Signal domain

When measuring a signal, one records the magnitude of the output or the response of a measurement device as a function of an independent variable. For instance, in chromatography the signal of a Flame Ionization Detector (FID) is measured as a function of time. In spectrometry the signal of a photomultiplier or diode array is measured as a function of the wavelength. In a potentiometric titration the current of an electrode is measured as a function of the added volume of titrant. 

wavelength and added volume in the above-mentioned examples are the domains of the measurement. A chromatogram is measured in the time domain, whereas a spectrum is measured in the wavelength domain. Usually, signals in these domains are directly translated into chemical information. In spectrometry for example peak positions are calculated in the wavelength domain and in chromatography they are calculated in the time domain. Signals in these domains are directly interpretable in terms of the identity or amount of chemical substances in the sample. 

It may thus be necessary to calculate the Fourier transform of the measured signal to return to the domain of interpretation, here wavelength or wavenumber. In FTIR the signal is measured in the displacement domain 6 and transformed to the wavelength or wavenumber domain by a Fourier transform. Because the wavelength domain is the Fourier transform of the displacement domain, and vice versa, we say that the spectrum is measured in the Fourier domain. 

Instead of considering a spectrum as a signal which is measured as a function of wavelength, in this chapter we consider it measured as a function of time. The frequency scale in the Fourier domain is given in cycles (v) per second (Hz) or radians (to) per second (s ). These units are related by 1 Hz = 2k s . 

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Signal function (measurement function, analytical function in the signal domain)... 

By the operations coding (analytical measurement) and decoding (analytical evaluation) information will be transformed from the sample domain into the signal domain and vice versa as shown in Fig. 2.12. Therefore, quantities which correspond to that of the sample domain (Q and Xq) must also exist in the signal domain. The characteristics in the signal domain are ... 

Fig. 2.12. Relationship between sample domain and signal domain in element analysis (a) and structure analysis (b). The representation in the sample domains is shown in different forms, as a block diagram and a list in case of (a) and as constitution formula and structure matrix, respectively, in case (b)...

Fig. 2.17. The four analytical quantities in sample and signal domain and the six fundamental functions between them the functions Q = f l(x) and z = do not make...

The foreground of the representation depicts the relationship between the species Q and their characteristic signals zy while behind that, the relationship between signals zy their intensities yy and the species amounts x is established. Taken together, these relationships establish the composition of the sample (the sample domain) and the signal domain, too. 

Signals used in analytical chemistry have a definite origin from particular species or given structural relationships between constituents of samples. The relation of the sample domain and the signals domain, i.e. the coding and decoding process as represented in Fig. 2.12, must be as unambiguous as possible. 

In analytical chemistry, calibration represents a set of operations that connects quantities in the sample domain with quantities in the signal domain (see Sect. 2.3, Fig. 2.12). In Table 6.1 the real analytical quantities and properties behind the abstract input and output quantities are listed. 

It is difficult to comprehend why this measure has not been applied in analytical chemistry. Instead of this, in the last decades the signal-to-noise ratio has increasingly been used. Signal-to-noise ratio, see Eq. (7.1), is the measure that corresponds to r in the signal domain. In principle, quantities like S/N (Eq. (7.1)) and / (Eq. (7.7)) could represent measures of precision, but they have an unfavourable range of definition, namely range[r = range[S/N] = 0... oo. 

Limits characterize the detection capability of analytical methods and can be related to both analytical domains, sample domain as well as signal domain. Although there are several limits, namely lower and upper limits3 as well as thresholds, the most important problem in analytical chemistry is the distinction between real measurement values and zero values or blanks, respectively. 

Signal domain (measured values) Sample domain (analytical values)... 

Limit in the signal domain, estimated from the average blank plus its uncertainty, generally according... 

Xq. The transition to signal domain is done by calibration and analytical measurement. 

Wahlberg, J., and Spiess, M. (1997). Multiple determinants direct the orientation of signal-anchor proteins the topogenic role of the hydrophobic signal domain./ Cell... 

Schultz, J., et al., SMART, a simple modular architecture research tool identification of signaling domains. Proc Natl Acad Sci USA, 1998, 95(11), 5857-64. 

Fig. 7. The distribution of Fas gene mutations within the coding region. The codon number indicated on the x-axis corresponds to the lower horizontal boxes, which indicate the exon numbers of the Fas gene. Mutations are obviously concentrated in exons 6 and 9, which encode the transmembrane domain and the intracytoplasmic region containing the death-signaling domain, respectively. No mutations have been reported in exons 1 or 5. The numbers on top of the bars (162, 234, 244, 251, and 253) show codons that are mutated at high frequency.

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