Signal processing Fourier filters

Table 1.3 provides an overview of chemometric methods. The main emphasis is on statistical-mathematical methods. Random data are characterized and tested by the descriptive and inference methods of statistics, respectively. Their importance increases in connection with the aims of quality control and quality assurance. Signal processing is carried out by means of algorithms for smoothing, filtering, derivation, and integration. Transformation methods such as the Fourier or Hadamard transformations also belong in this area. 

Unfortunately, real data from electrochemical experiments are usually confused by noise and experimental artifacts. Although, signal processing techniques, such as Fourier transformation and digital filtering, can be used to improve the quality of the data, there is still a need for techniques that can extract useful information where there is inherent data uncertainty which cannot be removed. Pattern recognition techniques are powerful tools for this purpose (34,, W). They have been applied to classify electrochemical data on the basis of electrode mechanism (37, ) and chemical structure (i9,4Q). 

Most modern infrared and NMR spectrometers collect data in the time domain with interferometers, and then the data are transformed to the familiar frequency domain by the Fourier transform. Filtering and signal enhancement in the Fourier domain before transformation is often an attractive approach to signal processing. 

The fact that only /7-polarized radiation is absorbed by surface species has been applied by a number of workers to circumvent the problem of digitization noise. These workers have used a photoelastic modulator (PEM) configured to modulate the plane of polarization rapidly between and p, as described in Chapter 12. The Fourier frequencies are removed with a high-pass electronic filter so that the only signal is caused by the difference between the absorption of p- and -polarized radiation, which is caused solely by the surface species. A description of the signal processing and computation was given in Section 12.3. 

On the other hand, additional spectroscopic information can be obtained by making use of this technique The Fourier transform of the frequency-filtered transient (inset in Fig. 8) shows that the time-dependent modulations occur with the vibrational frequencies of the A E and the 2 IIg state. In the averaged Na2+ transient there was only a vanishingly small contribution from the 2 IIg state, because in the absence of interference at the inner turning point ionization out of the 2 IIg state is independent of intemuclear distance, and this wavepacket motion was more difficult to detect. In addition, by filtering the Na2+ signal obtained for a slowly varying pump-probe delay with different multiples of the laser frequency, excitation processes of different order may be resolved. This application is, however, outside the scope of this contribution and will be published elsewhere. 

Certainly the most popular methods for noise reduction in audio signals to date are based upon short-time Fourier processing. These methods, which can be derived from non-stationary adaptations to the frequency-domain Wiener filter, are discussed fully in section 4.5.1. 

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