program had a veritable ground support army monitoring the safety and health of the 12 astronauts who performed lunar surface extravehicular activities (EVAs). Given the distances involved, this will not be possible on Mars. A spacesuit for Mars must be smart enough to replace that army. The next generation suits can do so using 2 software systems serving as virtual companions, LEGACI (Life support, Exploration Guidance Algorithm and Consumable Interrogator) and VIOLET (Voice Initiated Operator for Life support and Exploration Tracking). The system presented in this study integrates data inputs from a suite of sensors into the MIII suit s communications, avionics and informatics hardware for distribution to remote managers and data analysis. If successful, the system has application not only for Mars but for nearer term missions to the Moon, and the next generation suits used on ISS as well. Field tests are conducted to assess capabilities for next generation spacesuits at Johnson Space Center (JSC) as well as the Mars and Lunar analog (Devon Island, Canada). LEGACI integrates data inputs from a suite of noninvasive biosensors in the suit and the astronaut (heart rate, suit inlet/outlet lcg temperature and flowrate, suit outlet gas and dewpoint temperature, pCO2, suit O2 pressure, state vector (accelerometry) and others). In the Integrated Walkback Suit Tests held at NASA-JSC and the HMP tests at Devon Island, communication and informatics capabilities were tested (including routing by satellite from the suit at Devon Island to JSC in Houston via secure servers at VCU in Richmond, VA). Results. The input from all the sensors enable LEGACI to compute multiple independent assessments of metabolic rate, from which a "best" met rate is chosen based on statistical methods. This rate can compute detailed information about the suit, crew and EVA performance using test-derived algorithms. VIOLET gives LEGACI voice activation capability, allowing the crew to query the suit, and receive feedback and alerts that will lead to corrective action. LEGACI and VIOLET can also automatically control the astronaut's cooling and consumable use rate without crew input if desired. These findings suggest that non-invasive physiological and environmental sensors supported with data analysis can allow for more effective management of mission task performance during EVA. Integrated remote and local view of data metrics allow crewmember to receive real time feedback in synch with mission control in preventing performance shortcomings for EVA in exploration missions.

Kuznetz, Lawrence↗
NASA NTRS1993

Theory for noise of propellers in angular inflow with parametric studies and experimental verification

This report presents the derivation of a frequency domain theory and working equations for radiation of propeller harmonic noise in the presence of angular inflow. In applying the acoustic analogy, integration over the tangential coordinate of the source region is performed numerically, permitting the equations to be solved without approximation for any degree of angular inflow. Inflow angle is specified in terms of yaw, pitch, and roll angles of the aircraft. Since these can be arbitrarily large, the analysis applies with equal accuracy to propellers and helicopter rotors. For thickness and loading, the derivation is given in complete detail with working equations for near and far field. However, the quadrupole derivation has been carried only far enough to show feasibility of the numerical approach. Explicit formulas are presented for computation of source elements, evaluation of Green's functions, and location of observer points in various visual and retarded coordinate systems. The resulting computer program, called WOBBLE has been written in FORTRAN and follows the notation of this report very closely. The new theory is explored to establish the effects of varying inflow angle on axial and circumferential directivity. Also, parametric studies were performed to evaluate various phenomena outside the capabilities of earlier theories, such as an unsteady thickness effect. Validity of the theory was established by comparison with test data from conventional propellers and Prop Fans in flight and in wind tunnels under a variety of operating conditions and inflow angles.

Propeller acoustics↗
NASA NTRS2006

Parallel, Gradient-Based Anisotropic Mesh Adaptation for Re-entry Vehicle Configurations

Two gradient-based adaptation methodologies have been implemented into the Fun3d refine GridEx infrastructure. A spring-analogy adaptation which provides for nodal movement to cluster mesh nodes in the vicinity of strong shocks has been extended for general use within Fun3d, and is demonstrated for a 70 sphere cone at Mach 2. A more general feature-based adaptation metric has been developed for use with the adaptation mechanics available in Fun3d, and is applicable to any unstructured, tetrahedral, flow solver. The basic functionality of general adaptation is explored through a case of flow over the forebody of a 70 sphere cone at Mach 6. A practical application of Mach 10 flow over an Apollo capsule, computed with the Felisa flow solver, is given to compare the adaptive mesh refinement with uniform mesh refinement. The examples of the paper demonstrate that the gradient-based adaptation capability as implemented can give an improvement in solution quality.

Bibb, Karen L.↗
NASA NTRS2012

An Empirical Temperature Variance Source Model in Heated Jets

An acoustic analogy approach is implemented that models the sources of jet noise in heated jets. The equivalent sources of turbulent mixing noise are recognized as the differences between the fluctuating and Favre-averaged Reynolds stresses and enthalpy fluxes. While in a conventional acoustic analogy only Reynolds stress components are scrutinized for their noise generation properties, it is now accepted that a comprehensive source model should include the additional entropy source term. Following Goldstein s generalized acoustic analogy, the set of Euler equations are divided into two sets of equations that govern a non-radiating base flow plus its residual components. When the base flow is considered as a locally parallel mean flow, the residual equations may be rearranged to form an inhomogeneous third-order wave equation. A general solution is written subsequently using a Green s function method while all non-linear terms are treated as the equivalent sources of aerodynamic sound and are modeled accordingly. In a previous study, a specialized Reynolds-averaged Navier-Stokes (RANS) solver was implemented to compute the variance of thermal fluctuations that determine the enthalpy flux source strength. The main objective here is to present an empirical model capable of providing a reasonable estimate of the stagnation temperature variance in a jet. Such a model is parameterized as a function of the mean stagnation temperature gradient in the jet, and is evaluated using commonly available RANS solvers. The ensuing thermal source distribution is compared with measurements as well as computational result from a dedicated RANS solver that employs an enthalpy variance and dissipation rate model. Turbulent mixing noise predictions are presented for a wide range of jet temperature ratios from 1.0 to 3.20.

Khavaran, Abbas↗
NASA NTRS2014

SpaceCube v2.0 Space Flight Hybrid Reconfigurable Data Processing System

This paper details the design architecture, design methodology, and the advantages of the SpaceCube v2.0 high performance data processing system for space applications. The purpose in building the SpaceCube v2.0 system is to create a superior high performance, reconfigurable, hybrid data processing system that can be used in a multitude of applications including those that require a radiation hardened and reliable solution. The SpaceCube v2.0 system leverages seven years of board design, avionics systems design, and space flight application experiences. This paper shows how SpaceCube v2.0 solves the increasing computing demands of space data processing applications that cannot be attained with a standalone processor approach.The main objective during the design stage is to find a good system balance between power, size, reliability, cost, and data processing capability. These design variables directly impact each other, and it is important to understand how to achieve a suitable balance. This paper will detail how these critical design factors were managed including the construction of an Engineering Model for an experiment on the International Space Station to test out design concepts. We will describe the designs for the processor card, power card, backplane, and a mission unique interface card. The mechanical design for the box will also be detailed since it is critical in meeting the stringent thermal and structural requirements imposed by the processing system. In addition, the mechanical design uses advanced thermal conduction techniques to solve the internal thermal challenges.The SpaceCube v2.0 processing system is based on an extended version of the 3U cPCI standard form factor where each card is 190mm x 100mm in size The typical power draw of the processor card is 8 to 10W and scales with application complexity. The SpaceCube v2.0 data processing card features two Xilinx Virtex-5 QV Field Programmable Gate Arrays (FPGA), eight memory modules, a monitor FPGA with analog monitoring, Ethernet, configurable interconnect to the Xilinx FPGAs including gigabit transceivers, and the necessary voltage regulation. The processor board uses a back-to-back design methodology for common parts that maximizes the board real estate available. This paper will show how to meet the IPC 6012B Class 3A standard with a 22-layer board that has two column grid array devices with 1.0mm pitch. All layout trades such as stack-up options, via selection, and FPGA signal breakout will be discussed with feature size results. The overall board design process will be discussed including parts selection, circuit design, proper signal termination, layout placement and route planning, signal integrity design and verification, and power integrity results. The radiation mitigation techniques will also be detailed including configuration scrubbing options, Xilinx circuit mitigation and FPGA functional monitoring, and memory protection.Finally, this paper will describe how this system is being used to solve the extreme challenges of a robotic satellite servicing mission where typical space-rated processors are not sufficient enough to meet the intensive data processing requirements. The SpaceCube v2.0 is the main payload control computer and is required to control critical subsystems such as autonomous rendezvous and docking using a suite of vision sensors and object avoidance when controlling two robotic arms.

Xilinx FPGA↗
NASA NTRS2001

Evolution, language and analogy in functional genomics

Almost a century ago, Wittgenstein pointed out that theory in science is intricately connected to language. This connection is not a frequent topic in the genomics literature. But a case can be made that functional genomics is today hindered by the paradoxes that Wittgenstein identified. If this is true, until these paradoxes are recognized and addressed, functional genomics will continue to be limited in its ability to extrapolate information from genomic sequences.

Evolution, Molecular↗
NASA NTRS1990

Chaotic rhythms of a dripping faucet

An experiment was conducted which showed that a leaky faucet can offer valuable insights on predicting fluid flow. In this experiment, a flow control and drop detector were connected to the printer port of an IBM PC, which computed and saved the time intervals using a program for droptime compiled with Turbo C. It is noted that the time intervals change from periodic to doubly periodic as the flow rate is increased and then to various forms of chaos, interrupted by windows of periodicity. A number of two- and three-dimensional plots are displayed and discussed. Attention is focused on one of the simpler plots which is approximately parabolic, where each successive time interval is a quadratic function of the preceding interval, with a steepness which depends upon the flow rate. It is shown that a single past analog can predict a dripping faucet with reasonable accuracy 7-10 drops ahead. While such methods are more difficult to apply in higher-dimensional systems, this experiment aids in understanding how fluid flow may be predicted even under conditions of unstable flows caused by increase in velocity.

Cahalan, Robert F.↗
NASA NTRS2013

A Framework for Robust Multivariable Optimization of Integrated Circuits in Space Applications

Application Specific Integrated Circuit (ASIC) design for space applications involves multiple challenges of maximizing performance, minimizing power and ensuring reliable operation in extreme environments. This is a complex multidimensional optimization problem which must be solved early in the development cycle of a system due to the time required for testing and qualification severely limiting opportunities to modify and iterate. Manual design techniques which generally involve simulation at one or a small number of corners with a very limited set of simultaneously variable parameters in order to make the problem tractable are inefficient and not guaranteed to achieve the best possible results within the performance envelope defined by the process and environmental requirements. What is required is a means to automate design parameter variation, allow the designer to specify operational constraints and performance goals, and to analyze the results in a way which facilitates identifying the tradeoffs defining the performance envelope over the full set of process and environmental corner cases. The system developed by the Mixed Signal ASIC Group (MSAG) at the Goddard Space Flight Center is implemented as framework of software modules, templates and function libraries. It integrates CAD tools and a mathematical computing environment, and can be customized for new circuit designs with only a modest amount of effort as most common tasks are already encapsulated. Customization is required for simulation test benches to determine performance metrics and for cost function computation. Templates provide a starting point for both while toolbox functions minimize the code required. Once a test bench has been coded to optimize a particular circuit, it is also used to verify the final design. The combination of test bench and cost function can then serve as a template for similar circuits or be re-used to migrate the design to different processes by re-running it with the new process specific device models. The system has been used in the design of time to digital converters for laser ranging and time-of-flight mass spectrometry to optimize analog, mixed signal and digital circuits such as charge sensitive amplifiers, comparators, delay elements, radiation tolerant dual interlocked (DICE) flip-flops and two of three voter gates.

DuMonthier, Jeffrey↗
NASA NTRS1973

Binary selectable detector holdoff circuit: Design, testing, and application

A very high speed switching circuit, part of a laser radar data acquisition system, has been designed and tested. The primary function of this circuit was to provide computer controlled switching of photodiode detector preamplifier power supply voltages, typically less than plus or minus 20 volts, in approximately 10 nanoseconds. Thus, in actual use, detector and/or detector preamplifier damage can be avoided as a result of sudden extremely large values of backscattered radiation being detected, such as might be due to short range, very thin atmospheric dust layers. Switching of the power supply voltages was chosen over direct switching the photodiode detector input to the preamplifier, based on system noise considerations. Also, the circuit provides a synchronized trigger pulse output for triggering devices such as the Biomation Model 8100 100 MHz analog to digital converter.

Kadrmas, K. A.↗
NASA NTRS2007

Modeling of Turbulence Effect on Liquid Jet Atomization

Recent studies indicate that turbulence behaviors within a liquid jet have considerable effect on the atomization process. Such turbulent flow phenomena are encountered in most practical applications of common liquid spray devices. This research aims to model the effects of turbulence occurring inside a cylindrical liquid jet to its atomization process. The two widely used atomization models Kelvin-Helmholtz (KH) instability of Reitz and the Taylor analogy breakup (TAB) of O'Rourke and Amsden portraying primary liquid jet disintegration and secondary droplet breakup, respectively, are examined. Additional terms are formulated and appropriately implemented into these two models to account for the turbulence effect. Results for the flow conditions examined in this study indicate that the turbulence terms are significant in comparison with other terms in the models. In the primary breakup regime, the turbulent liquid jet tends to break up into large drops while its intact core is slightly shorter than those without turbulence. In contrast, the secondary droplet breakup with the inside liquid turbulence consideration produces smaller drops. Computational results indicate that the proposed models provide predictions that agree reasonably well with available measured data.

Trinh, H. P.↗
NASA NTRS2008

Digital Receiver Phase Meter

The software of a commercially available digital radio receiver has been modified to make the receiver function as a two-channel low-noise phase meter. This phase meter is a prototype in the continuing development of a phase meter for a system in which radiofrequency (RF) signals in the two channels would be outputs of a spaceborne heterodyne laser interferometer for detecting gravitational waves. The frequencies of the signals could include a common Doppler-shift component of as much as 15 MHz. The phase meter is required to measure the relative phases of the signals in the two channels at a sampling rate of 10 Hz at a root power spectral density <5 microcycle/(Hz)1/2 and to be capable of determining the power spectral density of the phase difference over the frequency range from 1 mHz to 1 Hz. Such a phase meter could also be used on Earth to perform similar measurements in laser metrology of moving bodies. To illustrate part of the principle of operation of the phase meter, the figure includes a simplified block diagram of a basic singlechannel digital receiver. The input RF signal is first fed to the input terminal of an analog-to-digital converter (ADC). To prevent aliasing errors in the ADC, the sampling rate must be at least twice the input signal frequency. The sampling rate of the ADC is governed by a sampling clock, which also drives a digital local oscillator (DLO), which is a direct digital frequency synthesizer. The DLO produces samples of sine and cosine signals at a programmed tuning frequency. The sine and cosine samples are mixed with (that is, multiplied by) the samples from the ADC, then low-pass filtered to obtain in-phase (I) and quadrature (Q) signal components. A digital signal processor (DSP) computes the ratio between the Q and I components, computes the phase of the RF signal (relative to that of the DLO signal) as the arctangent of this ratio, and then averages successive such phase values over a time interval specified by the user.

Marcin, Martin↗