Search NASA⌕ Search

SEARCH · Search NASA

Results for “Fast Fourier transform”

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 55 records · Page 3

Delaminations Investigated With Ultrasonic Spectroscopy

A previous study suggested that the ultrasonic spectroscopy technique identified possible disbonds or delaminations in polymer matrix composite (PMC) rings sectioned from flywheel rotors (ref. 1). These results went unsubstantiated by other nondestructive evaluation (NDE) methods. To explain the results, PMC rings were further investigated with ultrasonic spectroscopy (ref. 2). The ultrasonic spectroscopy system utilizes a continuous-swept sine waveform as the input. After the swept sine wave traverses the material, the captured waveform is subjected to two fast Fourier transforms. The second fast Fourier transform along with equalization of the frequency spectrum, allows for evaluation of the fundamental resonant frequency. The full-thickness resonance, the resonance corresponding to the location of the intentional disbond, and the frequency spectrum were examined in an effort to characterize the sensitivity of the NDE method to various delamination conditions.

Cosgriff, Laura M.↗

Breadboard Signal Processor for Arraying DSN Antennas

A recently developed breadboard version of an advanced signal processor for arraying many antennas in NASA s Deep Space Network (DSN) can accept inputs in a 500-MHz-wide frequency band from six antennas. The next breadboard version is expected to accept inputs from 16 antennas, and a following developed version is expected to be designed according to an architecture that will be scalable to accept inputs from as many as 400 antennas. These and similar signal processors could also be used for combining multiple wide-band signals in non-DSN applications, including very-long-baseline interferometry and telecommunications. This signal processor performs functions of a wide-band FX correlator and a beam-forming signal combiner. [The term "FX" signifies that the digital samples of two given signals are fast Fourier transformed (F), then the fast Fourier transforms of the two signals are multiplied (X) prior to accumulation.] In this processor, the signals from the various antennas are broken up into channels in the frequency domain (see figure). In each frequency channel, the data from each antenna are correlated against the data from each other antenna; this is done for all antenna baselines (that is, for all antenna pairs). The results of the correlations are used to obtain calibration data to align the antenna signals in both phase and delay. Data from the various antenna frequency channels are also combined and calibration corrections are applied. The frequency-domain data thus combined are then synthesized back to the time domain for passing on to a telemetry receiver

Jongeling, Andre↗

Wavelet Filter Banks for Super-Resolution SAR Imaging

This paper discusses Innovative wavelet-based filter banks designed to enhance the analysis of super resolution Synthetic Aperture Radar (SAR) images using parametric spectral methods and signal classification algorithms, SAR finds applications In many of NASA's earth science fields such as deformation, ecosystem structure, and dynamics of Ice, snow and cold land processes, and surface water and ocean topography. Traditionally, standard methods such as Fast-Fourier Transform (FFT) and Inverse Fast-Fourier Transform (IFFT) have been used to extract Images from SAR radar data, Due to non-parametric features of these methods and their resolution limitations and observation time dependence, use of spectral estimation and signal pre- and post-processing techniques based on wavelets to process SAR radar data has been proposed. Multi-resolution wavelet transforms and advanced spectral estimation techniques have proven to offer efficient solutions to this problem.

Sheybani, Ehsan O.↗

A new hybrid algorithm for computing a fast discrete Fourier transform

For certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, with the Mersenne-prime number theoretic transform. This new algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithm.

Reed, I. S.↗

A new hybrid algorithm for computing a fast discrete Fourier transform

In this paper for certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform (DFT) is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, with the Mersenne prime number-theoretic transform developed originally by Rader. This new algorithm requires fewer multiplications than either the standard fast Fourier transform (FFT) or Winograd's more conventional algorithm. However, more additions are required.

Reed, I. S.↗

Efficient Two-Dimensional-FFT Program

Program computes 64 X 64-point fast Fourier transform in less than 17 microseconds. Optimized 64 X 64 Point Two-Dimensional Fast Fourier Transform combines performance of real- and complex-valued one-dimensional fast Fourier transforms (FFT's) to execute two-dimensional FFT and coefficients of power spectrum. Coefficients used in many applications, including analyzing spectra, convolution, digital filtering, processing images, and compressing data. Source code written in C, 8086 Assembly, and Texas Instruments TMS320C30 Assembly languages.

Miko, J.↗

A fast Karhunen-Loeve transform for a class of random processes

It is shown that for a class of finite first-order Markov signals, the Karhunen-Loeve (KL) transform for data compression is a set of periodic sine functions if the boundary values of the signal are fixed or known. These sine functions are shown to be related to the Fourier transform so that a fast Fourier transform algorithm can be used to implement the KL transform. Extension to two dimensions with reference to images with separable contravariance function is shown.

Jain, A. K.↗

Aircraft on-board SAR processing using a frequency-domain fast correlation technique

The design of a frequency-domain fast correlation processor for aircraft onboard synthetic-aperture radar (SAR) applications is described. The design uses the fast Fourier transform (FFT) fast correlation technique to perform both range and azimuth pulse compression functions for the NASA/JPL L-band, quad-polarization airborne SAR. The subject processor is computationally efficient and requires a simple control unit. It is capable of producing single-look, 8-m (slant range) by 10-m (azimuth) resolution, SAR images of a selected polarization over a swath width of up to 15 km in real time onboard the aircraft.

Liu, Kuang Y.↗

Algorithm for Wavefront Sensing Using an Extended Scene

A recently conceived algorithm for processing image data acquired by a Shack-Hartmann (SH) wavefront sensor is not subject to the restriction, previously applicable in SH wavefront sensing, that the image be formed from a distant star or other equivalent of a point light source. That is to say, the image could be of an extended scene. (One still has the option of using a point source.) The algorithm can be implemented in commercially available software on ordinary computers. The steps of the algorithm are the following: 1. Suppose that the image comprises M sub-images. Determine the x,y Cartesian coordinates of the centers of these sub-images and store them in a 2xM matrix. 2. Within each sub-image, choose an NxN-pixel cell centered at the coordinates determined in step 1. For the ith sub-image, let this cell be denoted as si(x,y). Let the cell of another subimage (preferably near the center of the whole extended-scene image) be designated a reference cell, denoted r(x,y). 3. Calculate the fast Fourier transforms of the sub-sub-images in the central NxN portions (where N < N and both are preferably powers of 2) of r(x,y) and si(x,y). 4. Multiply the two transforms to obtain a cross-correlation function Ci(u,v), in the Fourier domain. Then let the phase of Ci(u, v) constitute a phase function, phi(u,v). 5. Fit u and v slopes to phi (u,v) over a small u,v subdomain. 6. Compute the fast Fourier transform, Si(u,v) of the full NxN cell si(x,y). Multiply this transform by the u and phase slopes obtained in step 4. Then compute the inverse fast Fourier transform of the product. 7. Repeat steps 4 through 6 in an iteration loop, cumulating the u and slopes, until a maximum iteration number is reached or the change in image shift becomes smaller than a predetermined tolerance. 8. Repeat steps 4 through 7 for the cells of all other sub-images.

Sidick, Erkin↗

The application of digital signal processing techniques to a teleoperator radar system

A digital signal processing system was studied for the determination of the spectral frequency distribution of echo signals from a teleoperator radar system. The system consisted of a sample and hold circuit, an analog to digital converter, a digital filter, and a Fast Fourier Transform. The system is interfaced to a 16 bit microprocessor. The microprocessor is programmed to control the complete digital signal processing. The digital filtering and Fast Fourier Transform functions are implemented by a S2815 digital filter/utility peripheral chip and a S2814A Fast Fourier Transform chip. The S2815 initially simulates a low-pass Butterworth filter with later expansion to complete filter circuit (bandpass and highpass) synthesizing.

Pujol, A.↗

Application and sensitivity investigation of Fourier transforms for microwave radiometric inversions

Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature equation, an unstable Fredholm integral equation of the first kind was solved. Fast Fourier Transform techniques were used to invert the integral after it is placed into a cross-correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system were included. The instability of the Fredholm equation was then demonstrated and a restoration procedure was included which smooths the resulting oscillations. With the recent availability and advances of Fast Fourier Transform techniques, the method presented becomes very attractive in the evaluation of large quantities of data. Actual radiometric measurements of sea water are inverted using the restoration method, incorporating the advantages of the Fast Fourier Transform algorithm for computations.

Holmes, J. J.↗

A Fourier transform with speed improvements for microprocessor applications

A fast Fourier transform algorithm for the RCA 1802microprocessor was developed for spacecraft instrument applications. The computations were tailored for the restrictions an eight bit machine imposes. The algorithm incorporates some aspects of Walsh function sequency to improve operational speed. This method uses a register to add a value proportional to the period of the band being processed before each computation is to be considered. If the result overflows into the DF register, the data sample is used in computation; otherwise computation is skipped. This operation is repeated for each of the 64 data samples. This technique is used for both sine and cosine portions of the computation. The processing uses eight bit data, but because of the many computations that can increase the size of the coefficient, floating point form is used. A method to reduce the alias problem in the lower bands is also described.

Lokerson, D. C.↗

Propagation Characteristics Of Weakly Guiding Optical Fibers

Report discusses electromagnetic propagation characteristics of weakly guiding optical-fiber structures having complicated shapes with cross-sectional dimensions of order of wavelength. Coupling, power-dividing, and transition dielectric-waveguide structures analyzed. Basic data computed by scalar-wave, fast-Fourier-transform (SW-FFT) technique, based on numerical solution of scalar version of wave equation by forward-marching fast-Fourier-transform method.

Manshadi, Farzin↗

New correction procedures for the fast field program which extend its range

A fast field program (FFP) algorithm was developed based on the method of Lee et al., for the prediction of sound pressure level from low frequency, high intensity sources. In order to permit accurate predictions at distances greater than 2 km, new correction procedures have had to be included in the algorithm. Certain functions, whose Hankel transforms can be determined analytically, are subtracted from the depth dependent Green's function. The distance response is then obtained as the sum of these transforms and the Fast Fourier Transformation (FFT) of the residual k dependent function. One procedure, which permits the elimination of most complex exponentials, has allowed significant changes in the structure of the FFP algorithm, which has resulted in a substantial reduction in computation time.

West, M.↗

Computing the Power-Density Spectrum for an Engineering Model

Computer program for calculating of power-density spectrum (PDS) from data base generated by Advanced Continuous Simulation Language (ACSL) uses algorithm that employs fast Fourier transform (FFT) to calculate PDS of variable. Accomplished by first estimating autocovariance function of variable and then taking FFT of smoothed autocovariance function to obtain PDS. Fast-Fourier-transform technique conserves computer resources.

Dunn, H. J.↗

Ultrasonic Resonance Spectroscopy of Composite Rings for Flywheel Rotors

Flywheel energy storage devices comprising multilayered composite rotor systems are being studied extensively for utilization in the International Space Station. These composite material systems were investigated with a recently developed ultrasonic resonance spectroscopy technique. The system employs a swept frequency approach and performs a fast Fourier transform on the frequency spectrum of the response signal. In addition. the system allows for equalization of the frequency spectrum, providing all frequencies with equal amounts of energy to excite higher order resonant harmonics. Interpretation of the second fast Fourier transform, along with equalization of the frequency spectrum, offers greater assurance in acquiring and analyzing the fundamental frequency, or spectrum resonance spacing. The range of frequencies swept in a pitch-catch mode was varied up to 8 MHz, depending on the material and geometry of the component. Single and multilayered material samples, with and without known defects, were evaluated to determine how the constituents of a composite material system affect the resonant frequency. Amplitude and frequency changes in the spectrum and spectrum resonance spacing domains were examined from ultrasonic responses of a flat composite coupon, thin composite rings, and thick composite rings. Also, the ultrasonic spectroscopy responses from areas with an intentional delamination and a foreign material insert, similar to defects that may occur during manufacturing malfunctions, were compared with those from defect-free areas in thin composite rings. A thick composite ring with varying thickness was tested to investigate the full-thickness resonant frequency and any possible bulk interfacial bond issues. Finally, the effect on the frequency response of naturally occurring single and clustered voids in a composite ring was established.

Harmon, Laura M.↗