Fast Fourier Transform frequency measurement

The methods presented in this article make use of the FFT (Fast Fourier transform) of measured acceleration data on a selected frequency band around the modes of interest. The modes are assumed to be classically damped. 

The m/z values of peptide ions are mathematically derived from the sine wave profile by the performance of a fast Fourier transform operation. Thus, the detection of ions by FTICR is distinct from results from other MS approaches because the peptide ions are detected by their oscillation near the detection plate rather than by collision with a detector. Consequently, masses are resolved only by cyclotron frequency and not in space (sector instruments) or time (TOF analyzers). The magnetic field strength measured in Tesla correlates with the performance properties of FTICR. The instruments are very powerful and provide exquisitely high mass accuracy, mass resolution, and sensitivity—desirable properties in the analysis of complex protein mixtures. FTICR instruments are especially compatible with ESI29 but may also be used with MALDI as an ionization source.30 FTICR requires sophisticated expertise. Nevertheless, this technique is increasingly employed successfully in proteomics studies. 

A spectrum is the distribution of physical characteristics in a system. In this sense, the Power Spectrum Density (PSD) provides information about fundamental frequencies (and their harmonics) in dynamical systems with oscillatory behavior. PSD can be used to study periodic-quasiperiodic-chaotic routes [27]. The filtered temperature measurements y t) were obtained as discrete-time functions, then PSD s were computed from Fast Fourier Transform (FFT) in order to compute the fundamental frequencies. 

There are two ways to collect FLIM data freqnency-domain or time-domain data acqnisition (Alcala et al. 1985 Jameson et al. 1984). Briefly, in freqnency domain FLIM, the fluorescence lifetime is determined by its different phase relative to a freqnency modulated excitation signal nsing a fast Fourier transform algorithm. This method requires a frequency synthesizer phase-locked to the repetition freqnency of the laser to drive an RF power amplifier that modulates the amplification of the detector photomultiplier at the master frequency plus an additional cross-correlation freqnency. In contrast, time-domain FLIM directly measures t using a photon connting PMT and card. 

Figure 4. The Na+ and Na2+ transient signals obtained from pump-probe measurements using 80-fs pulses at 618 nm. The power spectra (insets) obtained from a fast Fourier transformation (FFT) show the different frequency components of the two transients.

Pseudostochastic random binary sequences in combination with fast Fourier transform and correlation techniques avoid these problems and allow for a direct measurement of g(t) with high spectral power density and frequency multiplexing (stochastic TDFRS). Tailoring of the pseudostochastic sequences even allows for a selective enhancement and suppression of certain frequencies and, hence, of certain molecular species [74]. 

The impedance can be measured using various instalments and techniques, ranging from a simple oscilloscope display to a fast Fourier transform (FFT) analyzer. The most common instrument used is a frequency response analyzer (FRA), e.g., the Solartron FRA. A potentiostat or a load bank combined with a frequency response analyzer can perform the EIS measurements. The electrical connection between the FRA, the potentiostat (or the load bank), and the fuel cell is illustrated in Figure 3.19. 

By means of a fast Fourier transform (FFT) algorithm, the measured data can be transformed into the frequency domain. This Fourier transform is needed for several reasons. One is comparison with the data that have been measured in the frequency domain. The second is the actual requirement of results at specific frequencies. The third is interpretation of the data [82],... 

The power spectra may be directly obtained using dynamic signal analyzers that measure signals as a function of time and perform the fast Fourier transform. The coherence function takes values betweaen 0 and 1 and characterizes statistical validity of the frequency response measurements ... 

One of the most important limitations of derivative spectroscopy is the background noise associated with any experimental measurement. This random noise usually has a higher frequency than the signal to be measured. This means that it will give weak but narrow peaks. The use of derivatives will strengthen this kind of peaks in front of the broader and stronger ones of the compounds, which are the most important in the usual spectrum. A solution to this problem is to use the Fourier transform (or indeed better, the fast Fourier transform, FFT), which allows the use of filters in order to remove high-frequency... 

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