Frequency Domain Plots Research Articles

Shah convolution Fourier transform detection: multiple-sample injection technique.

For the direct measurement of electrophoretic mobility, multiple-point (Shah function) detected, time-domain detector signals were converted into frequency-domain plots by means of Fourier transformation. Multiple sample plugs (up to a maximum of three) were introduced into the separation channel and the resultant time-domain signals were then Fourier-transformed. The multiple-sample injection technique has been successfully demonstrated for a one-component system and a separation. Though the number of fluorescing zones flowing through the illuminated length of the channel is greater than the number of analytes in the solution, Shah convolution Fourier transform detection (SCOFT) is able to identify the number of fluorescent species in the solution based on their migration velocities. The height of the fundamental peak increases as the number of injected sample plugs is increased. More importantly, the signal-to-noise ratio (S/N) is found to be proportional to the number of injected sample plugs. With these findings, the multiple-sample injection technique certainly has got many potential applications in trace analysis. The technique would be equally applicable to other separation techniques (e.g., high-performance liquid chromatography) and detection methods (e.g., absorption, refractive index).

Characterisation of Shah convolution Fourier transform detection

Multiple-point (Shah function) detected, time-domain detector signals were converted into frequency-domain plots by means of Fourier transformation. Signal-to-noise ratio enhancement by Shah convolution Fourier transform detection (SCOFT), compared with single-point detection, was obtained. Hence SCOFT could lower the detection limits and have many potential applications in trace analysis. The frequency of the fundamental peak obtained by SCOFT increases linearly with increasing migration velocity of the analyte. SCOFT is capable of extracting multiple frequency components contained in the time-domain detector signals, e.g., in a separation. Hence SCOFT could be used to interrogate a separation based on the differences in the migration velocities of the compounds in the mixture.

Shah Convolution Fourier Transform Detection

A new convolution-detection method was developed which converts multiple-point (Shah function) detection, time-domain electropherograms into frequency-domain plots by means of a Fourier transformation, allowing the analytes' speeds to be viewed in terms of their "blinking" frequency; we have named this method Shah convolution Fourier transform detection, or SCOFT. This paper represents proof of principle of the detection concept. A micromachined glass stucture with a patterned layer of Cr on its top surface to form regularly spaced detection slits was used to perform capillary electrophoresis separations with 55-point, laser-induced fluorescence detection over 3.78 cm of the 6.6 cm separation channel. While this method can be easily integrated into a miniaturized total analysis system (μ-TAS), the principle is equally applicable to detection in full-sized analytical instrumentation. Single-component samples (fluorescein) migrating through the separation channel yielded a single peak in the frequency domain, and two-component samples (fluorescein and fluorescein isothiocyanate) yielded two resolved peaks, each at the expected frequency; harmonics were also observed. Advantages were seen in terms of isolation of the analyte peaks from interference such as baseline drift and line noise. Resolution is somewhat inferior to that seen in single-point detection, but it is thought that improved chip design and mathematical and instrument optimization will lead to performance superior to that of single-point detection.

Actuator Dynamics and Delay Compensation Using Neurocontrollers

This study compares the performances of a conventional feedforward controller and a neurocontroller in compensating the effects of the actuator dynamics and computational phase delay in a simple digital vibration control system. The model of this system is based on an earlier experimental study where a two-degree-of-freedom dynamic system was constructed in the laboratory. This system consisted of two electrohydraulic, position-controlled actuator-mass systems, mounted one on top of the other. Bode frequency domain plots were used to identify the governing parameters of the system. Based on the identified model of the experimental setup, a conventional feedforward controller and a neurocontroller are designed to compensate for the adverse effects of actuator dynamics and computational phase delay. The identified model is used to generate training information for the neurocontroller in a frequency domain of interest. To accomplish this endeavor, a neural network simulator is developed. This software uses a modified generalized delta rule with an adaptive momentum term for its learning mechanism and has a dynamic network topology capability. Through experiments and numerical simulations, it is shown that the neurocontroller is far more effective in compensating for actuator dynamics and time delay than the conventional feedforward controller. Factors contributing to the superior performance of the neurocontroller are identified and discussed.

Identification of dynamic models for the Shell benchmark problem

Dynamic process and disturbance models are identified for the 2×2 distillation column described in the summary paper by Cott. Process models are identified using both classical least squares and the newer AUDI identification algorithm developed at the University of Alberta. The identified models are validated and gain-adjusted in the frequency domain by comparing the magnitude spectrum of the models, | G (e −iω )|, versus the spectrum obtained by fast Fourier transformation of the original plant I/O time series. The noise/disturbance models are identified using standard time series tools and all models are verified by showing that the filtered residuals (measured process output minus model based estimate of the output) are essentially white noise. The estimated SISO models are all first-order and very close to the actual process whether compared on the basis of step-response coefficients, model parameters or frequency domain plots. The control problem is so simple that two standard PID feedback loops with one-way (lead/lag) interaction compensation produce results that are essentially identical to a 2×2 multivariable, model-based (GPC) controller.

Frequency domain criteria for robust stability of perturbed systems with uncoupled variations in odd and even coefficients

Abstract Sets of (characteristic) polynomials with uncoupled variations in odd and even coefficients arise when systems experience parameter variations. This paper derives frequency domain criteria for robust stability of polynomial sets with uncoupled variations in odd and even coefficients. The frequency domain criteria only require one frequency domain plot to check the robustness of polynomial sets with uncoupled variations in odd and even coefficients. Furthermore, the largest stable polynomial set can be graphically estimated from the same frequency domain plot

Frequency domain criteria for strict aperiodicity of linear interval systems

Abstract Interval systems arise when systems experience parameter variations. This paper derives frequency domain criteria for interval systems to be strictly aperiodic. The frequency domain criteria only requires one frequency domain plot to check for strict aperiodicity of linear interval systems. Furthermore, the largest allowable perturbation bounds can be graphically estimated from the same frequency domain plot.

Radiation and Dispersion Effects from Frequency-Modulated (FM) Sources

Abstract We consider the Far-zone field radiated bv a frequency-modulated (FM) source in open-ended circular waveguide. The source is uniformly distributed over the waveguide cross-section. Possible multimode effects are included. The radiated fields are derived from an eauivalent source in the aperture. Far-zone fields are first obtained in the frequency domain with time-domain results following through an inverse Fourier transform. Results are given first in standard time and frequency domain plots. These are followed by short-time Fourier transforms and spectrograms that clearly show frequency modulation effects from the source and from the dispersion inherent in the wave propagation.

Dynamics and control of a distillation train without recycle streams

A detailed study on the dynamics and control of a complex configuration of two distillation columns without recycle has been carried out. The train separates a mixture of benzene, toluene, and o-xylene (BTX) and consists of a prefractionator and a side-stream column. The dynamic aspects were explored with the help of time and frequency domain plots. The addition of controllers at the prefractionator minimizes the disturbances affecting column 2 most severely. After the variables were properly paired, the open-loop plots were identified and the controllers were designed. A comparison of the results yielded by different multivariate control design methods for some input-output configurations is presented. The resulting schemes had good spectral properties, and they were also treated via linear and nonlinear simulations with satisfactory results

Surface Current and Charge Density Induced on Aircraft

The usefulness of the geometrical theory of diffraction (GTD) in computing the surface current and charge density induced on aircraft is illustrated. This is a high-frequency solution for an arbitrary incident plane wave and fuselage observation points. A pattem is presented for an arbitrary incident plane wave as well as a series of frequency and time domain plots for roil plane incidence. A 3-dimensional pattem is presented for plane wave incidence (as a function of incidence angle) as well as examples of roll plane results in both the frequency and time domain.

Surface current and charge density induced on aircraft

The usefulness of the geometrical theory of diffraction (GTD) in computing the surface current and charge density induced on aircraft is illustrated. This is a high-frequency solution for an arbitrary incident plane wave and fuselage observation points. A pattern is presented for an arbitrary incident plane wave as well as a series of frequency and time domain plots for roll plane incidence. A 3-dimensional pattern is presented for plane wave incidence (as a function of incidence angle) as well as examples of roll plane results in both the frequency and time domain.

Determination of optical transfer function by inspection of frequency-domain plot

In cases in which there are zeros in the optical transfer function, display of the absolute value of the Fourier transform of a blurred image may allow these zeros to be seen, if the noise level is low enough. This can be used to identify the optical transfer function, provided that it is one of the suitable common simple forms, or to determine certain parameters of the optical transfer function if its form is known. Examples of the use of this technique in the generation of restoring filters for image enhancement are presented.