Fourier transformed alternating current

Study of the underlying electrochemistry of polycrystalline gold electrodes in aqueous solution and electro-catalysis by large amplitude Fourier transformed alternating current voltammetry, A. P. O MuUane, A. M. Bond, L. D. Burke, et al., Langmuir, 2008,24, 2856. 

At the end of the 2D experiment, we will have acquired a set of N FIDs composed of quadrature data points, with N /2 points from channel A and points from channel B, acquired with sequential (alternate) sampling. How the data are processed is critical for a successful outcome. The data processing involves (a) dc (direct current) correction (performed automatically by the instrument software), (b) apodization (window multiplication) of the <2 time-domain data, (c) Fourier transformation and phase correction, (d) window multiplication of the t domain data and phase correction (unless it is a magnitude or a power-mode spectrum, in which case phase correction is not required), (e) complex Fourier transformation in Fu (f) coaddition of real and imaginary data (if phase-sensitive representation is required) to give a magnitude (M) or a power-mode (P) spectrum. Additional steps may be tilting, symmetrization, and calculation of projections. A schematic representation of the steps involved is presented in Fig. 3.5. 

Noise is characterized by the time dependence of noise amplitude A. The measured value of A (the instantaneous value of potential or current) depends to some extent on the time resolution of the measuring device (its frequency bandwidth A/). Since noise always is a signal of alternating sign, its intensity is characterized in terms of the mean square of amplitude, A, over the frequency range A/, and is called (somewhat unfortunately) noise power. The Fourier transform of the experimental time dependence of noise intensity leads to the frequency dependence of noise intensity. In the literature these curves became known as PSD (power spectral density) plots. 

DGE a AC AMS APCI API AP-MALDI APPI ASAP BIRD c CAD CE CF CF-FAB Cl CID cw CZE Da DAPCI DART DC DE DESI DIOS DTIMS EC ECD El ELDI EM ESI ETD eV f FAB FAIMS FD FI FT FTICR two-dimensional gel electrophoresis atto, 10 18 alternating current accelerator mass spectrometry atmospheric pressure chemical ionization atmospheric pressure ionization atmospheric pressure matrix-assisted laser desorption/ionization atmospheric pressure photoionization atmospheric-pressure solids analysis probe blackbody infrared radiative dissociation centi, 10-2 collision-activated dissociation capillary electrophoresis continuous flow continuous flow fast atom bombardment chemical ionization collision-induced dissociation continuous wave capillary zone electrophoresis dalton desorption atmospheric pressure chemical ionization direct analysis in real time direct current delayed extraction desorption electrospray ionization desorption/ionization on silicon drift tube ion mobility spectrometry electrochromatography electron capture dissociation electron ionization electrospray-assisted laser desorption/ionization electron multiplier electrospray ionization electron transfer dissociation electron volt femto, 1CT15 fast atom bombardment field asymmetric waveform ion mobility spectrometry field desorption field ionization Fourier transform Fourier transform ion cyclotron resonance... 

Fourier transformation — In common with many other technologies, electrochemical instruments nowadays produce data in the form of a time series - a large array of numbers equally spaced in time. As an alternative to inspecting the data - usually electric current in electrochemical applications - in its raw time-series form, an alternative is to determine the amplitudes of the sinusoidal frequencies present in the signal. Fourier transformation is the procedure by which the time series is analyzed into its component frequencies. This task is delegated to a computer, usually through a fast Fourier transform or FFT program. 

Modern Fourier transform (FT) NMR spectroscopy excites all the nuclei of interest at once with a radiofrequency (rf) pulse and detects the alternating current produced by the precessing spins in a coil surrounding the sample. This signal, or free induction decay (FID), is collected in the time domain and then processed to the frequency domain to generate the NMR spectrum. 

In a different approach, the time record of potential or current is converted into a power spectral density (PSD), which is the distrihution of the power in the frequency domain. This transformation is usually made hy means of the fast Fourier transform (FFT) algorithm [115]. Alternatively, the maximum entropy method (MEM) can also be used [116], although with some limitations [117]. In corrosion systems, both the potential noise and current noise are of the 1// type, that is, the maximum occms at low frequencies. 

Another interesting photoelectroanalytical method for the characterization of polymer films is a method which might be called photoimpedance spectrum. A small-amplitude sine-wave signal is applied to the working electrode and the resulting absorbance response is recorded at different frequencies. Alternatively, several frequencies are applied simultaneously and the response analyzed by using Fourier transform. The main advantage compared with the conventional electrical impedance measurements is naturally that only faradaic current... 

Alternatively, power spectral densities (PSD) of the noise can be calculated by means of the fast Fourier transform (FFT) or the maximum entropy method (MEM) (Schauer et al., 1998). The square root of the ratio of the voltage PSD to the current PSD also has the dimension of resistance and is a function of the frequency /. 

It is demonstrated that the above technique can detect and identify (by chemical formulae) dyes in solid PMMA commercial plastics at concentrations at least on order of magnitude lower (0.1% vs l-2wt%) than those obtained by the best currently-available alternative method (ATR Fourier transform IR spectrometry). Both untreated and redissolved PMMA can be characterised, in the presence and absence of up to three dyes in a single sample. 44 refs. USA... 

Large amplitude Fourier transformed high harmonic alternating current cyclic voltammetry kinetic discrimination of interfering faradaic processes at glassy carbon and at boron doped diamond electrodes, J. Zhang, S.-X. Guo, and A. M. Bond, Anal. Chem., 2004, 76, 3619. 

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