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At least 397 records · Page 22

Spatiotemporal Path-Matching for Comparisons Between Ground- Based and Satellite Lidar Measurements

The spatiotemporal sampling differences between ground-based and satellite lidar data can contribute to significant errors for direct measurement comparisons. Improvement in sample correspondence is examined by the use of radiosonde wind velocity to vary the time average in ground-based lidar data to spatially match coincident satellite lidar measurements. Results are shown for the 26 February 2004 GLAS/ICESat overflight of a ground-based lidar stationed at NASA GSFC. Statistical analysis indicates that improvement in signal correlation is expected under certain conditions, even when a ground-based observation is mismatched in directional orientation to the satellite track.

Berkoff, Timothy A.↗

Organic contamination detection for isotopic analysis of water by laser spectroscopy

Hydrogen and oxygen stable isotope ratios (δ 2 H, δ 17 O, and δ 18 O values) are commonly used tracers of water. These ratios can be measured by isotope ratio infrared spectroscopy (IRIS). However, IRIS approaches are prone to errors induced by organic compounds present in plant, soil, and natural water samples. A novel approach using 17 O-excess values has shown promise for flagging spectrally contaminated plant samples during IRIS analysis. A systematic assessment of this flagging system is needed to prove it useful. Errors induced by methanol and ethanol water mixtures on measured IRIS and isotope ratio mass spectrometry (IRMS) results were evaluated. For IRIS analyses both liquid- and vapour-mode (via direct vapour equilibration) methods are used. The δ 2 H, δ 17 O, and δ 18 O values were measured and compared with known reference values to determine the errors induced by methanol and ethanol contamination. In addition, the 17 O-excess contamination detection approach was tested. This is a post-processing detection tool for both liquid and vapour IRIS triple-isotope analyses, utilizing calculated 17 O-excess values to flag contaminated samples. Organic contamination induced significant errors in IRIS results, not seen in IRMS results. Methanol caused larger errors than ethanol. Results from vapour-IRIS analyses had larger errors than those from liquid-IRIS analyses. The 17 O-excess approach identified methanol driven error in liquid- and vapour-mode IRIS samples at levels where isotope results became unacceptably erroneous. For ethanol contaminated samples, a mix of erroneous and correct flagging occurred with the 17 O-excess method. Here our results indicate that methanol is the more problematic contaminant for data corruption. The 17 O-excess method was therefore useful for data quality control. Organic contamination caused significant errors in IRIS stable isotope results. These errors were larger during vapour analyses than during liquid IRIS analyses, and larger for methanol than ethanol contamination. The 17 O-excess method is highly sensitive for detecting narrowband (methanol) contamination error in vapour and liquid analysis modes in IRIS.

60 APPLIED LIFE SCIENCES↗

Superconducting Material Growth for Radio-Frequency (RF) Cavities

Superconducting radio-frequency (SRF) cavities, usually manufactured from Niobium (Nb), are vital components of modern particle accelerators because of their ability to achieve high acceleration gradients with little power dissipation. Naturally forming Nb surface oxides significantly alter cavity performance by changing surface resistance. A nondestructive characterization of oxide thickness is helpful for relating surface processing treatments to cavity performance. This work develops a protocol to measure Nb oxide thickness using Angle-Resolved X-ray Photoelectron Spectroscopy (ARXPS) while correcting instrumental errors. Using uniform bulk standard samples (Silver, Aluminum oxide, and Germanium), we determined a baseline correction factor to account for analyzer-related intensity evolution as the measurement angle increases. The correction factor was then applied to Nb 3d ARXPS data. Applying the Strohmeier equation to the corrected data yielded a Nb2O5 thickness of 6.04 nm, closely matching the 5.5 (±.05) nm value obtained from cross-sectional transmission electron microscopy. Our approach will bring a method to incorporate inherent errors in the thickness measurements using ARXPS and can be broadly applied to improve the accuracy of thickness measurements in a wide range of heterostructures.

Lambert, Nathan [Fermilab]↗

Superconducting Material Growth for Radio-Frequency (RF) Cavities

Superconducting radio-frequency (SRF) cavities, usually manufactured from Niobium (Nb), are vital components of modern particle accelerators because of their ability to achieve high acceleration gradients with little power dissipation. Naturally forming Nb surface oxides significantly alter cavity performance by changing surface resistance. A nondestructive characterization of oxide thickness is helpful for relating surface processing treatments to cavity performance. This work develops a protocol to measure Nb oxide thickness using Angle-Resolved X-ray Photoelectron Spectroscopy (ARXPS) while correcting instrumental errors. Using uniform bulk standard samples (Silver, Aluminum oxide, and Germanium), we determined a baseline correction factor to account for analyzer-related intensity evolution as the measurement angle increases. The correction factor was then applied to Nb 3d ARXPS data. Applying the Strohmeier equation to the corrected data yielded a Nb2O5 thickness of 6.04 nm, closely matching the 5.5 (±.05) nm value obtained from cross-sectional transmission electron microscopy. Our approach will bring a method to incorporate inherent errors in the thickness measurements using ARXPS and can be broadly applied to improve the accuracy of thickness measurements in a wide range of heterostructures.

Lambert, Nathan [Fermilab]↗

Spectrometric Estimation of Total Nitrogen Concentration in Douglas-Fir Foliage

Spectral measurements of fresh and dehydrated Douglas-fir foliage, from trees cultivated under three fertilization treatments, were acquired with a laboratory spectrophotometer. The slope (first-derivative) of the fresh- and dry-leaf absorbance spectra at locations near known protein absorption features was strongly correlated with total nitrogen (TN) concentration of the foliage samples. Particularly strong correlation was observed between the first-derivative spectra in the 2150-2170 nm region and TN, reaching a local maximum in the fresh-leaf spectra of -0.84 at 2 160 nm. Stepwise regression was used to generate calibration equations relating first derivative spectra from fresh, dry/intact, and dry/ground samples to TN concentration. Standard errors of calibration were 1.52 mg g-1 (fresh), 1.33 (dry/intact), and 1.20 (dry/ground), with goodness-of-fit 0.94 and greater. Cross-validation was performed with the fresh-leaf dataset to examine the predictive capability of the regression method; standard errors of prediction ranged from 1.47 - 2.37 mg g(exp -1) across seven different validation sets, prediction goodness of fit ranged from .85-.94, and wavelength selection was fairly insensitive to the membership of the calibration set. All regressions in this study tended to select wavelengths in the 2100-2350 nm region, with the primary selection in the 2142-2172 nm region. The study provides positive evidence concerning the feasibility of assessing TN status of fresh-leaf samples by spectrometric means. We assert that the ability to extract biochemical information from fresh-leaf spectra is a necessary but insufficient condition regarding the use of remote sensing for canopy-level biochemical estimation.

Johnson, Lee F.↗

TRMM On-Orbit Performance Re-Accessed After Control Change

The Tropical Rainfall Measuring Mission (TRMM) spacecraft, a joint mission between the U.S. and Japan, launched onboard an HI1 rocket on November 27,1997 and transitioned in August, 2001 from an average operating altitude of 350 kilometers to 402.5 kilometers. Due to problems using the Earth Sensor Assembly (ESA) at the higher altitude, TRMM switched to a backup attitude control mode. Prior to the orbit boost TRMM controlled pitch and roll to the local vertical using ESA measurements while using gyro data to propagate yaw attitude between yaw updates from the Sun sensors. After the orbit boost, a Kalman filter used 3-axis gyro data with Sun sensor and magnetometers to estimate onboard attitude. While originally intended to meet a degraded attitude accuracy of 0.7 degrees, the new control mode met the original 0.2 degree attitude accuracy requirement after improving onboard ephemeris prediction and adjusting the magnetometer calibration onboard. Independent roll attitude checks using a science instrument, the Precipitation Radar (PR) which was built in Japan, provided a novel insight into the pointing performance. The PR data helped identify the pointing errors after the orbit boost, track the performance improvements, and show subtle effects from ephemeris errors and gyro bias errors. It also helped identify average bias trends throughout the mission. Roll errors tracked by the PR from sample orbits pre-boost and post-boost are shown in Figure 1. Prior to the orbit boost the largest attitude errors were due to occasional interference in the ESA. These errors were sometime larger than 0.2 degrees in pitch and roll, but usually less, as estimated from a comprehensive review of the attitude excursions using gyro data. Sudden jumps in the onboard roll show up as spikes in the reported attitude since the control responds within tens of seconds to null the pointing error. The PR estimated roll tracks well with an estimate of the roll history propagated using gyro data. After the orbit boost, the attitude errors shown by the PR roll have a smooth sine-wave type signal because of the way that attitude errors propagate with the use of gyro data. Yaw errors couple at orbit period to roll with '/4 orbit lag. By tracking the amplitude, phase, and bias of the sinusoidal PR roll error signal, it was shown that the average pitch rotation axis tends to be offset from orbit normal in a direction perpendicular to the Sun direction, as shown in Figure 2 for a 200 day period following the orbit boost. This is a result of the higher accuracy and stability of the Sun sensor measurements relative to the magnetometer measurements used in the Kalman filter. In November, 2001 a magnetometer calibration adjustment was uploaded which improved the pointing performance, keeping the roll and yaw amplitudes within about 0.1 degrees. After the boost, onboard ephemeris errors had a direct effect on the pitch pointing, being used to compute the Earth pointing reference frame. Improvements after the orbit boost have kept the the onboard ephemeris errors generally below 20 kilometers. Ephemeris errors have secondary effects on roll and yaw, especially during high beta angle when pitch effects can couple into roll and yaw. This is illustrated in figure 3. The onboard roll bias trends as measured by PR data show correlations with the Kalman filter's gyro bias error. This particularly shows up after yaw turns (every 2 to 4 weeks) as shown in Figure 3, when a slight roll bias is observed while the onboard computed gyro biases settle to new values. As for longer term trends, the PR data shows that the roll bias was influenced by Earth horizon radiance effects prior to the boost, changing values at yaw turns, and indicated a long term drift as shown in Figure 4. After the boost, the bias variations were smaller and showed some possible correlation with solar beta angle, probably due to sun sensor misalignment effects.

Bilanow, Steve↗

TRMM On-Orbit Performance Reassessed After Control Change

The Tropical Rainfall Measuring Mission (TRMM) spacecraft, a joint mission between the U.S. and Japan, launched onboard an H-I1 rocket on November 27, 1997, and transitioned in August, 2001, from an average operating altitude of 350 kilometers to 402.5 kilometers. Due to problems using the Earth Sensor Assembly (ESA) at the higher altitude, TRMM switched to a backup attitude control mode. Prior to the orbit boost TRMM controlled pitch and roll to the local vertical using ESA measurements while using gyro data to propagate yaw attitude between yaw updates from the Sun sensors. After the orbit boost, a Kalman filter used 3-axis gyro data with Sun sensor and magnetometers to estimate onboard attitude. While originally intended to meet a degraded attitude accuracy of 0.7 degrees, the new control mode met the original 0.2 degree attitude accuracy requirement after improving onboard ephemeris prediction and adjusting the magnetometer calibration onboard. Independent roll attitude checks using a science instrument, the Precipitation Radar (PR) which was built in Japan, provided a novel insight into the pointing performance. The PR data helped identify the pointing errors after the orbit boost, track the performance improvements, and show subtle effects from ephemeris errors and gyro bias errors. It also helped identify average bias trends throughout the mission. Roll errors tracked by the PR from sample orbits pre-boost and post-boost are shown in Figure 1. Prior to the orbit boost, the largest attitude errors were due to occasional interference in the ESA. These errors were sometime larger than 0.2 degrees in pitch and roll, but usually less, as estimated from a comprehensive review of the attitude excursions using gyro data. Sudden jumps in the onboard roll show up as spikes in the reported attitude since the control responds within tens of seconds to null the pointing error. The PR estimated roll tracks well with an estimate of the roll history propagated using gyro data. After the orbit boost, the attitude errors shown by the PR roll have a smooth sine-wave type signal because of the way that attitude errors propagate with the use of gyro data. Yaw errors couple at orbit period to roll with 1/4 orbit lag. By tracking the amplitude, phase, and bias of the sinusoidal PR roll error signal, it was shown that the average pitch rotation axis tends to be offset from orbit normal in a direction perpendicular to the Sun direction, as shown in Figure 2 for a 200 day period following the orbit boost. This is a result of the higher accuracy and stability of the Sun sensor measurements relative to the magnetometer measurements used in the Kalman filter. In November, 2001 a magnetometer calibration adjustment was uploaded which improved the pointing performance, keeping the roll and yaw amplitudes within about 0.1 degrees.

Bilanow, Stephen↗

Error analysis in the measurement of average power with application to switching controllers

Power measurement errors due to the bandwidth of a power meter and the sampling of the input voltage and current of a power meter were investigated assuming sinusoidal excitation and periodic signals generated by a model of a simple chopper system. Errors incurred in measuring power using a microcomputer with limited data storage were also considered. The behavior of the power measurement error due to the frequency responses of first order transfer functions between the input sinusoidal voltage, input sinusoidal current, and the signal multiplier was studied. Results indicate that this power measurement error can be minimized if the frequency responses of the first order transfer functions are identical. The power error analysis was extended to include the power measurement error for a model of a simple chopper system with a power source and an ideal shunt motor acting as an electrical load for the chopper. The behavior of the power measurement error was determined as a function of the chopper's duty cycle and back EMF of the shunt motor. Results indicate that the error is large when the duty cycle or back EMF is small. Theoretical and experimental results indicate that the power measurement error due to sampling of sinusoidal voltages and currents becomes excessively large when the number of observation periods approaches one-half the size of the microcomputer data memory allocated to the storage of either the input sinusoidal voltage or current.

Maisel, J. E.↗

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↗

Comparison of ISCCP and other cloud amounts

A new 8-year global cloud climatology has been produced by the International Satellite Cloud Climatology Project (ISCCP) that provides information every 3 h at 280-km spatial resolution covering the period from July 1983 through June 1991. If cloud detection errors and differences in area sampling are neglected, individual ISCCP cloud amounts agree with individual surface observations to within 15% rms with biases of only a few percent. When measurements of small-scale, broken clouds are isolated in the comparison, the rms differences between satellite and surface cloud amounts are about 25%, similar to the rms difference between ISCCP and Landsat determinations of cloud amount. For broken clouds, the average ISCCP cloud amounts are about 5% smaller than estimated by surface observers (difference between earth cover and sky cover), but about 5% larger than estimated from very high spatial resolution satellite observations (overestimate due to low spatial resolution offset by underestimate due to finite radiance thresholds). Detection errors caused by errors in the ISCCP clear-sky radiances or incorrect radiance threshold magnitudes, are the dominant source of error in monthly average cloud amounts. The ISCCP cloud amounts appear to be too low over land by about 10%, somewhat less in summer and somewhat more in winter, and about right (maybe slightly low) over oceans. In polar regions, ISCCP cloud amounts are probably too low by about 15%-25% in summer and 5%-10% in winter. Comparison of the ISCCP climatology to three other cloud climatologies shows excellent agreement in the geographic distribution and seasonal variation of cloud amounts; there is little agreement about day/night contrasts in cloud amount. Notable results from ISCCP are that the gobal annual mean cloud amount is about 63%, being about 23% higher over oceans than over land, that it varies by less than 1% rms from month to month, and that it has varied by about 4% on a time scale approximately equal to 2-4 years. The magnitude of interannual variations of local (280-km scale) monthly mean cloud amounts is about 7%-9%. Longitudinal contrasts in cloud amount are just as large as latitudinal contrasts. The largest seasonal variation of cloud amount occurs in the tropics, being larger in summer than in winter; the seasonal variation in the middle latitudes has the opposite phase. Polar regions may have little seasonable variability in cloud amount. The ISCCP results show slightly more nightime than daytime cloud amount over oceans and more daytime than nightime cloud amount over land.

Rossow, William B.↗

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: N-body mock challenge for the eBOSS emission line galaxy sample

ABSTRACT Cosmological growth can be measured in the redshift space clustering of galaxies targeted by spectroscopic surveys. Accurate prediction of clustering of galaxies will require understanding galaxy physics, which is a very hard and highly non-linear problem. Approximate models of redshift space distortion (RSD) take a perturbative approach to solve the evolution of dark matter and galaxies in the universe. In this paper, we focus on extended Baryon Oscillation Spectroscopic (eBOSS) emission line galaxies (ELGs) that live in intermediate mass haloes. We create a series of mock catalogues using haloes from the Multidark and outer rim dark matter only N-body simulations. Our mock catalogues include various effects inspired by baryonic physics such as assembly bias and the characteristics of satellite galaxies kinematics, dynamics, and statistics deviating from dark matter particles. We analyse these mocks using the TNS RSD model in Fourier space and the convolution Lagrangian perturbation theory (CLPT) in configuration space. We conclude that these two RSD models provide an unbiased measurement of RSD within the statistical error of our mocks. We obtain the conservative theoretical systematic uncertainty of $3.3{{\ \rm per\ cent}}$, $1.8{{\ \rm per\ cent}}$, and $1.5{{\ \rm per\ cent}}$ in fσ8, α∥, and α⊥, respectively, for the TNS and CLPT models. We note that the estimated theoretical systematic error is an order of magnitude smaller than the statistical error of the eBOSS ELG sample and hence are negligible for the purpose of the current eBOSS ELG analysis.

Alam, Shadab↗

Bayesian Inference with Latent Hamiltonian Neural Networks (L-HNNs)

When sampling for Bayesian inference, one popular approach is to use Hamiltonian Monte Carlo (HMC) and the No-U-Turn Sampler (NUTS). However, HMC and NUTS can require numerous numerical gradients of the target density and can prove slow in practice. We propose Hamiltonian neural networks (HNNs) with HMC and NUTS for solving Bayesian inference problems [1, 2]. Once trained, HNNs do not require gradients of the target density while sampling. Moreover, they satisfy important properties such as perfect time reversibility and Hamiltonian conservation, making them well suited for use within HMC and NUTS because stationarity can be shown. We also propose an HNN extension called latent HNNs (L-HNNs), which predict latent variable outputs. Compared to HNNs, L-HNNs offer improved expressivity and a reduction in integration errors. Finally, we propose employing L-HNNs in NUTS with an online error monitoring scheme to prevent degeneracy of the sampling in regions of low probability density. We demonstrate L-HNNs in NUTS with online error monitoring by using several example cases involving complex, heavy-tailed, and high local curvature probability densities. Overall, L-HNNs in NUTS with online error monitoring satisfactorily inferred these probability densities. Compared to traditional NUTS, L-HNNs in NUTS with online error monitoring improved the effective sample size (ESS) per gradient by an order of magnitude.

97 MATHEMATICS AND COMPUTING↗

Factors affecting the sticking of insects on modified aircraft wings

Previous work showed that the total number of insects sticking to an aluminum surface was reduced by coating the aluminum surface with elastomers. Due to a large number of possible experimental errors, no correlation between the modulus of elasticity, the elastomer, and the total number of insects sticking to a given elastomer was obtained. One of the errors assumed to be introduced during the road test is a variable insect flux so the number of insects striking one surface might be different from that striking another sample. To eliminate this source of error, the road test used to collect insects was simulated in a laboratory by development of an insect impacting technique using a pipe and high pressure compressed air. The insects are accelerated by a compressed air gun to high velocities and are then impacted with a stationary target on which the sample is mounted. The velocity of an object exiting from the pipe was determined and further improvement of the technique was achieved to obtain a uniform air velocity distribution.

Yi, O.↗

Efficient Probabilistic Prediction and Uncertainty Quantification of Tropical Cyclone–Driven Storm Tides and Inundation

Abstract This study proposes and assesses a methodology to obtain high-quality probabilistic predictions and uncertainty information of near-landfall tropical cyclone–driven (TC-driven) storm tide and inundation with limited time and resources. Forecasts of TC track, intensity, and size are perturbed according to quasi-random Korobov sequences of historical forecast errors with assumed Gaussian and uniform statistical distributions. These perturbations are run in an ensemble of hydrodynamic storm tide model simulations. The resulting set of maximum water surface elevations are dimensionality reduced using Karhunen–Loève expansions and then used as a training set to develop a polynomial chaos (PC) surrogate model from which global sensitivities and probabilistic predictions can be extracted. The maximum water surface elevation is extrapolated over dry points incorporating energy head loss with distance to properly train the surrogate for predicting inundation. We find that the surrogate constructed with third-order PCs using elastic net penalized regression with leave-one-out cross validation provides the most robust fit across training and test sets. Probabilistic predictions of maximum water surface elevation and inundation area by the surrogate model at 48-h lead time for three past U.S. landfalling hurricanes (Irma in 2017, Florence in 2018, and Laura in 2020) are found to be reliable when compared to best track hindcast simulation results, even when trained with as few as 19 samples. The maximum water surface elevation is most sensitive to perpendicular track-offset errors for all three storms. Laura is also highly sensitive to storm size and has the least reliable prediction. Significance Statement The purpose of this study is to develop and evaluate a methodology that can be used to provide high-quality probabilistic predictions of hurricane-induced storm tide and inundation with limited time and resources. This is important for emergency management purposes during or after the landfall of hurricanes. Our results show that sampling forecast errors using quasi-random sequences combined with machine learning techniques that fit polynomial functions to the data are well suited to this task. The polynomial functions also have the benefit of producing exact sensitivity indices of storm tide and inundation to the forecasted hurricane properties such as path, intensity, and size, which can be used for uncertainty estimation. The code implementing the presented methodology is publicly available on GitHub.

54 ENVIRONMENTAL SCIENCES↗

A novel multistage estimation of the signal parameters of a possibly data-modulated sinusoid under very high dynamics

A novel multistage estimation scheme is presented for estimating the parameters of a received carrier signal possibly phase-modulated by unknown data, and experiencing very high Doppler, Doppler rate, etc. Such a situation arises, for example, in the case of Global Positioning Systems (GPS) where the signal parameters are directly related to the position, velocity, acceleration and jerk of the GPS receiver. In the proposed multistage scheme, the first stage estimator operates as a coarse estimator resulting in higher rms estimation errors but with a relatively small probability of the frequency estimation error exceeding one-half of the sampling frequency (an event termed cycle slip). The second state of the estimator operates on the error signal available from the first stage, refining the overall estimates, and in the process also reduces the number of cycle slips. The first stage algorithm is selected to be a modified least squares algorithm operating upon the differential signal model and referred to as differential least squares. This estimation stage provides relatively coarse estimates of the frequency and its derivatives. The second algorithm is simply an extended Kalman filter which also yields the estimate of the phase along with a more refined estimate of frequency as well. A major advantage of the proposed algorithm is a reduction in the threshold on received carrier power-to-noise power spectral density ratio as compared to the threshold achievable by either of these algorithms alone. In fact, it appears from the simulations that for the case of an unmodulated carrier, the proposed scheme achieves the same threshold as for an almost exact and computationally intensive implementation of the maximum likelihood estimator.

Kumar, Rajendra↗

Sampling Downconverter For Radio-Frequency Signals

Phase and delay errors reduced greatly. Proposed GaAs integrated-circuit for receiver of radio signals at gigahertz frequencies samples incoming signal in phase and in quadrature, digitizes it, and down-converts it to baseband in single step. Incorporates both digital and analog components in design offering improved stability, versatility, and sampling bandwidth. Eliminates need for several components found in conventional analog designs, including mixers, postmixer filters, and 90 degree phase shifter.

Thomas, J. B.↗