Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Integrated mean squared error”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Integrated controls-structures design methodology development for a class of flexible spacecraft

Future utilization of space will require large space structures in low-Earth and geostationary orbits. Example missions include: Earth observation systems, personal communication systems, space science missions, space processing facilities, etc., requiring large antennas, platforms, and solar arrays. The dimensions of such structures will range from a few meters to possibly hundreds of meters. For reducing the cost of construction, launching, and operating (e.g., energy required for reboosting and control), it will be necessary to make the structure as light as possible. However, reducing structural mass tends to increase the flexibility which would make it more difficult to control with the specified precision in attitude and shape. Therefore, there is a need to develop a methodology for designing space structures which are optimal with respect to both structural design and control design. In the current spacecraft design practice, it is customary to first perform the structural design and then the controller design. However, the structural design and the control design problems are substantially coupled and must be considered concurrently in order to obtain a truly optimal spacecraft design. For example, let C denote the set of the 'control' design variables (e.g., controller gains), and L the set of the 'structural' design variables (e.g., member sizes). If a structural member thickness is changed, the dynamics would change which would then change the control law and the actuator mass. That would, in turn, change the structural model. Thus, the sets C and L depend on each other. Future space structures can be roughly divided into four mission classes. Class 1 missions include flexible spacecraft with no articulated appendages which require fine attitude pointing and vibration suppression (e.g., large space antennas). Class 2 missions consist of flexible spacecraft with articulated multiple payloads, where the requirement is to fine-point the spacecraft and each individual payload while suppressing the elastic motion. Class 3 missions include rapid slewing of spacecraft without appendages, while Class 4 missions include general nonlinear motion of a flexible spacecraft with articulated appendages and robot arms. Class 1 and 2 missions represent linear mathematical modeling and control system design problems (except for actuator and sensor nonlinearities), while Class 3 and 4 missions represent nonlinear problems. The development of an integrated controls/structures design approach for Class 1 missions is addressed. The performance for these missions is usually specified in terms of (1) root mean square (RMS) pointing errors at different locations on the structure, and (2) the rate of decay of the transient response. Both of these performance measures include the contributions of rigid as well as elastic motion.

Maghami, P. G.↗
NASA NTRS1990

Ridge regression processing

Current navigation requirements depend on a geometric dilution of precision (GDOP) criterion. As long as the GDOP stays below a specific value, navigation requirements are met. The GDOP will exceed the specified value when the measurement geometry becomes too collinear. A new signal processing technique, called Ridge Regression Processing, can reduce the effects of nearly collinear measurement geometry; thereby reducing the inflation of the measurement errors. It is shown that the Ridge signal processor gives a consistently better mean squared error (MSE) in position than the Ordinary Least Mean Squares (OLS) estimator. The applicability of this technique is currently being investigated to improve the following areas: receiver autonomous integrity monitoring (RAIM), coverage requirements, availability requirements, and precision approaches.

Kuhl, Mark R.↗
NASA NTRS1992

Modeling of the WSTF frictional heating apparatus in high pressure systems

In order to develop a computer program able to model the frictional heating of metals in high pressure oxygen or nitrogen a number of additions have been made to the frictional heating model originally developed for tests in low pressure helium. These additions include: (1) a physical property package for the gases to account for departures from the ideal gas state; (2) two methods for spatial discretization (finite differences with quadratic interpolation or orthogonal collocation on finite elements) which substantially reduce the computer time required to solve the transient heat balance; (3) more efficient programs for the integration of the ordinary differential equations resulting from the discretization of the partial differential equations; and (4) two methods for determining the best-fit parameters via minimization of the mean square error (either a direct search multivariable simplex method or a modified Levenburg-Marquardt algorithm). The resulting computer program has been shown to be accurate, efficient and robust for determining the heat flux or friction coefficient vs. time at the interface of the stationary and rotating samples.

Skowlund, Christopher T.↗
NASA NTRS2021

Quantifying the Observational Requirements of a Space-borne LiDAR Snow Mission

This study quantifies the level of observational accuracy required from a spaceborne light detection and ranging (LiDAR) snow depth retrieval mission for enabling beneficial impacts for snow estimation. The study is conducted over a region in Western Colorado using a suite of observing system simulation experiments(OSSEs).The Joint UK Land Environment Simulator, version 5.0 (JULES v5.0) is employed to simulate a suite of idealized LiDAR observations, considering a range of LiDAR snow depth retrieval errors, different hypothetical sensor swath widths, and the impact of cloud cover on observability. These simulated observations are then assimilated into the Noah land surface modelwith multi-parameterization options, version 3.6 (Noah-MP v3.6) model. This data assimilation setup is used to systematically evaluate the potential utility of LiDAR observations for improving modeled snow water equivalent (SWE)estimates and water budget variables such as runoff. Results from the OSSE runsshow that, in general, assimilation of synthetic LiDAR observations provide beneficial impacts when theLiDAR snow depth retrieval error standard deviation (σerror) is below 60 cm.Based on comparisons between the realistic (i.e., swath-limited and cloud-attenuated) case and the idealized (i.e., infinite swath width in the absence of cloud cover) case,this study concludes that observations with a conservative error standard deviation threshold of 40 cm (i.e., upper limit of the snow depth retrieval error that adds value to the SWE estimates viaassimilation) are needed for improving modeled snow estimates. More than a 33% reduction in SWEroot mean square errors and more than a 15% increase in correlation coefficientsare achieved when σ error ≤ 40 cmusing a 170-km sensor swath width in the presence of cloud attenuation effects. Further, the integrated hydrologic response, as represented by total (surface and subsurface) runoff estimates during the snow ablation season, are also enhanced when assimilating synthetic LiDAR snow depth retrievals with errors below this level.

Yonghwan Kwon↗
NASA NTRS1974

Model of human dynamic orientation

The dynamics associated with the perception of orientation were modelled for near-threshold and suprathreshold vestibular stimuli. A model of the information available at the peripheral sensors which was consistent with available neurophysiologic data was developed and served as the basis for the models of the perceptual responses. The central processor was assumed to utilize the information from the peripheral sensors in an optimal (minimum mean square error) manner to produce the perceptual estimates of dynamic orientation. This assumption, coupled with the models of sensory information, determined the form of the model for the central processor. The problem of integrating information from the semi-circular canals and the otoliths to predict the perceptual response to motions which stimulated both organs was studied. A model was developed which was shown to be useful in predicting the perceptual response to multi-sensory stimuli.

Ormsby, C. C.↗
NASA NTRS2010

Wavefront Sensing of X-Ray Telescopes

Phase Retrieval analysis of off-axis or defocused focal-plane data from telescope optics has been proven effective in understanding misalignments and optical aberrations in normal incidence telescopes. The approach is used, e.g., in commissioning of the James Webb Space Telescope (JWST) segmented primary mirror. There is a similar need for evaluating low-order figure errors of grazing incidence mirrors and nested telescope assemblies. When implemented in these systems, phase retrieval does not depend on normal incidence access to each mirror (shell) surface and, therefore, provides an effective means for evaluating nested x-ray telescopes during integration and test. We have applied a well-known phase retrieval algorithm to grazing incidence telescopes. The algorithm uses the Levenberg-Marquardt optimization procedure to perform a non-linear least-squares fit of the telescope Point Spread Function (PSF). The algorithm can also retrieve low order figure errors at visible wavelengths where optical diffraction is the dominant defect in the PSF. In this paper we will present the analytical approach and its implementation for grazing incidence mirrors of the International X-Ray Observatory (IXO). We analyze the effects of low order axial surface errors individually, and in combination on the system PSF at 633 nanometers. We demonstrate via modeling that the wavefront sensing algorithm can recover axial errors (of the grazing incidence mirrors) to a small fraction of the known axial figure errors using simulated PSFs as input data to the algorithm.

Saha, Timo↗
NASA NTRS1992

Flight evaluation of differential GPS aided inertial navigation systems

Algorithms are described for integration of Differential Global Positioning System (DGPS) data with Inertial Navigation System (INS) data to provide an integrated DGPS/INS navigation system. The objective is to establish the benefits that can be achieved through various levels of integration of DGPS with INS for precision navigation. An eight state Kalman filter integration was implemented in real-time on a twin turbo-prop transport aircraft to evaluate system performance during terminal approach and landing operations. A fully integrated DGPS/INS system is also presented which models accelerometer and rate-gyro measurement errors plus position, velocity, and attitude errors. The fully integrated system was implemented off-line using range-domain (seventeen-state) and position domain (fifteen-state) Kalman filters. Both filter integration approaches were evaluated using data collected during the flight test. Flight-test data consisted of measurements from a 5 channel Precision Code GPS receiver, a strap-down Inertial Navigation Unit (INU), and GPS satellite differential range corrections from a ground reference station. The aircraft was laser tracked to determine its true position. Results indicate that there is no significant improvement in positioning accuracy with the higher levels of DGPS/INS integration. All three systems provided high-frequency (e.g., 20 Hz) estimates of position and velocity. The fully integrated system provided estimates of inertial sensor errors which may be used to improve INS navigation accuracy should GPS become unavailable, and improved estimates of acceleration, attitude, and body rates which can be used for guidance and control. Precision Code DGPS/INS positioning accuracy (root-mean-square) was 1.0 m cross-track and 3.0 m vertical. (This AGARDograph was sponsored by the Guidance and Control Panel.)

Mcnally, B. David↗
NASA NTRS2015

Effects of Resolution and Spectral Nudging in Simulation the Effects of Wintertime Atmospheric River Landfalls in the Western US

Landfalling atmospheric rivers (ARs) play a crucial role in the climate of the US Pacific coast region as they are frequently related with heavy precipitation and flash flooding events. Thus, the capability of climate models to accurately simulate AR landfalls and their key hydrologic effects is an important practical concern for WUS, from flood forecasting to future water resources projections. In order to examine the effects of model configuration, including the resolution and spectral nudging, in simulating the climatology of key weather events in the conterminous US, a NASA team has performed a hindcast experiment using the GEOS5 global and the NU-WRF regional models for Nov 1999 - Oct 2010. This study examines the skill of these hindcasts, with different models and their configurations, in simulating key footprints of landfalling ARs in the WUS region. Using an AR-landfall chronology based on the vertically-integrated water vapor flux calculated from the MERRA2 reanalysis, we have analyzed the observed and simulated precipitation and temperature anomalies associated with wintertime AR landfalls along the US Pacific coast. Model skill is measured using metrics including regional means, a skill score based on correlations and mean-square errors, and Taylor diagrams in four WUS Bukovsky regions. Results show that the AR-related anomalies of precipitation is more reliable than of surface temperatures. Model skill also varies according to regions. The AR temperature anomalies are well simulated in most of the WUS region except PNW. For precipitation, simulations with finer spatial resolution tend to generate larger spatial variability and agree better with the PRISM data in most regions. Such a resolution dependence of spatial variability is not found for temperatures; e.g., the MERRA2 reanalysis often outperforms, with similar spatial variability and higher pattern correlations with the PRISM data, finer-resolution NU-WRF runs in simulating temperature variations within subregions. Results from this study will be summarized to assist future (regional) climate experiments for climate change impact assessments and developing adaptationmitigation strategies, the key elements of the National Climate Assessment.

Simulation↗
NASA NTRS2012

Evaluation of Moderate-Resolution Imaging Spectroradiometer (MODIS) Snow Albedo Product (MCD43A) over Tundra

This study assesses the MODIS standard Bidirectional Reflectance Distribution Function (BRDF)/Albedo product, and the daily Direct Broadcast BRDF/Albedo algorithm at tundra locations under large solar zenith angles and high anisotropic diffuse illumination and multiple scattering conditions. These products generally agree with ground-based albedo measurements during the snow cover period when the Solar Zenith Angle (SZA) is less than 70deg. An integrated validation strategy, including analysis of the representativeness of the surface heterogeneity, is performed to decide whether direct comparisons between field measurements and 500- m satellite products were appropriate or if the scaling of finer spatial resolution airborne or spaceborne data was necessary. Results indicate that the Root Mean Square Errors (RMSEs) are less than 0.047 during the snow covered periods for all MCD43 albedo products at several Alaskan tundra areas. The MCD43 1- day daily albedo product is particularly well suited to capture the rapidly changing surface conditions during the spring snow melt. Results also show that a full expression of the blue sky albedo is necessary at these large SZA snow covered areas because of the effects of anisotropic diffuse illumination and multiple scattering. In tundra locations with dark residue as a result of fire, the MODIS albedo values are lower than those at the unburned site from the start of snowmelt.

Wang, Zhuosen↗
NASA NTRS1994

Gravity model development for TOPEX/POSEIDON: Joint gravity models 1 and 2

The TOPEX/POSEIDON (T/P) prelaunch Joint Gravity Model-1 (JGM-1) and the postlaunch JGM-2 Earth gravitational models have been developed to support precision orbit determination for T/P. Each of these models is complete to degree 70 in spherical harmonics and was computed from a combination of satellite tracking data, satellite altimetry, and surface gravimetry. While improved orbit determination accuracies for T/P have driven the improvements in the models, the models are general in application and also provide an improved geoid for oceanographic computations. The postlaunch model, JGM-2, which includes T/P satellite laser ranging (SLR) and Doppler orbitography and radiopositioning integrated by satellite (DORIS) tracking data, introduces radial orbit errors for T/P that are only 2 cm RMS with the commission errors of the marine geoid for terms to degree 70 being +/- 25 cm. Errors in modeling the nonconservative forces acting on T/P increase the total radial errors to only 3-4 cm root mean square (RMS), a result much better than premission goals. While the orbit accuracy goal for T/P has been far surpassed geoid errors still prevent the absolute determination of the ocean dynamic topography for wavelengths shorter than about 2500 km. Only a dedicated gravitational field satellite mission will likely provide the necessary improvement in the geoid.

Nerem, R. S.↗
NASA NTRS2011

Tropospheric Correction for InSAR Using Interpolated ECMWF Data and GPS Zenith Total Delay

To mitigate atmospheric errors caused by the troposphere, which is a limiting error source for spaceborne interferometric synthetic aperture radar (InSAR) imaging, a tropospheric correction method has been developed using data from the European Centre for Medium- Range Weather Forecasts (ECMWF) and the Global Positioning System (GPS). The ECMWF data was interpolated using a Stretched Boundary Layer Model (SBLM), and ground-based GPS estimates of the tropospheric delay from the Southern California Integrated GPS Network were interpolated using modified Gaussian and inverse distance weighted interpolations. The resulting Zenith Total Delay (ZTD) correction maps have been evaluated, both separately and using a combination of the two data sets, for three short-interval InSAR pairs from Envisat during 2006 on an area stretching from northeast from the Los Angeles basin towards Death Valley. Results show that the root mean square (rms) in the InSAR images was greatly reduced, meaning a significant reduction in the atmospheric noise of up to 32 percent. However, for some of the images, the rms increased and large errors remained after applying the tropospheric correction. The residuals showed a constant gradient over the area, suggesting that a remaining orbit error from Envisat was present. The orbit reprocessing in ROI_pac and the plane fitting both require that the only remaining error in the InSAR image be the orbit error. If this is not fulfilled, the correction can be made anyway, but it will be done using all remaining errors assuming them to be orbit errors. By correcting for tropospheric noise, the biggest error source is removed, and the orbit error becomes apparent and can be corrected for

Webb, Frank H.↗
NASA NTRS2011

Space-Time Data Fusion

Space-time Data Fusion (STDF) is a methodology for combing heterogeneous remote sensing data to optimally estimate the true values of a geophysical field of interest, and obtain uncertainties for those estimates. The input data sets may have different observing characteristics including different footprints, spatial resolutions and fields of view, orbit cycles, biases, and noise characteristics. Despite these differences all observed data can be linked to the underlying field, and therefore the each other, by a statistical model. Differences in footprints and other geometric characteristics are accounted for by parameterizing pixel-level remote sensing observations as spatial integrals of true field values lying within pixel boundaries, plus measurement error. Both spatial and temporal correlations in the true field and in the observations are estimated and incorporated through the use of a space-time random effects (STRE) model. Once the models parameters are estimated, we use it to derive expressions for optimal (minimum mean squared error and unbiased) estimates of the true field at any arbitrary location of interest, computed from the observations. Standard errors of these estimates are also produced, allowing confidence intervals to be constructed. The procedure is carried out on a fine spatial grid to approximate a continuous field. We demonstrate STDF by applying it to the problem of estimating CO2 concentration in the lower-atmosphere using data from the Atmospheric Infrared Sounder (AIRS) and the Japanese Greenhouse Gasses Observing Satellite (GOSAT) over one year for the continental US.

Greenhouse Gases Observing Satellite (GOSAT)↗
NASA NTRS2021

Description of the NASA GEOS Composition Forecast Modeling System GEOS-CF v1.0

The Goddard Earth Observing System composition forecast (GEOS-CF) system is a high-resolution (0.25 degree) global constituent prediction system from NASA’s Global Modeling and Assimilation Office (GMAO). GEOS-CF offers a new tool for atmospheric chemistry research, with the goal to supplement NASA’s broad range of space-based and in-situ observation sand to support flight campaign planning, support of satellite observations, and air quality research. GEOS-CF expands on the GEOS weather and aerosol modeling system by introducing the GEOS-Chem chemistry module to provide analyses and 5-day forecasts of atmospheric constituents including ozone (O3), carbon monoxide (CO), nitrogen dioxide (NO2), and fine particulate matter (PM2.5). The chemistry module integrated in GEOS-CF is identical to the offline GEOS-Chem model and readily benefits from the innovations provided by the GEOS-Chem community.Evaluation of GEOS-CF against satellite, ozone sonde and surface observations show realistic simulated concentrations of O3, NO2, and CO, with normalized mean biases of -0.1 to -0.3, normalized root mean square errors (NRMSE) between 0.1-0.4, and correlations between 0.3-0.8. Comparisons against surface observations highlight the successful representation of air pollutants under a variety of meteorological conditions, yet also highlight current limitations, such as an over prediction of summertime ozone over the Southeast United States. GEOS-CFv1.0 generally overestimates aerosols by 20-50% due to known issues in GEOS-Chem v12.0.1 that have been addressed in later versions.The 5-day hourly forecasts have skill scores comparable to the analysis. Model skills can be improved significantly by applying a bias-correction to the surface model output using a machine-learning approach.

GEOS-CF↗
NASA NTRS1999

A Diagnostic Analysis of the Kennedy Space Center LDAR Network: Data Characteristics - 1

An analytical framework is developed in which to analyze climatological VHF (66 MHz) radiation measurements taken by the Kennedy Space Center Lightning Detection and Ranging (LDAR) network. A 19-month noise-filtered sample of LDAR observations is examined using this framework. It is found that the climatological VHF source density as observed by LDAR falls off approximately 10 dB every 71 km of ground range away from the network centroid (a 31 km e-folding scale). From this framework it is inferred that the underlying source distribution is likely inverse exponential in amplitude, with a log-slope of 126-147 mW(sup -1/2). The underlying vertical distribution of VHF sources is approximately normally distributed with a mean altitude of 9 km and a standard deviation of 2.7 km; this implies that the loss of below-horizon sources has a negligible effect on column-integrated source densities within 200 km ground range. At medium to far ranges, location errors are primarily radial and have a slightly asymmetric distribution whose first moment increases as range squared. Error moments estimated from observed lightning are significantly higher than those from aircraft-based signal generator or analytic solution estimates, suggesting that timing errors arising from poor signal identification and discrimination may dominate over timing errors arising from nominal sensor resolution. The VHF source properties of individual LDAR-observed flashes are computed and an analytic expression for flash detection efficiency vs. range is derived. This reveals nearly constant flash detection efficiency to 80-94 km range from the network centroid.

Boccippio, D. J.↗
NASA NTRSDate not supplied

Assessing the Viability of Using GEOS-Forecast Product for Landslides Forecasting: A Step Toward Early Warning System

Landslides across the globe are mostly triggered by extreme rainfall events affecting infrastructure, transportation and livelihoods. The risks are rarely quantified due to lack of data, analytical skills and limited modeling techniques. Knowledge of local to global scale landslide risks provides communities and national agencies the ability to adapt disaster management practices to mitigate and recover from these hazards. In order to minimize the risks and improve characterization of community resilience to landslides, it is vital to have reliable information about the factors triggering landslides such as rainfall, well ahead in time. Forecasting potential landslide activity and impacts can be achieved through reliable precipitation forecast models. However, it is challenging because of the temporal and spatial variability of precipitation, an important factor in triggering landslides. Evaluation of the precipitation field, associated errors, and sampling uncertainties is integral for development of efficient and reliable landslide forecasting and early warning system. This study develops a methodology to assess the viability of using a precipitation field provided by a global model and its potential integration in the landslide forecasting system. The study focuses on the comparison between the IMERG (Integrated Multi-satellitE Retrievals for Global Precipitation Mission) and GEOS (NASA Goddard Earth Observing System)-Forecast product over contiguous United States (CONUS). GEOS model assimilates new observations every 6 hours, at 00, 06, 12, and 18 UTC. The framework is tested on the GEOS-Forecast Model initialized at 00 UTC using daily IMERG early product as reference using both categorical and continuous statistics. The categorical statistics includes the probability of detection (POD), success ratio (SR), critical success index (CSI), and the hit bias. Continuous statistics such as correlation, normalized standard deviation, and root-mean-square error are also evaluated. Overall, GEOS-Forecast precipitation field over the analysis period (~1 year) show underestimation with respect to IMERG early for the daily accumulated rainfall. However, the probability distribution function and cumulative distribution function of both show similar patterns. In terms of correlations, POD, SR, CSI, hit bias, the performance varies with respect to the rainfall threshold used.

Sana Khan↗
NASA NTRS1983

A function space approach to state and model error estimation for elliptic systems

An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed.

Rodriguez, G.↗
NASA NTRS1983

A function space approach to state and model error estimation for elliptic systems

An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal esimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed. While this paper focuses on theoretical developments, applications arising in the area of large structure static shape determination are contained in a closely related paper (Rodriguez and Scheid, 1982).

Rodriguez, G.↗
NASA NTRS1997

Root-Raised Cosine Filter Implementation That Uses Canonical Signed Digits for High-Speed Digital Filter Applications

NASA Lewis Research Center's Space Communications Division has been investigating high-speed digital filters that can operate at a higher speed than those in current use for a digital modulator and demodulator (modem). Using the Canonical Signed Digits (CSD) number representation for filter coefficients is a very effective way to increase the filter's speed while reducing complexity in the digital filter hardware design. This approach is a good alternative to using an expensive parallel-processing design technique or custom, application-specific integrated circuits. Such integrated circuits may not be suitable for applications that require filter speeds faster than what application-specific integrated circuits digital signal processors can offer for a dedicated channel. When a communication channel is a dedicated, multiplication process--a costly, time-consuming process--it can be greatly simplified by a replacement of the filter coefficients with CSD numbers. A computer code written with the MATLAB software package runs the program and generates CSD-represented filter coefficients that are based on minimizing minimum mean square errors. Also, the Alta Group of Cadence's Signal Processing Workstation is used to simulate and analyze the CSD filter responses. The impulse response of the root-raised cosine filter that is used as a base model is defined. From this filter, a set of coefficients is sampled and stored in a file. For the all coefficients, the optimal CSD number for each coefficient is searched on the basis of the minimum-mean-square-errors criterion. Because the distribution of CSD numbers is not uniform, quantization errors tend to be bigger for coefficients greater than 1/2. To offset errors that occur in a region of coefficients between 1/2 to 1 and to better represent fractions with CSD numbers, an extra nonzero digit is allowed for any coefficients exceeding 1/2. This will greatly improve frequency response as well as intersymbol interference at the receiver. The frequency response of a set of collected CSD-represented filter coefficients was compared with the same filter that was conventionally implemented. Analyses show CSD-implemented filters perform as well as conventional filters. Comparison of eye diagrams and bit-error-rate curves between CSD filters and traditionally implemented filters are almost indistinguishable. However, filter complexity was reduced from almost 3.5 to 1 for CSD filters. Complete computer simulation results are available. In the near future, work will focus on building actual working digital filter hardware in a field programmable gate array (FPGA).

Kim, Heechul↗