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NASA NTRS2010

Optimization of A 2-Micron Laser Frequency Stabilization System for a Double-Pulse CO2 Differential Absorption Lidar

A carbon dioxide (CO2) Differential Absorption Lidar (DIAL) for accurate CO2 concentration measurement requires a frequency locking system to achieve high frequency locking precision and stability. We describe the frequency locking system utilizing Frequency Modulation (FM), Phase Sensitive Detection (PSD), and Proportional Integration Derivative (PID) feedback servo loop, and report the optimization of the sensitivity of the system for the feed back loop based on the characteristics of a variable path-length CO2 gas cell. The CO2 gas cell is characterized with HITRAN database (2004). The method can be applied for any other frequency locking systems referring to gas absorption line.

Chen, Songsheng↗

NASA NTRS2002

Ground Radar Polarimetric Observations of High-Frequency Earth-Space Communication Links

Strategic roadmaps for NASA's Human Exploration and Development of Space (REDS) enterprise support near-term high-frequency communication systems that provide moderate to high data rates with dependable service. Near-earth and human planetary exploration will baseline Ka-Band, but may ultimately require the use of even higher frequencies. Increased commercial demand on low-frequency earth-space bands has also led to increased interest in the use of higher frequencies in regions like K u - and K,- band. Data is taken from the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR), which operates at 13.8 GHz, and the true radar reflectivity profile is determined along the PR beam via low-frequency ground based polarimetric observations. The specific differential phase (Kdp) is measured along the beam and a theoretical model is used to determine the expected specific attenuation (k). This technique, called the k-Kdp method, uses a Fuzzy-Logic model to determine the hydrometeor type along the PR beam from which the appropriate k-Kdp relationship is used to determine k and, ultimately, the total path-integrated attenuation (PIA) on PR measurements. Measurements from PR and the NCAR S-POL radar were made during the TEFLUN-B experiment that took place near Melbourne, FL in 1998, and the TRMM-LBA campaign near Ji-Parana, Brazil in 1999.

Bolen, Steve↗

NASA NTRS2010

Robust Optimization Design Algorithm for High-Frequency TWTs

Traveling-wave tubes (TWTs), such as the Ka-band (26-GHz) model recently developed for the Lunar Reconnaissance Orbiter, are essential as communication amplifiers in spacecraft for virtually all near- and deep-space missions. This innovation is a computational design algorithm that, for the first time, optimizes the efficiency and output power of a TWT while taking into account the effects of dimensional tolerance variations. Because they are primary power consumers and power generation is very expensive in space, much effort has been exerted over the last 30 years to increase the power efficiency of TWTs. However, at frequencies higher than about 60 GHz, efficiencies of TWTs are still quite low. A major reason is that at higher frequencies, dimensional tolerance variations from conventional micromachining techniques become relatively large with respect to the circuit dimensions. When this is the case, conventional design- optimization procedures, which ignore dimensional variations, provide inaccurate designs for which the actual amplifier performance substantially under-performs that of the design. Thus, this new, robust TWT optimization design algorithm was created to take account of and ameliorate the deleterious effects of dimensional variations and to increase efficiency, power, and yield of high-frequency TWTs. This design algorithm can help extend the use of TWTs into the terahertz frequency regime of 300-3000 GHz. Currently, these frequencies are under-utilized because of the lack of efficient amplifiers, thus this regime is known as the "terahertz gap." The development of an efficient terahertz TWT amplifier could enable breakthrough applications in space science molecular spectroscopy, remote sensing, nondestructive testing, high-resolution "through-the-wall" imaging, biomedical imaging, and detection of explosives and toxic biochemical agents.

Wilson, Jeffrey D.↗

NASA NTRS2003

Software for Displaying High-Frequency Test Data

An easy-to-use, intuitive computer program was written to satisfy a need of test operators and data requestors to quickly view and manipulate high-frequency test data recorded at the East and West Test Areas at Marshall Space Flight Center. By enabling rapid analysis, this program makes it possible to reduce times between test runs, thereby potentially reducing the overall cost of test operations. The program can be used to perform quick frequency analysis, using multiple fast- Fourier-transform windowing and amplitude options. The program can generate amplitude-versus-time plots with full zoom capabilities, frequency-component plots at specified time intervals, and waterfall plots (plots of spectral intensity versus frequency at successive small time intervals, showing the changing frequency components over time). There are options for printing of the plots and saving plot data as text files that can be imported into other application programs. The program can perform all of the aforementioned plotting and plot-data-handling functions on a relatively inexpensive computer; other software that performs the same functions requires computers with large amounts of power and memory.

Elmore, Jason L.↗

NASA NTRS2011

Reconfigurable Microwave Phase Delay Element for Frequency Reference and Phase-Shifter Applications

A technique was developed to provide a reconfigurable high-precision micro - wave electrical phase delay for resonators and phase shifters. The invention employs multiple branches of transmission lines with open-ended or ground-ended terminations as configurable bits or digits. This technique minimizes the errors due to limited precision of switching devices. In addition, the proposed linear analytical approach significantly produces a much simpler design than that of other prior inventions at the time of this reporting. Microwave components such as filters, phase delay elements, or resonators require a method that can accurately adjust their frequency responses. Most tuning techniques offer very wide frequency tuning range; however, it is often difficult and expensive to tune their response in a very narrow operating frequency, especially when the tuning element reaches its minimum discrete step due to fabrication tolerances. The problem becomes worse as the operating frequency is in mm-wave frequency range (>26 GHz). The electrical tuning sensitivity of a microwave line is dependent on the position of the tuning element with respect to the reference termination. By placing this tuning element away from this reference with the main transmission line connecting the two elements together the sensitivity of the tuning element can change significantly. This concept can be used in the system that requires multiple tuning sensitivities. In this case, multiple tuning branches are superimposed in the main transmission line. The proposed invention allows the transmission-line electrical length to be accurately programmed using switching elements that have limited accuracy. The invention consists of multiple branches of transmission lines connected to discrete switching devices with open-ended terminations. They are used as discrete tuning elements. These elements are connected to the main microwave transmission line and are separated by a well-defined electrical degree spacing. Each branch is programmed to have different electrical degree sensitivity, such as a combination of discrete steps in each branch, which results in a reflective line with a unique effective phase response. To reduce the number of switching devices, it is desirable to program the devices in binary configuration where each branch represents one bit in the base-2 number system. This invention allows the transmission line electrical length to be tuned precisely with customizable sensitivity based on the known sensitivity of the base tuning circuit. The tuning resolution is dependent on the distance among tuning branches.

Hsieh, Wen-Ting↗

NASA NTRS2011

Laser Frequency Stabilization

Laser ranging and interferometry are essential technologies allowing for many astounding new spacebased missions such as the Laser Interferometer Space Antenna (LISA) to measure gravitational radiation emitted from distant super massive black hole mergers or distributed aperture telescopes with unprecedented angular resolution in the NIR or visible regime. The requirements on laser frequency noise depend on the residual motion and the distances between the spacecraft forming the interferometer. The intrinsic frequency stability of commercial lasers is several orders of magnitude above these requirements. Therefore, it is necessary for lasers to be stabilized to an ultrastable frequency reference so that they can be used to sense and control distances between spacecraft. Various optical frequency references and frequency stabilization schemes are considered and investigated for the applicability and usefulness for space-based interferometry missions.

Donelan, Darsa↗

NASA NTRS2013

Multimode Directional Coupler for Utilization of Harmonic Frequencies from TWTAs

A novel waveguide multimode directional coupler (MDC) intended for the measurement and potential utilization of the second and higher order harmonic frequencies from high-power traveling wave tube amplifiers (TWTAs) has been successfully designed, fabricated, and tested. The design is based on the characteristic multiple propagation modes of the electrical and magnetic field components of electromagnetic waves in a rectangular waveguide. The purpose was to create a rugged, easily constructed, more efficient waveguide- based MDC for extraction and exploitation of the second harmonic signal from the RF output of high-power TWTs used for space communications. The application would be a satellitebased beacon source needed for Qband and V/W-band atmospheric propagation studies. The MDC could function as a CW narrow-band source or as a wideband source for study of atmospheric group delay effects on highdata- rate links. The MDC is fabricated from two sections of waveguide - a primary one for the fundamental frequency and a secondary waveguide for the second harmonic - that are joined together such that the second harmonic higher order modes are selectively coupled via precision- machined slots for propagation in the secondary waveguide. In the TWTA output waveguide port, both the fundamental and the second harmonic signals are present. These signals propagate in the output waveguide as the dominant and higher order modes, respectively. By including an appropriate mode selective waveguide directional coupler, such as the MDC presented here at the output of the TWTA, the power at the second harmonic can be sampled and amplified to the power level needed for atmospheric propagation studies. The important conclusions from the preliminary test results for the multimode directional coupler are: (1) the second harmonic (Ka-band) can be measured and effectively separated from the fundamental (Ku-band) with no coupling of the latter, (2) power losses in the fundamental frequency are negligible, and (3) the power level of the extracted second harmonic is sufficient for further amplification to power levels needed for practical applications. It was also demonstrated that third order and potentially higher order harmonics are measurable with this device. The design is frequency agnostic, and with the appropriate choice of waveguides, is easily scaled to higher frequency TWTs. The MDC has the same function but with a number of important advantages over the conventional diplexer.

Simmons, Rainee N.↗

NASA NTRS2014

Frequency-Modulated, Continuous-Wave Laser Ranging Using Photon-Counting Detectors

Optical ranging is a problem of estimating the round-trip flight time of a phase- or amplitude-modulated optical beam that reflects off of a target. Frequency- modulated, continuous-wave (FMCW) ranging systems obtain this estimate by performing an interferometric measurement between a local frequency- modulated laser beam and a delayed copy returning from the target. The range estimate is formed by mixing the target-return field with the local reference field on a beamsplitter and detecting the resultant beat modulation. In conventional FMCW ranging, the source modulation is linear in instantaneous frequency, the reference-arm field has many more photons than the target-return field, and the time-of-flight estimate is generated by balanced difference- detection of the beamsplitter output, followed by a frequency-domain peak search. This work focused on determining the maximum-likelihood (ML) estimation algorithm when continuous-time photoncounting detectors are used. It is founded on a rigorous statistical characterization of the (random) photoelectron emission times as a function of the incident optical field, including the deleterious effects caused by dark current and dead time. These statistics enable derivation of the Cramér-Rao lower bound (CRB) on the accuracy of FMCW ranging, and derivation of the ML estimator, whose performance approaches this bound at high photon flux. The estimation algorithm was developed, and its optimality properties were shown in simulation. Experimental data show that it performs better than the conventional estimation algorithms used. The demonstrated improvement is a factor of 1.414 over frequency-domainbased estimation. If the target interrogating photons and the local reference field photons are costed equally, the optimal allocation of photons between these two arms is to have them equally distributed. This is different than the state of the art, in which the local field is stronger than the target return. The optimal processing of the photocurrent processes at the outputs of the two detectors is to perform log-matched filtering followed by a summation and peak detection. This implies that neither difference detection, nor Fourier-domain peak detection, which are the staples of the state-of-the-art systems, is optimal when a weak local oscillator is employed.

Erkmen, Baris I.↗

NASA NTRS2014

Time and Frequency-Domain Cross-Verification of SLS 6DOF Trajectory Simulations

The SLS GNC team and its partners have developed several time- and frequency-based simulations for development and analysis of the proposed SLS launch vehicle. The simulations differ in fidelity and some have unique functionality that allows them to perform specific analyses. Some examples of the purposes of the various models are: trajectory simulation, multi-body separation, Monte Carlo, hardware in the loop, loads, and frequency domain stability analyses. While no two simulations are identical, many of the models are essentially six degree-of-freedom (6DOF) representations of the SLS plant dynamics, hardware implementation, and flight software. Thus at a high level all of those models should be in agreement. Comparison of outputs from several SLS trajectory and stability analysis tools are ongoing as part of the program's current verification effort. The purpose of these comparisons is to highlight modeling and analysis differences, verify simulation data sources, identify inconsistencies and minor errors, and ultimately to verify output data as being a good representation of the vehicle and subsystem dynamics. This paper will show selected verification work in both the time and frequency domain from the current design analysis cycle of the SLS for several of the design and analysis simulations. In the time domain, the tools that will be compared are MAVERIC, CLVTOPS, SAVANT, STARS, ARTEMIS, and POST 2. For the frequency domain analysis, the tools to be compared are FRACTAL, SAVANT, and STARS. The paper will include discussion of these tools including their capabilities, configurations, and the uses to which they are put in the SLS program. Determination of the criteria by which the simulations are compared (matching criteria) requires thoughtful consideration, and there are several pitfalls that may occur that can severely punish a simulation if not considered carefully. The paper will discuss these considerations and will present a framework for responding to these issues when they arise. For example, small event timing differences can lead to large differences in mass properties if the criteria are to measure those properties at the same time, or large differences in altitude if the criteria are to measure those properties when the simulation experiences a staging event. Similarly, a tiny difference in phase can lead to large gain margin differences for frequency-domain comparisons of gain margins.

VanZwieten, Tannen↗

NASA NTRS2016

A Multi-Frequency Wide-Swath Spaceborne Cloud and Precipitation Imaging Radar

Microwave and millimeter-wave radars have proven their effectiveness in cloud and precipitation observations. The NASA Earth Science Decadal Survey (DS) Aerosol, Cloud and Ecosystems (ACE) mission calls for a dual-frequency cloud radar (W band 94 GHz and Ka-band 35 GHz) for global measurements of cloud microphysical properties. Recently, there have been discussions of utilizing a tri-frequency (KuKaW-band) radar for a combined ACE and Global Precipitation Measurement (GPM) follow-on mission that has evolved into the Cloud and Precipitation Process Mission (CaPPM) concept. In this presentation we will give an overview of the technology development efforts at the NASA Goddard Space Flight Center (GSFC) and at Northrop Grumman Electronic Systems (NGES) through projects funded by the NASA Earth Science Technology Office (ESTO) Instrument Incubator Program (IIP). Our primary objective of this research is to advance the key enabling technologies for a tri-frequency (KuKaW-band) shared-aperture spaceborne imaging radar to provide unprecedented, simultaneous multi-frequency measurements that will enhance understanding of the effects of clouds and precipitation and their interaction on Earth climate change. Research effort has been focused on concept design and trade studies of the tri-frequency radar; investigating architectures that provide tri-band shared-aperture capability; advancing the development of the Ka band active electronically scanned array (AESA) transmitreceive (TR) module, and development of the advanced radar backend electronics.

imaging↗

NASA NTRS2016

On the Importance of High Frequency Gravity Waves for Ice Nucleation in the Tropical Tropopause Layer

Recent investigations of the influence of atmospheric waves on ice nucleation in cirrus have identified a number of key processes and sensitivities: (1) ice concentrations produced by homogeneous freezing are strongly dependent on cooling rates, with gravity waves dominating upper tropospheric cooling rates; (2) rapid cooling driven by high-frequency waves are likely responsible for the rare occurrences of very high ice concentrations in cirrus; (3) sedimentation and entrainment tend to decrease ice concentrations as cirrus age; and (4) in some situations, changes in temperature tendency driven by high-frequency waves can quench ice nucleation events and limit ice concentrations. Here we use parcel-model simulations of ice nucleation driven by long-duration, constant-pressure balloon temperature time series, along with an extensive dataset of cold cirrus microphysical properties from the recent ATTREX high-altitude aircraft campaign, to statistically examine the importance of high-frequency waves as well as the consistency between our theoretical understanding of ice nucleation and observed ice concentrations. The parcel-model simulations indicate common occurrence of peak ice concentrations exceeding several hundred per liter. Sedimentation and entrainment would reduce ice concentrations as clouds age, but 1-D simulations using a wave parameterization (which underestimates rapid cooling events) still produce ice concentrations higher than indicated by observations. We find that quenching of nucleation events by high-frequency waves occurs infrequently and does not prevent occurrences of large ice concentrations in parcel simulations of homogeneous freezing. In fact, the high-frequency variability in the balloon temperature data is entirely responsible for production of these high ice concentrations in the simulations.

simulation↗

NASA NTRS2015

Three-Dimensional Vibration Isolator for Suppressing High-Frequency Responses for Sage III Contamination Monitoring Package (CMP)

The Stratospheric Aerosol and Gas Experiment (SAGE) III - International Space Station (ISS) instrument will be used to study ozone, providing global, long-term measurements of key components of the Earth's atmosphere for the continued health of Earth and its inhabitants. SAGE III is launched into orbit in an inverted configuration on SpaceX;s Falcon 9 launch vehicle. As one of its four supporting elements, a Contamination Monitoring Package (CMP) mounted to the top panel of the Interface Adapter Module (IAM) box experiences high-frequency response due to structural coupling between the two structures during the SpaceX launch. These vibrations, which were initially observed in the IAM Engineering Development Unit (EDU) test and later verified through finite element analysis (FEA) for the SpaceX launch loads, may damage the internal electronic cards and the Thermoelectric Quartz Crystal Microbalance (TQCM) sensors mounted on the CMP. Three-dimensional (3D) vibration isolators were required to be inserted between the CMP and IAM interface in order to attenuate the high frequency vibrations without resulting in any major changes to the existing system. Wire rope isolators were proposed as the isolation system between the CMP and IAM due to the low impact to design. Most 3D isolation systems are designed for compression and roll, therefore little dynamic data was available for using wire rope isolators in an inverted or tension configuration. From the isolator FEA and test results, it is shown that by using the 3D wire rope isolators, the CMP high-frequency responses have been suppressed by several orders of magnitude over a wide excitation frequency range. Consequently, the TQCM sensor responses are well below their qualification environments. It is indicated that these high-frequency responses due to the typical instrument structural coupling can be significantly suppressed by a vibration passive control using the 3D vibration isolator. Thermal and contamination issues were also examined during the isolator selection period for meeting the SAGE III-ISS instrument requirements.

Li, Y.↗

NASA NTRS2017

Time and Frequency-Domain Cross-Verification of SLS 6DOF Trajectory Simulations

The Space Launch System (SLS) Guidance, Navigation, and Control (GNC) team and its partners have developed several time- and frequency-based simulations for development and analysis of the proposed SLS launch vehicle. The simulations differ in fidelity and some have unique functionality that allows them to perform specific analyses. Some examples of the purposes of the various models are: trajectory simulation, multi-body separation, Monte Carlo, hardware in the loop, loads, and frequency domain stability analyses. While no two simulations are identical, many of the models are essentially six degree-of-freedom (6DOF) representations of the SLS plant dynamics, hardware implementation, and flight software. Thus at a high level all of those models should be in agreement. Comparison of outputs from several SLS trajectory and stability analysis tools are ongoing as part of the program's current verification effort. The purpose of these comparisons is to highlight modeling and analysis differences, verify simulation data sources, identify inconsistencies and minor errors, and ultimately to verify output data as being a good representation of the vehicle and subsystem dynamics. This paper will show selected verification work in both the time and frequency domain from the current design analysis cycle of the SLS for several of the design and analysis simulations. In the time domain, the tools that will be compared are MAVERIC, CLVTOPS, SAVANT, STARS, ARTEMIS, and POST 2. For the frequency domain analysis, the tools to be compared are FRACTAL, SAVANT, and STARS. The paper will include discussion of these tools including their capabilities, configurations, and the uses to which they are put in the SLS program. Determination of the criteria by which the simulations are compared (matching criteria) requires thoughtful consideration, and there are several pitfalls that may occur that can severely punish a simulation if not considered carefully. The paper will discuss these considerations and will present a framework for responding to these issues when they arise. For example, small event timing differences can lead to large differences in mass properties if the criteria are to measure those properties at the same time, or large differences in altitude if the criteria are to measure those properties when the simulation experiences a staging event. Similarly, a tiny difference in phase can lead to large gain margin differences for frequency-domain comparisons of gain margins.

Johnson, Matthew↗

NASA NTRS2017

Mercury Trapped Ion Frequency Standard for Ultra-Stable Reference Applications

An atomic clock including an ion trap assembly, a C-field coil positioned for generating a first magnetic field in the interrogation region of the ion trap assembly, a compensation coil positioned for generating a second magnetic field in the interrogation region, wherein the combination of the first and second magnetic fields produces an ion number-dependent second order Zeeman shift (Zeeman shift) in the resonance frequency that is opposite in sign to an ion number-dependent second order Doppler shift (Doppler shift) in the resonance frequency, the C-field coil has a radius selected using data indicating how changes in the radius affect an ion-number-dependent shift in the resonance frequency, such that a difference in magnitude between the Doppler shift and the Zeeman shift is controlled or reduced, and the resonance frequency, including the adjustment by the Zeeman shift, is used to obtain the frequency standard.

Burt, Eric A.↗

NASA NTRS2018

Natural Frequency Testing and Model Correlation of Rocket Engine Structures in Liquid Hydrogen - Phase I, Cantilever Beam

Many structures in the launch vehicle industry operate in liquid hydrogen (LH2), from the hydrogen fuel tanks through the ducts and valves and into the pump sides of the turbopumps. Calculating the structural dynamic response of these structures is critical for successful qualification of this hardware, but accurate knowledge of the natural frequencies is based entirely on numerical or analytical predictions of frequency reduction due to the added-fluid-mass effect because testing in LH2 has always been considered too difficult and dangerous. This fluid effect is predicted to be approximately 4-5% using analytical formulations for simple cantilever beams. As part of a comprehensive test/analysis program to more accurately assess pump inducers operating in LH2, a series of frequency tests in LH2 were performed at NASA/Marshall Space Flight Center's unique cryogenic test facility. These frequency tests are coupled with modal tests in air and water to provide critical information not only on the mass effect of LH2, but also the cryogenic temperature effect on Young's Modulus for which the data is not extensive. The authors are unaware of any other reported natural frequency testing in this media. In addition to the inducer, a simple cantilever beam was also tested in the tank to provide a more easily modeled geometry as well as one that has an analytical solution for the mass effect. This data will prove critical for accurate structural dynamic analysis of these structures, which operate in a highly-dynamic environment.

Brown, Andrew M.↗

NASA NTRS2017

Kinetic Scale Structure of Low-Frequency Waves and Fluctuations

The dissipation of solar wind turbulence at kinetic scales is believed to be important for the heating of the corona and for accelerating the wind. The linear Vlasov kinetic theory is a useful tool for identifying various wave modes, including kinetic Alfven, fast magnetosonic/whistler, and ion-acoustic (or kinetic slow), and their possible roles in the dissipation. However, the kinetic mode structure in the vicinity of ion-cyclotron modes is not clearly understood. The present paper aims to further elucidate the structure of these low-frequency waves by introducing discrete particle effects through hybrid simulations and Klimontovich formalism of spontaneous emission theory. The theory and simulation of spontaneously emitted low-frequency fluctuations are employed to identify and distinguish the detailed mode structures associated with ion-Bernstein modes versus quasi-modes. The spontaneous emission theory and simulation also confirm the findings of the Vlasov theory in that the kinetic Alfven waves can be defined over a wide range of frequencies, including the proton cyclotron frequency and its harmonics, especially for high-beta plasmas. This implies that these low-frequency modes may play predominant roles even in the fully kinetic description of kinetic scale turbulence and dissipation despite the fact that cyclotron harmonic and Bernstein modes may also play important roles in wave-particle interactions.

waves↗

NASA NTRS2018

Dynamic Modeling using Output-Error Parameter Estimation based on Frequency Responses Estimated with Multisine Inputs

A method is developed for estimating model parameters, such as nondimensional stability and control derivatives, by fitting transfer function or state-space models to empirical frequency response data using the output-error approach. The frequency response data were computed using Fourier transforms of measured input and output data. The control surfaces were excited with periodic multisine inputs which facilitated time-ecient estimation of multiple-input multiple-output frequency responses. The method was applied to lateral data from a nonlinear flight dynamics simulation of the F-16 aircraft, and to longitudinal data from multiple repeated flight test maneuvers of the NASA T-2 subscale aircraft. Results using simulation data showed the frequency response method compared well to other standard methods for parameter estimation. In addition to including all the available inputs, outputs, and harmonic frequencies in the estimation, relatively small subsets of the measured data could also be used to focus on identifying specific parts of the model. Results from flight test data showed that parameter estimates and uncertainties determined from repeated maneuvers were accurate and in statistical agreement with each other.

Grauer, Jared A.↗

NASA NTRS2018

Practical Aspects of the Frequency Domain Approach for Aircraft System Identification

Practical aspects of the frequency-domain approach for aircraft system identification are explained and demonstrated. Topics related to experiment design, flight data analysis, and dynamic modeling are included. For demonstration purposes, simulated time series data and simulated flight data from an F-16 nonlinear simulation with realistic noise are used. This approach enables detailed evaluations of the techniques and results, because the true characteristics of the data and aircraft dynamics are known for the simulated data. Analytical techniques and practical considerations are examined for the finite Fourier transform, nonparametric frequency response estimation, parametric modeling in the frequency domain, experiment design for frequency-domain modeling, data analysis and modeling in the frequency domain, and real-time calculations. Flight data from a subscale jet transport aircraft are used to demonstrate some of the techniques and technical issues.

Morelli, Eugene A.↗