Discrete Fourier Transform Approach Research Articles

Optimized sinewave test of waveform digitizers by a DFT approach

This paper presents a particularly simple and effective discrete Fourier transform (DFT)-based approach for digitizing waveform recorder testing. Its implementation is straightforward and signal processing requirements are confined to the calculation of the DFT, which can be carried out by a readily implemented fast Fourier transform algorithm. Adjustments to the test generator can be determined to ensure that tests are carried out under optimal conditions, providing accurate and reliable estimates of digitizer performance parameters.

Discrete Fourier Transform Approach to a Constrained H2 Mixed Sensitivity Minimization

This paper proposes a controller synthesis method for MIMO discrete-time systems by approximately solving an H2 mixed sensitivity minimization problem with a steady state constraint. Working in the Discrete Fourier Transform (DFT) domain, we convert the original constrained H2 design problem into a problem of solving a constrained vector minimization in the l2-space. The advantage of this approach is that the solution can be analytically expressed and efficiently calculated via multichannel algorithms due to the partially block circular structure of the matrices involved in the DFT domain. The controller is then constructed via its finite Markov parameters obtained from the inverse DFT of the l2 solution. The choice of the weighting factor is also briefly discussed.

Electromagnetic scattering from cylindricalarrays of infinitely long thin wires

Plane wave scattering by a cylindrical array of equally spaced infinitely long perfectly conducting thin wires is examined. The symmetry of the structure is exploited to derive a closed form expression for the currents excited on the wires, using the concept of circulant matrix and, alternatively, using a DFT (discrete Fourier transform) approach.

A comparison of autoregressive spectral estimation algorithms and order determination methods in ultrasonic tissue characterization

Several autoregressive (AR) methods for spectral estimation were applied toward the task of estimating ultrasonic backscatter coefficients from small volumes of tissue. Data were acquired from a homogeneous tissue-mimicking phantom and from a normal human liver in vivo. AR methods performed better at short record lengths than the traditional DFT (discrete Fourier Transform) approach. The DFT method consistently underestimated backscatter coefficients at small gate lengths. Burg's algorithm, the Modified Covariance algorithm, and the Recursive Maximum Likelihood Estimation algorithm performed comparably. The Yule-Walker algorithm did not perform as well as these but offered a slight improvement over the DFT. Several order determination methods were tested. These included residual variance (RV), final prediction error (FPE), Akaike information criterion (AIC), and Minimum Description Length (MDL). The AIC and MDL produced misleading results at higher orders. The RV and FPE yielded better results. The autoregressive method offers promise for enhanced spatial resolution and accuracy in ultrasonic tissue characterization and nondestructive evaluation of materials.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

High resolution ultrasonic backscatter coefficient estimation based on autoregressive spectral estimation using Burg's algorithm

An autoregressive (AR) method for spectral estimation was applied toward the task of estimating ultrasonic backscatter coefficients from small volumes of tissue. High spatial resolution is desirable for generating images of backscatter coefficient. Data was acquired from a homogeneous tissue-mimicking phantom and from a normal human liver in vivo. The AR method was much more resistant to gating artifacts than the traditional DFT (discrete Fourier transform) approach. The DFT method consistently underestimated backscatter coefficients at small gate lengths. Therefore backscatter coefficient image formation will be quantitatively more meaningful if based on AR spectral estimation rather than the DFT. The autoregressive method offers promise for enhanced spatial resolution and accuracy in ultrasonic tissue characterization and nondestructive evaluation of materials.

Simulation of Multivariate Random Processes: Hybrid DFT and Digital Filtering Approach

A numerical simulation technique is presented that combines the advantages of the discrete Fourier transform (DFT) algorithm and a digital filtering scheme to generate continuous long-duration multivariate random processes. This approach offers the simple convenience of conventional fast Fourier transform (FFT) based simulation schemes; however, it does not suffer from the drawback of the large computer memory requirement that in the past has precluded the generation of long-duration time series utilizing FFT-based approaches. Central to this technique is a simulation of a large number of time series segments by utilizing the FFT algorithm, which are subsequently synthesized by means of a digital filter to provide the desired duration of simulated processes. This approach offers computational efficiency, convenience, and robustness. The computer code based on the present methodology does not require users to have experience in determining optimal model parameters, unlike the procedures based on parametric models. The effectiveness of this methodology is demonstrated by means of examples concerning the simulation of a multivariate random wind field and the spatial variation of wave kinematics in a random sea with prescribed spectral descriptions. The simulated data showed excellent agreement with the target spectral characteristics. The proposed technique has immediate applications to the simulation of real-time processes.

Efficient analysis of dynamic response of linear systems

AbstractAfter reviewing briefly a recently proposed procedure for evaluating the dynamic transient response of a classically damped linear system from its corresponding steady‐state response, a modified procedure is presented which also appears to be highly efficient for non‐classically damped systems of the type encountered in studies of soil‐structure interaction. The concepts involved are developed by reference to viscously damped single‐degree‐of‐freedom systems, and numerical solutions are included to illustrate the accuracy and efficiency of the proposed procedure and its superiority over the classical Discrete Fourier Transform approach.

Dynamic Analysis by Extra Fast Fourier Transform

A method based on the Discrete Fourier Transform (DFT) is presented for evaluating the dynamic response of any discrete, time invariant, linear system to an excitation, the spatial distribution of which is constant and the timewise variation of which may be represented by a string of equally spaced impulses of arbitrary magnitudes. In addition to being faster and more efficient than available DFT approaches, the method may be adopted to the processing of arbitrarily long excitations as a series of short, independent segments. The length of the individual segments may be chosen to optimize computational efficiency. The method consists of taking advantage of the periodicity implicit in the DFT approach and evaluating first the response of the system to a periodic extension of the excitation. A simple corrective solution is then superposed which converts the periodic response to the desired transient response. The method is illustrated by two numerical examples.