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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Digital second-order phase-locked loop

A digital second-order phase-locked loop is disclosed in which a counter driven by a stable clock pulse source is used to generate a reference waveform of the same frequency as an incoming waveform, and to sample the incoming waveform at zero-crossover points. The samples are converted to digital form and accumulated over M cycles, reversing the sign of every second sample. After every M cycles, the accumulated value of samples is hard limited to a value SGN = + or - 1 and multiplied by a value delta sub 1 equal to a number of n sub 1 of fractions of a cycle. An error signal is used to advance or retard the counter according to the sign of the sum by an amount equal to the sum.

Holes, J. K.↗
NASA NTRS1995

Shuttle Laser Altimeter (SLA): A pathfinder for space-based laser altimetry and lidar

The Shuttle Laser Altimeter (SLA) is a Hitchhiker experiment now being integrated for first flight on STS-72 in November 1995. Four Shuttle flights of the SLA are planned at a rate of about a flight every 18 months. They are aimed at the transition of the Goddard Space Flight Center airborne laser altimeter and lidar technology to low Earth orbit as a pathfinder for operational space-based laser remote sensing devices. Future alser altimeter sensors such as the Geoscience Laser Altimeter System (GLAS), an Earth Observing System facility instrument, and the Multi-Beam Laser Altimeter (MBLA), the land and vegetation laser altimeter for the NASA TOPSAT (Topography Satellite) Mission, will utilize systems and approaches being tested with SLA. The SLA Instrument measures the distance from the Space Shuttle to the Earth's surface by timing the two-way propagation of short (approximately 10 na noseconds) laser pulses. laser pulses at 1064 nm wavelength are generated in a laser transmitter and are detected by a telescope equipped with a silicon avalanche photodiode detector. The SLA data system makes the pulse time interval measurement to a precision of about 10 nsec and also records the temporal shape of the laser echo from the Earth's surface for interpretation of surface height distribution within the 100 m diam. sensor footprint. For example, tree height can be determined by measuring the characteristic double-pulse signature that results from a separation in time of laser backscatter from tree canopies and the underlying ground. This is accomplished with a pulse waveform digitizer that samples the detector output with an adjustable resolution of 2 nanoseconds or wider intervals in a 100 sample window centered on the return pulse echo. The digitizer makes the SLA into a high resolution surface lidar sensor. It can also be used for cloud and atmospheric aerosol lidar measurements by lengthening the sampling window and degrading the waveform resolution. Detailed test objectives for the STS-72 mission center on the acquisition of sample data sets for land topography and vegetation height, waveform digitizer performance, and verification of data acquisition algorithms. The operational concept of SLA is illustrated in Fig. 1 where a series of 100 m footprints stretch in a profile of Earth surface topography along the nadir track of the Space Shuttle. The location of SLA as a dual canister payload on the Hitchhiker Bridge Assembly in Bay 12 of the Space Shuttle Endeavor can also be noted in this figure. Full interpretation of the SLA range measurement data set requires a 1 m knowledge of the Orbiter trajectory and better than 0.1 deg knowledge of Orbiter pointing angle. These ancillary data sets will be acquired during the STS-72 mission with an on-board Global Positioning System (GPS) receiver, K-band range and range-rate tracking of the Orbiter through TDRSS, and use of on-board inertial measurement units and star trackers. Integration and interpretation of all these different data sets as a pathfinder investigation for accurate determination of Earth surface elevation is the overall science of the SLA investigation.

Bufton, Jack↗
NASA NTRSDate not supplied

Uncertainty Quantification of CFD Model Assumptions Against Sonic Boom Noise Prediction of a Commercial Supersonic Transport

This paper presents the results of uncertainty modeling of sonic boom noise generation from commercial supersonic transport considering the Spalart-Allmaras (SA) turbulence modeling parameters as well as Mach number, angle of attack and altitude. Sample generation and analysis for this uncertainty model was performed by UQPCE, which is a software package developed at the NASA Langley Research Center. To build the uncertainty model, 42 cases of sonic boom noise calculation were performed. Computation of the ground noise can be briefly summarized in two steps. First, the near field pressure waveforms are sampled from CFD calculation using the NASA Langley’s FUN3D solver. Second, this information is passed to an atmospheric propagation code, sBOOM, which solves an augmented Burger’s equation and simulates how the near field waveforms will change while passing through the atmosphere. The ground signature is further processed to obtain the perceived loudness, PLdB. Having a high spatial resolution near the shockwave in the CFD calculation is critical in sonic boom noise prediction. Because the variation in the input parameters for the current uncertainty quantification (UQ) study is likely to lead to change in shock location, angle and strength, the grid adaptation for shock capturing is independently applied for each condition. The final mesh used in the CFD calculation consists of approximately 420 million cells. The pressure signatures are sampled at three, four and five body lengths away from the aircraft to make sure the three dimensional effects around the aircraft are resolved. The results of the UQ analysis shows that within the three aleatory variables, the angle of attack had the most impact against ground noise, followed by the altitude and the Mach number. Between the two SA model parameters, the Kármán constant (𝜅) was significantly more important than the turbulent Prandtl number (𝜎), but these two parameters were only marginally significant in the overall prediction variance in ground noise. The UQ procedure explained in this paper can be widely applied to other model parameters.

Uncertainty Quantification↗
NASA NTRSDate not supplied

Uncertainty Quantification of CFD Model Assumptions Against Sonic Boom Noise Prediction of a Commercial Supersonic Transport

This paper presents the results of uncertainty modeling of sonic boom noise generation from commercial supersonic transport considering the Spalart-Allmaras (SA) turbulence modeling parameters as well as Mach number, angle of attack and altitude. Sample generation and analysis for this uncertainty model was performed by UQPCE, which is a software package developed at the NASA Langley Research Center. To build the uncertainty model, 42 cases of sonic boom noise calculation were performed. Computation of the ground noise can be briefly summarized in two steps. First, the near field pressure waveforms are sampled from CFD calculation using the NASA Langley’s FUN3D solver. Second, this information is passed to an atmospheric propagation code, sBOOM, which solves an augmented Burger’s equation and simulates how the near field waveforms will change while passing through the atmosphere. The ground signature is further processed to obtain the perceived loudness, PLdB. Having a high spatial resolution near the shock wave in the CFD calculation is critical in sonic boom noise prediction. Because the variation in the input parameters for the current uncertainty quantification (UQ) study is likely to lead to change in shock location, angle and strength, the grid adaptation for shock capturing is independently applied for each condition. The final mesh used in the CFD calculation consists of approximately 420 million cells. The pressure signatures are sampled at three, four and five body lengths away from the aircraft to make sure the three dimensional effects around the aircraft are resolved. The results of the UQ analysis shows that within the three aleatory variables, the angle of attack had the most impact against ground noise, followed by the altitude and the Mach number. Between the two SA model parameters, the Kármán constant (𝜅) was significantly more important than the turbulent Prandtl number (𝜎), but these two parameters were only marginally significant in the overall prediction variance in ground noise. The UQ procedure explained in this paper can be widely applied to other model parameters.

Uncertainty Quantifications↗
NASA NTRS1994

Fine structure of Langmuir waves observed upstream of the bow shock at Venus

Highly structured Langmuir waves, also known as electron plasma oscillations, have been observed in the foreshock of Venus using the plasma wave experiment on the Galileo spacecraft during the gravity assist flyby on February 10, 1990. The Galileo wideband sampling system provides digital electric field waveform measurements at sampling rates up to 201,600 samples per second, much higher than any previous instrument of this type. The main Langmuir wave emission band occurs near the local electron plasma frequency, which was approximately 43 kHz. The Langmuir waves are observed to shift above and below the plasma frequency, sometimes by as much as 20 kHz. The shifts in frequency are closely correlated with the downstream distance from the tangent field line, implying that the shifts are controlled by the electron beam velocity. Considerable fine structure is also evident, with timescales as short as 0.15 ms, corresponding to spatial scales of a few tens of Debye lengths. The frequency spectrum often consists of beat-type waveforms, with beat frequencies ranging from 0.2 to 7 kHz, and in a few cases, isolated wave packets. The peak electric field strengths are approximately 1 mV/m. These field strengths are too small for strongly nonlinear processes to be important. The beat-type waveforms are suggestive of a parametric decay process.

Hospodarsky, G. B.↗
NASA NTRS1994

The fine structure of Langmuir waves observed upstream of the bow shock at Venus

Highly structured Langmuir waves, also known as electron plasma oscillations, have been observed in the foreshock of Venus using the plasma wave experiment on the Galileo spacecraft during the gravity assist flyby on February 10, 1990. The Galileo wideband sampling system provides digital electric field waveform measurements at sampling rates up to 201,600 samples per second, much higher than any previous instrument of this type. The main Langmuir wave emission band occurs near the local electron plasma frequency, which was approximately 43 kHz. The Langmuir waves are observed to shift above and below the plasma frequency, sometimes by as much as 20 kHz. The shifts in frequency are closely correlated with the downstream distance from the tangent field line, implying that the shifts are controlled by the electron beam velocity. Considerable fine structure is also evident, with time scales as short as 0.15 milliseconds, corresponding to spatial scales of a few tens of Debye lengths. The frequency spectrum often consists of beat-type waveforms, with beat frequencies ranging from 0.2 to 7 kHz, and in a few cases, isolated wavepackets. The peak electric field strengths are approximately 1 mV/m. These field strengths are too small for strongly nonlinear processes to be important. The beat-type waveforms are suggestive of a parametric decay process.

Hospodarsky, G. B.↗
NASA NTRS1983

Adaptive reference voltage generator for firing angle control of line-commutated inverters

A control system for a permanent-magnet motor driven by a multiphase line-commulated inverter is described. It is provided with integrators for integrating the back EMF of each phase of the motor for use in generating system control signals for an inverter gate logic using a sync and firing angle control generator connected to the outputs of the integrators. The firing angle control signals are produced by the control generator by means for combining 120 deg segments of the integrated back EMF signals symmetrical about their maxima into composite positive and negative waveforms, and means for sampling the maxima of each waveform every 120 deg. These samples are then used as positive and negative firing angle control signals. Whereby any change in amplitude of the integrated back EMF signals will not affect a change in the operating power factor of the motor and inverter.

Dolland, C. R.↗
NASA NTRS1996

Receiver design, performance analysis, and evaluation for space-borne laser altimeters and space-to-space laser ranging systems

We report here the design and the performance measurements of the breadboard receiver of the Geoscience Laser Altimeter System (GLAS). The measured ranging accuracy was better than 2 cm and 10 cm for 5 ns and 30 ns wide received laser pulses under the expected received signal level, which agreed well with the theoretical analysis. The measured receiver sensitivity or the link margin was also consistent with the theory. The effects of the waveform digitizer sample rate and resolution were also measured.

Davidson, Frederic M.↗
NASA NTRS2003

On the Hilbert-Huang Transform Data Processing System Development

One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). The Fourier view of nonlinear mechanics that had existed for a long time, and the associated FFT (fairly recent development), carry strong a-priori assumptions about the source data, such as linearity and of being stationary. Natural phenomena measurements are essentially nonlinear and nonstationary. A very recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT) proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using the Empirical Mode Decomposition (EMD) followed by the Hilbert Transform of the empirical decomposition data (HT), the HHT allows spectrum analysis of nonlinear and nonstationary data by using an engineering a-posteriori data processing, based on the EMD algorithm. This results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF) that can be further analyzed for spectrum interpretation by the classical Hilbert Transform. This paper describes phase one of the development of a new engineering tool, the HHT Data Processing System (HHTDPS). The HHTDPS allows applying the "T to a data vector in a fashion similar to the heritage FFT. It is a generic, low cost, high performance personal computer (PC) based system that implements the HHT computational algorithms in a user friendly, file driven environment. This paper also presents a quantitative analysis for a complex waveform data sample, a summary of technology commercialization efforts and the lessons learned from this new technology development.

Kizhner, Semion↗
NASA NTRS2017

Chorus Whistler Wave Source Scales As Determined From Multipoint Van Allen Probe Measurements

Whistler mode chorus waves are particularly important in outer radiation belt dynamics due to their key role in controlling the acceleration and scattering of electrons over a very wide energy range. The key parameters for both nonlinear and quasi-linear treatment of wave-particle interactions are the temporal and spatial scales of the wave source region and coherence of the wave field perturbations. Neither the source scale nor the coherence scale is well established experimentally, mostly because of a lack of multipoint VLF waveform measurements. We present an unprecedentedly long interval of coordinated VLF waveform measurements (sampled at 16384 s(exp -1)) aboard the two Van Allen Probes spacecraft-9 h (0800-1200 UT and 1700-2200 UT) during two consecutive apogees on 15 July 2014. The spacecraft separations varied from about 100 to 5000 km (mostly radially); measurements covered an L shell range from 3 to 6; magnetic local time 0430-0900, and magnetic latitudes were approximately 15 and approximately 5 deg during the two orbits. Using time-domain correlation techniques, the single chorus source spatial extent transverse to the background magnetic field has been determined to be about 550-650 km for upper band chorus waves with amplitudes less than 100 pT and up to 800 km for larger amplitude, lower band chorus waves. The ratio between wave amplitudes measured on the two spacecraft is also examined to reveal that the wave amplitude distribution within a single chorus element generation area can be well approximated by a Gaussian exp(-0.5 x r (exp 2)/r(sub 0)(exp 2)), with the characteristic scale r(sub 0) around 300 km. Waves detected by the two spacecraft were found to be coherent in phase at distances up to 400 km.

Agapitov, O.↗
NASA NTRS1977

Initial development of a method of significant waveheight estimation for GEOS-III

The numerical method by which ocean surface significant waveheight estimates are produced from the GEOS-3 radar altimeter data is described. Four parameters characterizing the expected radar mean return waveform are determined from the altimeter's sixteen sample-and-hold waveform samplers through use of an iterative, least squares approach. One of the four parameters is a risetime term which has contributions from both the transmitted radar pulse width and the rms ocean surface height; the estimated significant waveheight is extracted from this risetime. The noise character of the estimation process leads to occasional negative significant waveheight estimates, and the origin of these nonphysical negative results is discussed. Possible modifications and areas for additional investigation are indicated.

Hayne, G. S.↗
NASA NTRS1992

A study of the influence of the data acquisition system sampling rate on the accuracy of measured acceleration loads for transport aircraft

A research effort was initiated at National Aeronautics and Space Administration (NASA) Langley Research Center (LaRC), to describe the relationship between the sampling rate and the accuracy of acceleration loads obtained from the data acquisition system of a transport aircraft. An accelerometer was sampled and digitized at a rate of 100 samples per second onboard a NASA Boeing 737 (B-737) flight research aircraft. Numerical techniques were used to reconstruct 2.5 hours of flight data into its original input waveform and then re-sample the waveform into rates of 4, 8, 16, and 32 samples per second. Peak-between-means counting technique and power spectral analysis were used to evaluate each sampling rate using the 32 samples per second data as the comparison. This paper presents the results from these methods and includes in appendix A, the peak-between-means counting results used in a general fatigue analysis for each of the sampling rates.

Whitehead, Julia H.↗
NASA NTRS2002

Geoscience Laser Altimeter System (GLAS) for the ICESat Mission

The Geoscience Laser Altimeter System (GLAS) is a new generation lidar and is the primary science payload for NASA's ICESat Mission. The GLAS design combines a 10 cm precision surface lidar with a sensitive dual wavelength cloud and aerosol lidar. GLAS will precisely measure the heights of the Earth's polar ice sheets, establish a grid of accurate height profiles of the Earth's land topography, and profile the vertical distribution of clouds and aerosols on a global scale. GLAS will be integrated onto a small spacecraft built by Ball Aerospace, and will be launched into a polar orbit with a 590-630 km altitude at an inclination of 94 degrees. ICESat is is currently planned to launch in winter 2002/03 and GLAS is designed to operate continuously in space for a minimum of 3 years. GLAS will measure the vertical distance from orbit to the Earth's surface with pulses from a ND:YAG laser at a 40 Hz rate. Each 6 nsec wide 1064 nm laser pulse is used to produce a single range measurement. On the surface, the laser footprints have 66 m diameter and approx. 170 m center-center spacings. The GLAS receiver uses a I m diameter telescope to detect laser backscatter and a Si APD to detect the 1064 nm signals. The detector's output is sampled by a digital ranging receiver, which records each transmitted pulse and surface echo waveform with 1 nsec (15 cm) resolution. Each echo pulse is digitized and is reported to ground with a record length of from 200 to 544 samples, depending on the spacecraft's location . The GLAS location and epoch times are measured by a precision GPS receiver carried on the ICESat spacecraft. Initial processing of the echo waveforms within GLAS permits discrimination between cloud and surface echoes for selecting appropriate waveform samples. This selection is guided by an on-board DEM which is used to set the boundaries for the echo pulse search algorithm. Subsequent ground-based echo pulse analysis, along with GPS-based clock frequency estimates, permit final determination of the range to the surface, degree of pulse spreading, and vertical distribution of any vegetation illuminated by the laser. Accurate knowledge of the laser beam's pointing angle is needed to prevent height biases when measuring over tilted surfaces, such as near the boundaries of ice sheets. For surfaces with 2 deg. slopes, knowledge of pointing angle of the beam's centroid angle to better than 10 urad is needed. GLAS uses a stellar reference system (SRS) to measure the pointing angle of each laser firing relative to inertial space. The SRS uses a high precision star camera oriented toward local zenith and a gyroscope to determine the inertial orientation of the SRS optical bench. The far field pattern of each laser is measured pulse relative to the star camera with a laser reference system (LRS). GLAS will also measure the vertical distributions of clouds and aerosols by recording the vertical profiles of laser pulse backscatter at both 1064 and 532 nm. The 1064 rim measurements use the Si APD detector and will be used to measure the height and echo pulse shape from thicker clouds. The lidar receiver at 532 nm uses a narrow bandwidth etalon filter and highly sensitive photon counting detectors. The 532 nm backscatter profiles will be used to measure the vertical extent of thinner clouds and the atmospheric boundary layer. The GLAS instrument component development is complete and the instrument is undergoing final testing and qualification at NASA-Goddard. The GLAS "as-built" characteristics and its expected measurement performance will be discussed.

Abshire, James B.↗
NASA NTRS2012

NASA Tech Briefs, July 2012

Topics covered include: Instrument Suite for Vertical Characterization of the Ionosphere-Thermosphere System; Terahertz Radiation Heterodyne Detector Using Two-Dimensional Electron Gas in a GaN Heterostructure; Pattern Recognition Algorithm for High-Sensitivity Odorant Detection in Unknown Environments; Determining Performance Acceptability of Electrochemical Oxygen Sensors; Versatile Controller for Infrared Lamp and Heater Arrays; High-Speed Scanning Interferometer Using CMOS Image Sensor and FPGA Based on Multifrequency Phase-Tracking Detection; Ultra-Low-Power MEMS Selective Gas Sensors; Compact Receiver Front Ends for Submillimeter-Wave Applications; Dynamically Reconfigurable Systolic Array Accelerator; Blocking Losses With a Photon Counter; Motion-Capture-Enabled Software for Gestural Control of 3D Mod; Orbit Software Suite; CoNNeCT Baseband Processor Module Boot Code SoftWare (BCSW); Trajectory Software With Upper Atmosphere Model; ALSSAT Version 6.0; Employing a Grinding Technology to Assess the Microbial Density for Encapsulated Organisms; Demonstration of Minimally Machined Honeycomb Silicon Carbide Mirrors; Polyimide Aerogel Thin Films; Nanoengineered Thermal Materials Based on Carbon Nanotube Array Composites; Composite Laminate With Coefficient of Thermal Expansion Matching D263 Glass; Robust Tensioned Kevlar Suspension Design; Focal Plane Alignment Utilizing Optical CMM; Purifying, Separating, and Concentrating Cells From a Sample Low in Biomass; Virtual Ultrasound Guidance for Inexperienced Operators; Beat-to-Beat Blood Pressure Monitor; Non-Contact Conductivity Measurement for Automated Sample Processing Systems; An MSK Radar Waveform; Telescope Alignment From Sparsely Sampled Wavefront Measurements Over Pupil Subapertures; Method to Remove Particulate Matter from Dusty Gases at Low Pressures; Terahertz Quantum Cascade Laser With Efficient Coupling and Beam Profile; Measurement Via Optical Near-Nulling and Subaperture Stitching; 885-nm Pumped Ceramic Nd:YAG Master Oscillator Power Amplifier Laser System; Airborne Hyperspectral Imaging System; Heat Shield Employing Cured Thermal Protection Material Blocks Bonded in a Large-Cell Honeycomb Matrix; and Asymmetric Supercapacitor for Long-Duration Power Storage.

Source record↗
NASA NTRS2004

Automated Analysis, Classification, and Display of Waveforms

A computer program partly automates the analysis, classification, and display of waveforms represented by digital samples. In the original application for which the program was developed, the raw waveform data to be analyzed by the program are acquired from space-shuttle auxiliary power units (APUs) at a sampling rate of 100 Hz. The program could also be modified for application to other waveforms -- for example, electrocardiograms. The program begins by performing principal-component analysis (PCA) of 50 normal-mode APU waveforms. Each waveform is segmented. A covariance matrix is formed by use of the segmented waveforms. Three eigenvectors corresponding to three principal components are calculated. To generate features, each waveform is then projected onto the eigenvectors. These features are displayed on a three-dimensional diagram, facilitating the visualization of the trend of APU operations.

Kwan, Chiman↗
NASA NTRS2006

Use of Photoelastic Modulators for High-accuracy Spectropolarimetric Imaging of Aerosols

Passive multiangular, multispectral, and polarimetric sensing approaches each have unique strengths for the measurement of tropospheric aerosol column abundances and microphysical properties. Current spaceborne multispectral and multiangular aerosols sensors operate at approximately 1 km resolution. Under NASA's Instrument Incubator Program, we are developing an electro-optic imaging approach that will enable adding high-accuracy polarimetry to such observations. To achieve a degree of linear polarization (DOLP) uncertainty of 0.5%, our approach temporally modulates the linear-polarization component of incoming light at a rapid rate, enabling each detector within a focal-plane array, combined with polarization analyzers, to measure the relative proportions of the linear Stokes components Q or U to the total intensity. Our system uses tandem photoelastic modulators (PEMs) within a high-reflectance, low diattenuation camera design. The two PEMs vibrate at slightly different resonant frequencies, leading to modulation of the polarized light at a heterodyne frequency of ~25 Hz. High-speed (1 kHz) readout of the detector arrays samples the output waveforms from which Q/I and U/I are derived. We report on experimental and theoretical analyses of PEM and optical system performance, along with plans for developing ruggedized PEMs capable of withstanding launch and on-orbit stresses.

photoelastics↗
NASA NTRS2003

Aging Wire Insulation Assessment by Phase Spectrum Examination of Ultrasonic Guided Waves

Wire integrity has become an area of concern to the aerospace community including DoD, NASA, FAA, and Industry. Over time and changing environmental conditions, wire insulation can become brittle and crack. The cracks expose the wire conductor and can be a source of equipment failure, short circuits, smoke, and fire. The technique of using the ultrasonic phase spectrum to extract material properties of the insulation is being examined. Ultrasonic guided waves will propagate in both the wire conductor and insulation. Assuming the condition of the conductor remains constant then the stiffness of the insulator can be determined by measuring the ultrasonic guided wave velocity. In the phase spectrum method the guided wave velocity is obtained by transforming the time base waveform to the frequency domain and taking the phase difference between two waveforms. The result can then be correlated with a database, derived by numerical model calculations, to extract material properties of the wire insulator. Initial laboratory tests were performed on a simple model consisting of a solid cylinder and then a solid cylinder with a polymer coating. For each sample the flexural mode waveform was identified. That waveform was then transformed to the frequency domain and a phase spectrum was calculated from a pair of waveforms. Experimental results on the simple model compared well to numerical calculations. Further tests were conducted on aircraft or mil-spec wire samples, to see if changes in wire insulation stiffness can be extracted using the phase spectrum technique.

Anastasi, Robert F.↗
NASA NTRS1975

A minimax technique for time-domain design of preset digital equalizers using linear programming

A linear programming technique is presented for the design of a preset finite-impulse response (FIR) digital filter to equalize the intersymbol interference (ISI) present in a baseband channel with known impulse response. A minimax technique is used which minimizes the maximum absolute error between the actual received waveform and a specified raised-cosine waveform. Transversal and frequency-sampling FIR digital filters are compared as to the accuracy of the approximation, the resultant ISI and the transmitted energy required. The transversal designs typically have slightly better waveform accuracy for a given distortion; however, the frequency-sampling equalizer uses fewer multipliers and requires less transmitted energy. A restricted transversal design is shown to use the least number of multipliers at the cost of a significant increase in energy and loss of waveform accuracy at the receiver.

Vaughn, G. L.↗