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NASA NTRS1991

Characterization Of Electrical Response Of Photodetector

Fourier analysis is basis of method of characterizing electrical frequency or time response of photodetector. In method, detector stimulated by optical input signal, intensity modulated with square wave or other repetitive waveform of known frequency spectrum, and output of detector recorded. Electro-optical transfer function, which characterizes frequency response of detector, then computed as ratio between discrete Fourier transforms of output and input waveforms.

Hagopian, John G.↗

NASA NTRS1990

The aerodynamics of an oscillating cascade in a compressible flow field

Fundamental experiments are performed in the NASA Lewis Research Center Transonic Oscillating Cascade Facility to investigate and quantify the aerodynamics of a cascade of bioconvex airfoils executing torsion mode oscillations at realistic reduced frequency values. Both steady and unsteady airfoil surface pressures are measured at two inlet Mach numbers, 0.65 and 0.80, and two incidence angles, 0 and 7 deg, with the harmonic torsional airfoil cascade oscillations at realistic high reduced frequency and unsteady data obtained at several interblade phase angle values. The time-variant pressures are analyzed by means of discrete Fourier transform techniques, with these unique data compared with predictions from a linearized unsteady cascade model. The experimental results indicate that the interblade phase angle has a major effect on the chordwise distributions of the airfoil surface unsteady pressure, with the effect of reduced frequency, incidence angle, and Mach numbers somewhat less significant.

Buffum, D. H.↗

NASA NTRS1989

Efficient detection of a CW signal with a linear frequency drift

An efficient method is presented for the detection of a continuous wave (CW) signal with a frequency drift that is linear in time. Signals of this type occur in transmissions between any two locations that are accelerating relative to one another, e.g., transmissions from the Voyager spacecraft. We assume that both the frequency and the drift are unknown. We also assume that the signal is weak compared to the Gaussian noise. The signal is partitioned into subsequences whose discrete Fourier transforms provide a sequence of instantaneous spectra at equal time intervals. These spectra are then accumulated with a shift that is proportional to time. When the shift is equal to the frequency drift, the signal to noise ratio increases and detection occurs. Here, we show how to compute these accumulations for many shifts in an efficient manner using a variety of Fast Fourier Transformations (FFT). Computing time is proportional to L log L where L is the length of the time series.

Swarztrauber, Paul N.↗

NASA NTRS1991

The behavior of quantization spectra as a function of signal-to-noise ratio

An expression for the spectrum of quantization error in a discrete-time system whose input is a sinusoid plus white Gaussian noise is derived. This quantization spectrum consists of two components: a white-noise floor and spurious harmonics. The dithering effect of the input Gaussian noise in both components of the spectrum is considered. Quantitative results in a discrete Fourier transform (DFT) example show the behavior of spurious harmonics as a function of the signal-to-noise ratio (SNR). These results have strong implications for digital reception and signal analysis systems. At low SNRs, spurious harmonics decay exponentially on a log-log scale, and the resulting spectrum is white. As the SNR increases, the spurious harmonics figure prominently in the output spectrum. A useful expression is given that roughly bounds the magnitude of a spurious harmonic as a function of the SNR.

Flanagan, M. J.↗

NASA NTRS1992

The photometric period of the recurrent Nova T Pyxidis

The paper presents 1713 photometric measurements of T Pyx from 1966 to 1990. The light curve of T Pyx shows roughly sinusoidal variations with a typical amplitude of 0.09 mag and a time scale of 2 hr. Discrete Fourier transforms of data from individual nights and runs reveal a highly significant periodic modulation. This modulation is proven to be coherent only on time scales shorter than from 6 d to under 1 d. The present period for the modulation is 0.07616 +/- 0.00017 d. Since other stars have variable photometric periods (possibly related to the superhump phenomenon) which are slightly different from the orbital period, an orbital period of about 0.073 d for T Pyx is suggested.

Schaefer, Bradley E.↗

NASA NTRS1990

Rotordynamics analysis of a Jeffcott model with deadband

A method is developed for determining the stability margins of a simple Jeffcott model with deadband via analysis of the discrete Fourier transform of the system response. The model in question is of a uniform, unbalanced, flexible shaft that is supported by a bearing as it rotates about its x axis. This model is represented by a system of coupled nonlinear differential equations.

Zalik, R. A.↗

NASA NTRS1992

Transient scattering from dielectric cylinders - E-field, H-field, and combined field solutions

In this work, the problem of transient scattering by arbitrarily shaped two-dimensional dielectric cylinders is solved using the marching-on-in-time technique. The dielectric problem is approached via the equivalence principle. Three different formulations, namely, the electric field integral equation formulation, the magnetic field integral equation formulation, and the combined field integral equation formulation are considered. Numerical results are presented for two cross sections, namely, a circle and a square, and compared with inverse discrete Fourier transform (IDFT) techniques. In each case, good agreement is obtained with the IDFT solution.

Vechinski, Douglas A.↗

NASA NTRS1992

Transient scattering from two-dimensional dielectric cylinders of arbitrary shape

In this work, the problem of transient scattering by arbitrary shaped two-dimensional dielectric cylinders is solved using the marching-on-in-time (MOT) technique. The dielectric problem is approached via the surface equivalence principle. A pair of coupled integral equations are derived by enforcing the continuity of the electric and magnetic fields which are solved by using the method of moments. Numerical results are presented for two cross sections, viz. a circle and a square, and compared with inverse discrete Fourier transform (IDFT) techniques. In each case, good agreement is obtained with the IDFT solution.

Vechinski, Douglas A.↗

NASA NTRS1994

Solid state laser systems for space application

Since the last report several things have happened to effect the research effort. In laser metrology, measurements using Michelson type interferometers with an FM modulated diode laser source have been performed. The discrete Fourier transform technique has been implemented. Problems associated with this technique as well as the overall FM scheme were identified. The accuracy of the technique is not at the level we would expect at this point. We are now investigating the effect of various types of noise on the accuracy as well as making changes to the system. One problem can be addressed by modifying the original optical layout. Our research effort was also expanded to include the assembly and testing of a diode pumped\Nd:YAG laser pumped\Ti sapphire laser for possible use in sounding rocket applications. At this stage, the diode pumped Nd:YAG laser has been assembled and made operational.

Kay, Richard B.↗

NASA NTRS1994

Parameter estimation of the vibrational model for the SCOLE experimental facility

The objective of this study is to experimentally determine an empirical model of the vibrational dynamics of the Spacecraft COntrol Laboratory Experiment (SCOLE) facility. The first two flexible modes of this test article are identified using a linear least-square identification procedure and the data utilized for this procedure are obtained by exciting the structure from a quiescent state with torque wheels. The time history data of rate gyro sensors and accelerometers due to excitation and after excitation in terms of free-decay are used in the parameter estimation of the vibrational model. The free-decay portion of the data is analyzed using the Discrete Fourier transform to determine the optimal model order to use in modelling the response. Linear least-square analysis is then used to select the parameters that best fit the output of an Autoregressive (AR) model to the data. The control effectiveness of the torque wheels is then determined using the excitation portion of the test data, again using linear least squares.

Crotts, B. D.↗

NASA NTRS1994

Multi-velocity component LDV

A laser doppler velocimeter uses frequency shifting of a laser beam to provide signal information for each velocity component. A composite electrical signal generated by a light detector is digitized and a processor produces a discrete Fourier transform based on the digitized electrical signal. The transform includes two peak frequencies corresponding to the two velocity components. Ames Research Center, Mail Code 200-11A, Moffett Field, California, 94035. Approved NASA forms for application for nonexclusive or exclusive license are available from the above address.

Johnson, Dennis A.↗

NASA NTRS1994

On the application of under-decimated filter banks

Maximally decimated filter banks have been extensively studied in the past. A filter bank is said to be under-decimated if the number of channels is more than the decimation ratio in the subbands. A maximally decimated filter bank is well known for its application in subband coding. Another application of maximally decimated filter banks is in block filtering. Convolution through block filtering has the advantages that parallelism is increased and data are processed at a lower rate. However, the computational complexity is comparable to that of direct convolution. More recently, another type of filter bank convolver has been developed. In this scheme, the convolution is performed in the subbands. Quantization and bit allocation of subband signals are based on signal variance, as in subband coding. Consequently, for a fixed rate, the result of convolution is more accurate than is direct convolution. This type of filter bank convolver also enjoys the advantages of block filtering, parallelism, and a lower working rate. Nevertheless, like block filtering, there is no computational saving. In this article, under-decimated systems are introduced to solve the problem. The new system is decimated only by half the number of channels. Two types of filter banks can be used in the under-decimated system: the discrete Fourier transform (DFT) filter banks and the cosine modulated filter banks. They are well known for their low complexity. In both cases, the system is approximately alias free, and the overall response is equivalent to a tunable multilevel filter. Properties of the DFT filter banks and the cosine modulated filter banks can be exploited to simultaneously achieve parallelism, computational saving, and a lower working rate. Furthermore, for both systems, the implementation cost of the analysis or synthesis bank is comparable to that of one prototype filter plus some low-complexity modulation matrices. The individual analysis and synthesis filters have complex coefficients in the DFT filter banks but have real coefficients in the cosine modulated filter banks.

Lin, Y.-P.↗

NASA NTRS1996

Multi-Velocity Component LDV

Johnson, Dennis A.↗

NASA NTRS1997

Wavelet Analyses of F/A-18 Aeroelastic and Aeroservoelastic Flight Test Data

Time-frequency signal representations combined with subspace identification methods were used to analyze aeroelastic flight data from the F/A-18 Systems Research Aircraft (SRA) and aeroservoelastic data from the F/A-18 High Alpha Research Vehicle (HARV). The F/A-18 SRA data were produced from a wingtip excitation system that generated linear frequency chirps and logarithmic sweeps. HARV data were acquired from digital Schroeder-phased and sinc pulse excitation signals to actuator commands. Nondilated continuous Morlet wavelets implemented as a filter bank were chosen for the time-frequency analysis to eliminate phase distortion as it occurs with sliding window discrete Fourier transform techniques. Wavelet coefficients were filtered to reduce effects of noise and nonlinear distortions identically in all inputs and outputs. Cleaned reconstructed time domain signals were used to compute improved transfer functions. Time and frequency domain subspace identification methods were applied to enhanced reconstructed time domain data and improved transfer functions, respectively. Time domain subspace performed poorly, even with the enhanced data, compared with frequency domain techniques. A frequency domain subspace method is shown to produce better results with the data processed using the Morlet time-frequency technique.

Martin J Brenner↗

NASA NTRS1999

Carrier Estimation Using Classic Spectral Estimation Techniques for the Proposed Demand Assignment Multiple Access Service

In any satellite communication, the Doppler shift associated with the satellite's position and velocity must be calculated in order to determine the carrier frequency. If the satellite state vector is unknown then some estimate must be formed of the Doppler-shifted carrier frequency. One elementary technique is to examine the signal spectrum and base the estimate on the dominant spectral component. If, however, the carrier is spread (as in most satellite communications) this technique may fail unless the chip rate-to-data rate ratio (processing gain) associated with the carrier is small. In this case, there may be enough spectral energy to allow peak detection against a noise background. In this thesis, we present a method to estimate the frequency (without knowledge of the Doppler shift) of a spread-spectrum carrier assuming a small processing gain and binary-phase shift keying (BPSK) modulation. Our method relies on an averaged discrete Fourier transform along with peak detection on spectral match filtered data. We provide theory and simulation results indicating the accuracy of this method. In addition, we will describe an all-digital hardware design based around a Motorola DSP56303 and high-speed A/D which implements this technique in real-time. The hardware design is to be used in NMSU's implementation of NASA's demand assignment, multiple access (DAMA) service.

Scaife, Bradley James↗

NASA NTRS2001

An OFDM System Using Polyphase Filter and DFT Architecture for Very High Data Rate Applications

This paper presents a conceptual architectural design of a four-channel Orthogonal Frequency Division Multiplexing (OFDM) system with an aggregate information throughput of 622 megabits per second (Mbps). Primary emphasis is placed on the generation and detection of the composite waveform using polyphase filter and Discrete Fourier Transform (DFT) approaches to digitally stack and bandlimit the individual carriers. The four-channel approach enables the implementation of a system that can be both power and bandwidth efficient, yet enough parallelism exists to meet higher data rate goals. It also enables a DC power efficient transmitter that is suitable for on-board satellite systems, and a moderately complex receiver that is suitable for low-cost ground terminals. The major advantage of the system as compared to a single channel system is lower complexity and DC power consumption. This is because the highest sample rate is half that of the single channel system and synchronization can occur at most, depending on the synchronization technique, a quarter of the rate of a single channel system. The major disadvantage is the increased peak-to-average power ratio over the single channel system. Simulation results in a form of bit-error-rate (BER) curves are presented in this paper.

Kifle, Muli↗

NASA NTRS2002

Implementation of a 622 Mbps Digital Modem

This paper presents the implementation and initial test results of an Orthogonal Frequency Division Multiplexing (OFDM) digital modem (modulator and demodulator) with an aggregate information throughput of 622 megabits per second (Mbps). The OFDM waveform is constructed by dividing an incoming data stream into four channels, each channel using either a 16-ary Quadrature Amplitude Modulation (16QAM) scheme or an 8-Phase Shift Keying (8PSK) scheme. The generation and detection of the composite waveform are performed using Discrete Fourier Transform (DFT) and polyphase filtering, to digitally stack and band-limit the individual carriers respectively. The four-channel OFDM approach enables the implementation of a modem that can be both power and bandwidth efficient, with sufficient parallelism to meet higher data rate goals. As a result, the OFDM modem requires only a 240 MHz bandwidth to transmit 622 Mbps. Hardware and simulation results in the form of spectrum diagrams and bit-error-rate (BER) curves are also presented in this paper.

Kifle, Muli↗

NASA NTRS2003

Phase Retrieval Using a Genetic Algorithm on the Systematic Image-Based Optical Alignment Testbed

NASA s Marshall Space Flight Center s Systematic Image-Based Optical Alignment (SIBOA) Testbed was developed to test phase retrieval algorithms and hardware techniques. Individuals working with the facility developed the idea of implementing phase retrieval by breaking the determination of the tip/tilt of each mirror apart from the piston motion (or translation) of each mirror. Presented in this report is an algorithm that determines the optimal phase correction associated only with the piston motion of the mirrors. A description of the Phase Retrieval problem is first presented. The Systematic Image-Based Optical Alignment (SIBOA) Testbeb is then described. A Discrete Fourier Transform (DFT) is necessary to transfer the incoming wavefront (or estimate of phase error) into the spatial frequency domain to compare it with the image. A method for reducing the DFT to seven scalar/matrix multiplications is presented. A genetic algorithm is then used to search for the phase error. The results of this new algorithm on a test problem are presented.

Taylor, Jaime R.↗