Search for Chirality in Hydrogenated Magnesium Nanosilicates: A DFT and TD-DFT Investigation
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Kamil B. Stelmach↗
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VLSI Architectures for Computing DFT's
Simplifications result from use of residue Fermat number systems. System of finite arithmetic over residue Fermat number systems enables calculation of discrete Fourier transform (DFT) of series of complex numbers with reduced number of multiplications. Computer architectures based on approach suitable for design of very-large-scale integrated (VLSI) circuits for computing DFT's. General approach not limited to DFT's; Applicable to decoding of error-correcting codes and other transform calculations. System readily implemented in VLSI.
Truong, T. K.↗
A VLSI pipeline design of a fast prime factor DFT on a finite field
A conventional prime factor discrete Fourier transform (DFT) algorithm is used to realize a discrete Fourier-like transform on the finite field, GF(q sub n). A pipeline structure is used to implement this prime factor DFT over GF(q sub n). This algorithm is developed to compute cyclic convolutions of complex numbers and to decode Reed-Solomon codes. Such a pipeline fast prime factor DFT algorithm over GF(q sub n) is regular, simple, expandable, and naturally suitable for VLSI implementation. An example illustrating the pipeline aspect of a 30-point transform over GF(q sub n) is presented.
Truong, T. K.↗
On the number of multiplications necessary to compute a length-2 exp n DFT
The number of multiplications necessary and sufficient to compute a length-2 exp n DFT is determined. The method of derivation is shown to apply to the multiplicative complexity results of Winograd (1980, 1981) for a length-p exp n DFT, for p an odd prime number. The multiplicative complexity of the one-dimensional DFT is summarized for many possible lengths.
Heideman, M. T.↗
Outline of a fast hardware implementation of Winograd's DFT algorithm
The main characteristics of the discrete Fourier transform (DFT) algorithm considered by Winograd (1976) is a significant reduction in the number of multiplications. Its primary disadvantage is a higher structural complexity. It is, therefore, difficult to translate the reduced number of multiplications into faster execution of the DFT by means of a software implementation of the algorithm. For this reason, a hardware implementation is considered in the current study, taking into account a design based on the algorithm prescription discussed by Zohar (1979). The hardware implementation of a FORTRAN subroutine is proposed, giving attention to a pipelining scheme in which 5 consecutive data batches are being operated on simultaneously, each batch undergoing one of 5 processing phases.
Zohar, S.↗
Techniques for Computing the DFT Using the Residue Fermat Number Systems and VLSI
The integer complex multiplier and adder over the direct sum of two copies of a finite field is specialized to the direct sum of the rings of integers modulo Fermat numbers. Such multiplications and additions can be used in the implementation of a discrete Fourier transform (DFT) of a sequence of complex numbers. The advantage of the present approach is that the number of multiplications needed for the DFT can be reduced substantially over the previous approach. The architectural designs using this approach are regular, simple, expandable and, therefore, naturally suitable for VLSI implementation.
Truong, T. K.↗
A pipeline design of a fast prime factor DFT on a finite field
A conventional prime factor discrete Fourier transform (DFT) algorithm is used to realize a discrete Fourier-like transform on the finite field, GF(q sub n). This algorithm is developed to compute cyclic convolutions of complex numbers and to decode Reed-Solomon codes. Such a pipeline fast prime factor DFT algorithm over GF(q sub n) is regular, simple, expandable, and naturally suitable for VLSI implementation. An example illustrating the pipeline aspect of a 30-point transform over GF(q sub n) is presented.
Truong, T. K.↗
IR Spectra and Bond Energies Computed Using DFT
The combination of density functional theory (DFT) frequencies and infrared (IR) intensities and experimental spectra is a very powerful tool in the identification of molecules and ions. The computed and measured isotopic ratios make the identification much more secure than frequencies and intensities alone. This will be illustrated using several examples, such as Mn(CO)n and Mn(CO)n-. The accuracy of DFT metal-ligand bond energies will also be discussed.
Bauschlicher, Charles↗
The Application of DFT to Systems Containing Metal Atoms
The application of density functional theory (DFT) to a series of metal containing systems will be described. The focus will be on the calculation of accurate bond energies, especially metal-ligand successive bond energies. The DFT results will be compared with experiment and other levels of theory. If time permits, metal clusters will also be discussed.
Ricca, Alessandra↗
Adaptive DFT-based Interferometer Fringe Tracking
An automatic interferometer fringe tracking system has been developed, implemented, and tested at the Infrared Optical Telescope Array (IOTA) observatory at Mt. Hopkins, Arizona. The system can minimize the optical path differences (OPDs) for all three baselines of the Michelson stellar interferometer at IOTA. Based on sliding window discrete Fourier transform (DFT) calculations that were optimized for computational efficiency and robustness to atmospheric disturbances, the algorithm has also been tested extensively on off-line data. Implemented in ANSI C on the 266 MHz PowerPC processor running the VxWorks real-time operating system, the algorithm runs in approximately 2.0 milliseconds per scan (including all three interferograms), using the science camera and piezo scanners to measure and correct the OPDs. The adaptive DFT-based tracking algorithm should be applicable to other systems where there is a need to detect or track a signal with an approximately constant-frequency carrier pulse.
Wilson, Edward↗
Application of DFT Filter Banks and Cosine Modulated Filter Banks in Filtering
None given. This is a proposal for a paper to be presented at APCCAS '94 in Taipei, Taiwan. (From outline): This work is organized as follows: Sec. II is devoted to the construction of the new 2m channel under-decimated DFT filter bank. Implementation and complexity of this DFT filter bank are discussed therein. IN a similar manner, the new 2m channel cosine modulated filter bank is discussed in Sec. III. Design examples are given in Sec. IV.
filter bank subband coding coding block filtering ↗
Geometric interpretations of the Discrete Fourier Transform (DFT)
One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.
Campbell, C. W.↗
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↗
Using Density Functional Theory (DFT) for the Calculation of Atomization Energies
The calculation of atomization energies using density functional theory (DFT), using the B3LYP hybrid functional, is reported. The sensitivity of the atomization energy to basis set is studied and compared with the coupled cluster singles and doubles approach with a perturbational estimate of the triples (CCSD(T)). Merging the B3LYP results with the G2(MP2) approach is also considered. It is found that replacing the geometry optimization and calculation of the zero-point energy by the analogous quantities computed using the B3LYP approach reduces the maximum error in the G2(MP2) approach. In addition to the 55 G2 atomization energies, some results for transition metal containing systems will also be presented.
Bauschlicher, Charles W., Jr.↗
A fast DFT algorithm using complex integer transforms
Winograd's algorithm for computing the discrete Fourier transform is extended considerably for certain large transform lengths. This is accomplished by performing the cyclic convolution, required by Winograd's method, by a fast transform over certain complex integer fields. This algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithms.
Reed, I. S.↗
DFT algorithms for bit-serial GaAs array processor architectures
Systems and Processes Engineering Corporation (SPEC) has developed an innovative array processor architecture for computing Fourier transforms and other commonly used signal processing algorithms. This architecture is designed to extract the highest possible array performance from state-of-the-art GaAs technology. SPEC's architectural design includes a high performance RISC processor implemented in GaAs, along with a Floating Point Coprocessor and a unique Array Communications Coprocessor, also implemented in GaAs technology. Together, these data processors represent the latest in technology, both from an architectural and implementation viewpoint. SPEC has examined numerous algorithms and parallel processing architectures to determine the optimum array processor architecture. SPEC has developed an array processor architecture with integral communications ability to provide maximum node connectivity. The Array Communications Coprocessor embeds communications operations directly in the core of the processor architecture. A Floating Point Coprocessor architecture has been defined that utilizes Bit-Serial arithmetic units, operating at very high frequency, to perform floating point operations. These Bit-Serial devices reduce the device integration level and complexity to a level compatible with state-of-the-art GaAs device technology.
Mcmillan, Gary B.↗
Comparison of DFT with Traditional Methods for the Calculation of Vibrational Frequencies and Bond Energies
The vibrational frequencies of MO2 are computed at many levels of theory, including HF, B3LYP, BP86, CASSCF, MP2, and CCSD(T). The computed results are compared with the available experimental results. Most of the methods fail for at least one state of the systems considered. The accuracy of the results and the origin of the observed failures are discussed. The B3LYP bond energies are compared with traditional methods for a variety of systems, ranging from FeCOn+ to SiCln and its positive ions. The cases where B3LYP differs from the traditional methods are discussed.
Bauschlicher, Charles W.↗
The Effect of the Weight Scheme on DFT Vibrational Frequencies
All-electron B3LYP harmonic frequencies of Ge2H5 and Ge2H6 are computed for several choices of grid and using both the Becke and the Stratmann, Scuseria, and Frisch atomic partition functions (weight scheme). For large grids, the results are independent of the weighting scheme. The lowest frequency mode is much more stable with respect to the number of grid points when the Stratmann, Scuseria, and Frisch weights are used.
Bauschlicher, Charles↗