Time domain filtering

Filtering a time series, using Fourier time domain filters, however, involves multiplying die entire time series by a single function, so diat... 

First, either a Lorentzian or Gaussian filter is applied to the FID to reduce the amount of noise. The choice of lineshape will depend on the shape of the frequency domain spectrum, the lineshape is related to how the fluorine spins interact with their environment. The filter linewidth is generally similar to or slightly less than the T2 value (T2 can be estimated from the spectral linewidth). After application of the time domain filter, a fast Fourier transform (FFT) is performed. The resultant frequency domain spectrum will then need to undergo phase adjustment to obtain a pure absorption spectrum. The amount of receiver dead time (time lost between the end of the excitation pulse and the first useful detection time point) will determine the presence and extent of baseline artifact present as well as how difficult phase adjustment will be to accomplish. 

In an attempt to provide some meaningful comparisons between the two approaches, the authors have reformulated the time-domain filter described in reference (1) to accept frequency-domain data. In the same way as the time-domain filter accepts data samples at each time Increment so the frequency-domain filter accepts real and imaginary components of the frequency... 

Time domain filtering is based upon a simple mathematical manipulation. FID are multiplied by the term C, ... 

Time domain filter banks in Fig. 11 show the SWT there are also the iSWT synthesis filter banks for reconstruction. In the analysis filter... 

Quadrupole mass spectrometers (mass filters) allow ions at each m/z value to pass through sequentially for example, ions at m/z 100, 101, 102 will pass one after the other through the quadrupole assembly so that first m/z 100 is transmitted, then m/z 101, then m/z 102 (or vice versa), and so on. Therefore, the ion collector (or detector) at the end of the quadrupole unit needs to cover only one point or focus in space (Figure 29.1a), and a complete mass spectrum is recorded over a period of time. The ions arrive at the collector sequentially, and ions are detected in a time domain, not in a spatial domain. 

Several types of analyzers exist today that allow a time-domain signal to be eonverted to a frequeney-domain speetrum. The resulting speetrum of all speetrum analyzers is equivalent to the amplitude/frequeney plot, whieh is obtained by passing the given signal aeross a set of eonstant bandwidth filters and noting the output of eaeh filter at its eenter frequeney. 

In the analysis of vibration data there is often the need to transform the data from the time domain to the frequency domain or, in other words, to obtain a spectrum analysis of the vibration. The original and inexpensive system to obtain this analysis is the tuneable swept-filter analyzer. Because of inherent limitations of this system, this process, despite the use of automated sweep, is time-consuming when analyzing low frequencies. When the spectra data needs to be digitized for computer inputing, there are further limitations in capability of tuneable filter-analysis systems. 

In single-scale filtering, basis functions are of a fixed resolution and all basis functions have the same localization in the time-frequency domain. For example, frequency domain filtering relies on basis functions localized in frequency but global in time, as shown in Fig. 7b. Other popular filters, such as those based on a windowed Fourier transform, mean filtering, and exponential smoothing, are localized in both time and frequency, but their resolution is fixed, as shown in Fig. 7c. Single-scale filters are linear because the measured data or basis function coefficients are transformed as their linear sum over a time horizon. A finite time horizon results infinite impulse response (FIR) and an infinite time horizon creates infinite impulse response (HR) filters. A linear filter can be represented as... 

Spectral FLIM involves measuring the apparent lifetimes in a preparation at many wavelengths with the assistance of a spectrograph or a series of filters (see also Chapter 4, Figs. 4.7 and 4.8 depicting hyperspectral FLIM in the time domain). The goal of the measurement is similar to that of the multifrequency approach ... 

Historically, this has been the most constrained parameter, particularly for confocal laser scanning microscopes that require spatially coherent sources and so have been typically limited to a few discrete excitation wavelengths, traditionally obtained from gas lasers. Convenient tunable continuous wave (c.w.) excitation for wide-held microscopy was widely available from filtered lamp sources but, for time domain FLIM, the only ultrafast light sources covering the visible spectrum were c.w. mode-locked dye lasers before the advent of ultrafast Ti Sapphire lasers. 

How does one extract eigenpairs from Chebyshev vectors One possibility is to use the spectral method. The commonly used version of the spectral method is based on the time-energy conjugacy and extracts energy domain properties from those in the time domain.145,146 In particular, the energy wave function, obtained by applying the spectral density, or Dirac delta filter operator (8(E — H)), onto an arbitrary initial wave function ( (f)(0)))1 ... 

The linearity property of the Fourier transform does not hold for phase delay values. Let a, be the intrinsic, single measurement, time domain standard deviation of the filtered signal (in units of amplitude). Also let o>(n) be the standard deviation of the phase of the nth harmonic averaged j times. The phase noise as a function of harmonic (frequency) is given by... 

Processing of time domain data may cause artefacts in the frequency domain. One example for these distortions are truncations at the beginning or at the end of the FID which could lead to severe baseline artefacts which can be reduced by an appropriate filter. Undesired resonances leading to broad lines in the final spectra can be more easily eliminated in time domain by truncating the first few data points. Furthermore, the model functions in time domain are mathematically simpler to handle than the frequency domain analogues, which leads to a reduction of computation time. The advantage of the frequency domain analysis is that the quantification process can be directly interpreted visually. 

In the directly acquired dimension the spectral window can be opened up to cover all frequencies of interest on both sides of the carrier with a proportional increase in the overall data size. As an alternative, it may be sufficient to open the (audio)filters to allow signals to alias to empty regions (if any) with no intensity loss. Carrier shift using time domain tools in data processing can be applied to restore a more convenient arrangement of the spectrum [10]. 

Fig. 4. Two-dimensional (2D) spectra of cyclo(Pro-Gly), 10 mM in 70/30 volume/volume DMSO/H2O mixture at CLio/27r = 500 MHz and T = 263 K. (A) TCX SY, t = 55 ms. (B) NOESY, Tm = 300 ms. (C) ROESY, = 300 ms, B, = 5 kHz. (D) T-ROESY, Tin = 300 ms, Bi = 10 kHz. Contours are plotted in the exponential mode with the increment of 1.41. Thus, a peak doubles its intensity every two contours. All spectra are recorded with 1024 data points, 8 scans per ti increment, 512 fi increments repetition time was 1.3 s and 90 = 8 ps 512x512 time domain data set was zero filled up to 1024 x 1024 data points, filtered by Lorentz to Gauss transformation in u>2 domain (GB = 0.03 LB = -3) and 80° skewed sin" in u), yielding a 2D Fourier transformation 1024 x 1024 data points real spectrum. (Continued on subsequent pages)...

In this work, an inverse filtering technique based on Wiener s optimal theory (1-3) is presented. This approach is valid for time-varying systems, and is solved in the time domain in mtrix form. Also, it is in many respects equivalent to the numerically "effl- lent" Kalman filtering approach described in ( ). For this reason, a... 

Monmayrant, A., Joffre, M., Oksenhendler, T., Herzog, R., Kaplan, D., and Tournois, P. 2003. Time-domain interferometry for direct electric-field reconstruction by use of an acousto-optic programmable filter and a two-photon detector. Opt. Lett. 28(4) 278-80. 

This circuit is a bridge rectifier followed by a filter capacitor to produce a DC voltage with ripple at Vin. Connected to Vin is a linear regulator made from a Zener voltage reference and an NPN pass transistor. We will first run a Transient Analysis to see the operation of the circuit at room temperature (27°C). To set up a Transient Analysis, select PSpice and then New Simulation Profile from the Capture menus, enter a name for the profile and then click the Create button. By default the Time Domain (Transient) Analysis type is selected. Fill in the parameters as shown in the Time Domain dialog box below ... 

Therefore, in order to minimize the overlap between G+( ) and Fj+ oo) for general gapped baths, and thereby the transfer infidelity (4.198), we will design a narrow bandpass filter centered on the gap. Since G ( ) has a narrower gap than G+( ), we optimize the filter Fj o)) under the variational E-L method. We seek a narrow bandpass filter, whose form on time domain via Fourier transform decays as slowly as possible, so as to filter out the higher frequencies. This amounts to maximizing Fj- (t) = ( )e (f subject to the variational... 

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