Convolution In Frequency Domain Research Articles

The seismic magnitude of the 1989 Loma Prieta mainshock determined from strong motion records

The work investigates the usefulness of regional broadband recordings to estimate rapidly the size of large earthquakes. Strong motion records of the Loma Prieta earthquake from 20 free-field stations at distances 15 < Δ < 105 km from the source are used to compute the local magnitude of the mainshock. Frequency-domain convolution and integration are used to obtain appropriate synthesized signals. An azimuthal average of ML = (6.7 ± 0.09) was estimated from the maximum trace amplitudes measured on synthesized Wood-Anderson torsion records. The low-gain Wood-Anderson torsion seismograph (100 magnification) at the University of California Seismographic Station gave ML = 7.0. Comparison between published local and teleseismic estimates indicates that the usual strong motion accelerometers in the near field of large earthquakes yield acceptable values of magnitude. Efforts to obtain estimates of the overall average radiated seismic energy from the integrated ground velocity-squared records demonstrated the need for special site calibration.

A High-Resolution Spectral Study of Audiomagnetotelluric Data and Noise Interactions

This study is an investigation of the behaviour of audiomagnetotelluric (AMT) response estimates, in the presence of intense anthropogenic noise. The details of the data and noise interactions are studied by constructing highly resolved AMT response functions using the Maximum Entropy spectral analysis method, in its multichannel form. For low-noise, consistent data spectral estimates and their frequency resolution should be independent of the spectral technique used. Such behaviour is confirmed. When the data are contaminated by significant amounts of noise the highly-resolved estimates display detailed inconsistencies as a function of frequency. Such piecewise distortions can be understood if the response function is viewed as a polynomial. The results obtained enable the identification of response structure generated by both harmonic and subharmonic noise processes. High-resolution estimates provide a detailed view of data quality and narrow-band perturbations. The comparison of high-resolution response functions with conventional (discrete) estimates, shows that, in some cases, the latter may produce erroneous estimates. A discussion of the generation and received characteristics of noise waveforms is also included. A smoothing operation, involving frequency domain convolution, is described and applied to the results obtained. The technique exploits the minimum-delay properties exhibited by a valid impulse response function in the time domain.

Evaluation Methods and Accuracy in Probabilistic Load Flow Solutions

This paper presents a new method for obtaining a probabilistic load flow solution using a discrete frequency domain convolution technique. It is shown that this method has greater accuracy while providing a breakthrough in computational speed. A detailed example compares the numerical results with a Monte Carlo simulation. The effects of nonlinearity in the network equations are discussed.

The time domain solution of the Volterra functional equation: Application to nonlinear circuit analysis

An iterative technique to solve Volterra integral equations based on the Newton-Raphson method is presented which has a wide region of convergence, enabling the analysis of grossly nonlinear circuits. Instead of performing convolution in the frequency domain, the algorithm computes directly in the time domain which is found to be more efficient, if the number of time steps is maintained within a suitable range.