Frequency-domain techniques

The frequency-domain format eliminates the manual effort required to isolate the components that make up a time trace. Frequency-domain techniques convert time-domain data into discrete frequency components using a mathematical process called Fast Fourier Transform (FFT). Simply stated, FFT mathematically converts a time-based trace into a series of discrete frequency components (see Figure 43.19). In a frequency-domain plot, the X-axis is frequency and the Y-axis is the amplitude of displacement, velocity, or acceleration. 

T. Analysis of the signal has primarily been performed in the time-domain although some applications are beginning to appear using frequency-domain techniques. The main features of the time-domain signal that are used for analysis are ... 

The second chapter by Peter Verveer and Quentin Hanley describes frequency domain FLIM and global analysis. While the frequency domain technique for fluorescence lifetime measurement is sometimes counterintuitive, the majority of the 10 most cited papers using FLIM have taken advantage of the frequency domain method as stated by these authors. The global analysis of lifetime data in the frequency domain, resolving both E and /d has contributed significantly to this advantage. 

The development of new oximeters is also in progress, with the application of time- and frequency-domain techniques which are, in principle, capable of discriminating between the absorption and scattering contributions coming from human tissue, thus making possible the detection of tissue oxygenation37 39. 

Confocal fluorescence microscopy can be combined with time-domain and frequency-domain techniques to produce lifetime imaging (see Section 11.2.2.3). 

Frequency domain techniques offer advantages over time domain techniques for real-time applications. In the frequency domain the measurements are performed within limited frequency bandwidths. The noise in limited bandwidths is reduced, in most cases substantially. Figures 9.7 illustrates this concept. In Figure 9.7a the... 

The value of fEdetermines all other variables in the equations above. In turn, fE is determined by the temporal resolution of interest of the system studied. To resolve an average excited state lifetime t, the required data sampling rate, in frequency domain techniques is at least an order ofmagnitude slower than it is in the time domain as stated by the following relation (when Np > 32 and Nw= 1) ... 

This chapter is organized as follows By reference to a signal model, time-scale and pitch-scale modifications are defined in the first part. The second part presents frequency-domain techniques while the third part describes time-domain techniques. In the fourth part, the limitations of time-domain and frequency-domain methods are discussed along with improvements proposed in the last few years. 

Because they give access to the spectral representation of the signal, frequency-domain techniques are well suited for formant modification. The first step in frequency-domain formant modification techniques consists of obtaining a estimation of the spectral envelope. Based of the short-time representation of the signal, it. is possible to derive a spectral envelope function using a variety of different techniques. If the pitch of the signal is available, the short-time Fourier spectmm is searched for local maxima located around harmonic frequencies, then an envelope can be obtained by joining the local... 

In the next chapter we take a quantitative look at the dynamics of these CSTR systems using primarily rigorous nonlinear dynamic simulations (time-domain analysis). However, some of the powerful linear Laplace and frequency-domain techniques will be used to gain insight into the dynamics of these systems. 

Other frequency domain techniques which have been proposed include the commutative controller (31), sequential return difference (32), and the direct Nyquist array (33). In chemical pro-ess control, a number of recent applications of multivariable frequency response methods include distillation columns (34), (35), and reactors (36). 

The need for models has been envisioned from two angles a) as a tool to improve the understanding of the dynamic phenomena involved in impact testing, and b) as a way to connect the remote measurement (force exerted on the striker) to the sought measurement (force exerted on the material), with the purpose of extracting the latter from the former. This latter approach was taken in the past by Cain [5] who used frequency domain techniques to filter the load-time records out of spurious oscillations associated with the dynamics of impact testing. This author used a model of the same characteristics as the ones mentioned before, but no analytical development was performed. The model was just used to numerically estimate the type of filters that could be used to clean the recorded signals of unwanted oscillations. 

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. 

In spite of its prevalence in the fluorescence decay literature, we were not universally successful with this fitting method. Most reports of hi- or multiexponential decay analysis that use a time-domain technique (as opposed to a frequency-domain technique) use time-correlated photon counting, not the impulse-response method described in Section 2.1. In time-correlated photon-counting, noise in the data is assumed to have a normal distribution. Noise in data collected with our instrument is probably dominated by the pulse-to-pulse variation of the laser used for excitation this variation can be as large as 10-20%. Perhaps the distribution or the level of noise or the combination of the two accounts for our inconsistent results with Marquardt fitting. 

SJ Kendra and A Cinar. Controller performance assessment by frequency domain techniques. J. Process Control, 7(3) 181-194, 1997. 

Very fast fluorescence signals can be examined by a phase-resolved frequency domain technique. A high-frequency modulated light source is used to excite the sample according to... 

Time-Domain Techniques versus Frequency-Domain Techniques... 

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. 

In the following we assume that a sample is to be characterised by an optieal probing teehnique. It is excited by a modulated or pulsed light souree. The light emitted by the sample is recorded, and typical sample parameters are derived from the reeorded signal. Typical time-domain and frequency-domain techniques are shown in Fig. 1.2. 

Fig. 1.2 Time-domain left) and frequency-domain techniques right)...

Recently Liebert et al. have demonstrated that advanced TCSPC is able to record effects of brain activity with 50 ms time resolution, clear separation of scattering and absorption, and probably better depth resolution than CW or frequency-domain techniques [324, 327, 328]. A system of four parallel TCSPC modules with four individual detectors and several multiplexed laser diode lasers is used. A fast sequence of time-of-flight distributions is recorded in consecutive time intervals of 50 to 100 ms. Variations of the optical properties in the brain are derived from the intensity and the first and second moments of the time-of-flight distributions [325]. 

An overview of frequency-domain detection techniques is given in [88]. Frequency-domain techniques compare the phase shift and the modulation degree of the fluorescence with the modulated excitation. Modulation of the excitation is achieved either by actively modulating the light of a continuous laser or by using pulsed lasers of high repetition rate. With pulsed lasers, phase and modulation can be measured at the fundamental repetition frequency or at its harmonics. 

Both homodyne and heterodyne detection can use normal detectors with subsequent electronic mixers [82, 83]. Alternatively, mixing can be performed directly in the detector by modulating its gain [73, 470]. Frequency-domain techniques with single-point detectors make frill use of the depth resolution capability of confocal and two-photon imaging but do not work well at extremely high scan rates. 

Lifetime imaging by frequency-domain techniques can also be achieved by modulated image intensifiers [196, 304, 469, 479]. Lifetime imaging by a directly modulated CCD chip has been described in [364]. 

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