Frequency-Domain Design Techniques

Kuon, J. F., "Multivariable Frequency Domain Design Techniques," Ph.D. dissertation, University of Alberta,... 

Time-domain techniques record the intensity of the signal as a function of time, frequency-domain techniques record the phase and the amplitude of the signal as a function of frequency. Time domain and frequency domain are connected via the Fourier transform. Therefore, the time domain and the frequency domain are generally equivalent. However, this does not imply an equivalence between time-domain and frequency-domain recording techniques or the instruments used for each. An exhaustive comparison of the techniques is difficult and needs to include a number of different electronic design principles and applications. 

A comprehensive overview of frequency-domain DOT techniques is given in [88]. Particular instraments are described in [166, 347, 410]. It is commonly believed that modulation techniques are less expensive and achieve shorter acquisition times, whereas TCSPC delivers a better absolute accuracy of optical tissue properties. It must be doubted that this general statement is correct for any particular instrument. Certainly, relatively inexpensive frequency-domain instruments can be built by using sine-wave-modulated LEDs, standard avalanche photodiodes, and radio or cellphone receiver chips. Instruments of this type usually have a considerable amplitude-phase crosstalk". Amplitude-phase crosstalk is a dependence of the measured phase on the amplitude of the signal. It results from nonlinearity in the detectors, amplifiers, and mixers, and from synchronous signal pickup [6]. This makes it difficult to obtain absolute optical tissue properties. A carefully designed system [382] reached a systematic phase error of 0.5° at 100 MHz. A system that compensates the amplitude-phase crosstalk via a reference channel reached an RMS phase error of 0.2° at 100 MHz [370]. These phase errors correspond to a time shift of 14 ps and 5.5 ps RMS, respectively. 

Topics discussed above are some basic principles and techniques in voltammetry. Voltammetry in the frequency domain where i-E response is obtained at different frequencies from a single experiment known as AC voltammetry or impedance spectroscopy is well established. The use of ultramicroelectrodes in scanning electrochemical microscopy to scan surface redox sites is becoming useful in nanoresearch. There have been extensive efforts made to modify electrodes with enzymes for biosensor development. Wherever an analyte undergoes a redox reaction, voltammetry can be used as the primary sensing technique. Microsensor design and development has recently received... 

In Chap. 18 we will define mathematically the sampling process, derive the z transforms of common functions (learn our German vocabulary) and develop transfer functions in the z domain. These fundamentals are then applied to basic controller design in Chap. 19 and to advanced controllers in Chap. 20. We will find that practically all the stability-analysis and controller-design techniques that we used in the Laplace and frequency domains can be directly applied in the z domain for sampled-data systems. 

Sampled-data control systems can be designed in the frequency domain by using the same techniques that we employed for continuous systems. The Nyquist stability criterion is applied to the appropriate closedloop characteristic equation to find the number of zeros outside the unit circle. 

Historically, the first techniques designed to achieve independet control over pitch or duration were carried out in the time domain Fairbanks, Everitt and Jaeger s modified tape recorder [Fairbanks et al., 1954] probably is the first known automatic time-domain system for speech transposition. By contrast with frequency-domain methods, time-domain techniques for time or pitch scale modification manipulate short-duration time-segments extracted from the original signal, a mechanism usually called sampling or splicing As a result, they tend to require much fewer calculations and lend themselves quite well to real-time implementations. 

The introduction of the SWIFT technique (10,14,21,22) makes possible FT/ICR frequency-domain excitation with the same mass resolution as has already been demonstrated for FT/ICR detect ion, provided only that sufficient computer memory is available to store a sufficiently long time-domain waveform. When ejection must be performed with ultrahigh mass resolution over a wide mass range, a simple solution is to use two successive SWIFT waveforms first, a broad-band low-resolution excitation designed to eject ions except over (say) a 1 amu mass range and then a second SWIFT waveform, heterodyned to put 2 8K data points spanning a mass range of 1-2 amu. 

This part introduces methods used to measure impedance and other transfer functions. The chapters in this section are intended to provide an understanding of frequency-domain techniques and the approaches used by impedance instrumentation. This understanding provides a basis for evaluating and improving experimental design. The material covered in this section is integrated with the discussion of experimental errors and noise. The extension of impedance spectroscopy to other transfer-function techniques is developed in Part III. 

The third class of techniques include a frequency-domain method based on the identification of the sensitivity function S s)) and the complementary sensitivity function T s)) from plant data or CPM of multivariable systems [140]. Robust control system design methods seek to maximize closed-loop performance subject to specifications for bandwidth and peak... 

In the experiments described here, two separate techniques have been used for interferometric characterization of the shocked material s motion frequency domain interferometry (FDI) [69, 80-81] and ultrafast 2-d spatial interferometric microscopy [82-83]. Frequency domain interferometry was used predominantly in our early experiments designed to measure free surface velocity rise times [70-71]. The present workhorse in the chemical reaction studies presented below is ultrafast interferometric microscopy [82], This method can be schematically represented as in Figure 6. A portion of the 800 nm compressed spectrally-modified pulse from the seeded, chirped pulse amplified Ti sapphire laser system (Spectra Physics) was used to perform interferometry. The remainder of this compressed pulse drives the optical parametric amplifier used to generate tunable fs infrared pulses (see below). 

When using the Fourier transforms to transform from the frequency domain to the time and thus range domain, sidelobes are generated, and these sidelobes appear as false targets in range. Sidelobe suppression techniques are the same as employed in antenna sidelobe suppression design (Fig. 17.63). 

Mathematical models based on probability have been developed to analyze the system as a whole on the basis of the statistical behavior of the EMI [100]. These models are useiul in developing computer aided design and analysis procedures to solve EMI problems. Computational models of EMI and EMC problems from circuit level to a more complex system levels such as aircraft EMC have also been extensively studied. Techniques such as FEM, method of moments (MoM), Transmission Line method (TLM), Finite Difference Time Domain method (FDTD), Finite Difference Frequency Domain method (FDFD), Partial Element Equivalent Circuit model (PEEC) and a number of such methods have been used for this purpose for various applications. Interested readers can see reference 100 for a nice review of such approaches. 

For illustration, let us estimate the dispersion error of the aforementioned narrow-band technique and compare it with the one induced by the wideband method of (2.107)—(2.115). The cell dimensions are chosen as Ay = 2Ax and T2D = 0-85 in (5.46). Figure 5.5 gives the results for two mesh resolutions with respect to Ax. In contrast with the performance of the latter scheme, the narrow-band approach achieves a remarkable reduction around the design frequency, whereas its accuracy deteriorates at finer resolutions. This is, however, not a serious shortcoming, since a given computational domain appears to have a smaller electrical size at lower frequencies and, consequently, the dispersion error is not as considerable as in the high-frequency band. Moreover, it is noteworthy to observe that the narrow-band scheme generates smaller errors for coarser lattices and thus, its application to broadband simulations should not be ruled out. 

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