Smoothing, spectral

It is frequently found that the signal-to-noise ratio (SNR) of a spectrum is less than ideal. The optimal way to improve the SNR is to prepare a better sample or to use a better sampling technique. Alternatively, the spectrum may simply be remeasured by signal averaging a greater number of scans. It may be that these options are impossible or undesirable for example, because of time constraints. There are data processing procedures that can improve the SNR, but these are applied at 

One way to improve the signal-to-noise ratio is through convolution of the spectrum with an appropriate function such as a boxcar, Lorentzian, or Gaussian function. The operation of spectral convolution has been presented in Section 2.3 Such operations tend to distort the spectrum, as the lineshape function is altered. The broader the convolution function, the greater is the distortion of the spectrum. The most common such convolution is the Savitzky-Golay smoothing algorithm [13]. 

Another method by which spectral SNR improvement may be accomplished is by Fourier smoothing, which, in effect, is a form of apodization. Most condensed-phase infrared spectral bands have a bandshape that is very close to a Lorentzian function (see Section 1.4)  

Equation 10.7 describes a sinusoidal curve, exp(—27ii Vo x ), that corresponds to a single band at a wavenumber, vq, that has exponential decay of exp(—7iy x ). 

In summary, if spectral smoothing is applied to a spectrum, the resolution will suffer and the lineshape will change. The only manner in which these parameters will not be altered is to collect the spectrum and signal average for a larger number of scans, or to redesign the experiment so that the SNR is greater. 

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Chemometric techniques have gained enormous significance in the treatment of spectral information by virtue of their ability to process the vast amount of data produced by modern instruments over short periods of time with a view to extracting the information of interest they contain and improving the quality of the results. In some cases, the operator is unacquainted with the chemometric techniques (spectral smoothing, baseline drift correction) embedded in the software used by the instrument in others, the chemometric tools involved are inherent in the application of the spectroscopic technique concerned (e.g. in NIR spectroscopy) and thus indispensable to obtaining meaningful results. 

Spectral smoothing increases the signal-to-noise ratio of the spectrum at the expense of resolution. Thus, while smoothing produces smoother looking bands, some information content may be lost. Furthermore, it may cause changes in the measured peak position and band shape. Interpolation represents the inverse of smoothing. That is, the resolution is artificially enhanced to provide a better definition of band shape. This may be achieved by polynomial fitting of the spectral data points. 

Once we have found the units by our search, the actual S5mthesis process is often trivial. In pure unit selection, we have stored our units as waveforms, and so a simple overlap and add technique at the waveform boundaries is sufiicient. If we have stored the units in a more parametric representation (e.g. LP coefiicients and residuals), these can be S5mthesized in the same way as with second generation diphone synthesis. Some systems perform spectral smoothing between units, but again this can be performed with the same techniques as with second generation systems. 

One ofthe most widely used techniques is the STRAIGHT set of analysis tools [ ].This system is operates as high quality speech analysis-modification-synthesis method implemented as a channel vocoder and has separate components for instantaneous-ffequency-based FO extraction and pitch-adaptive spectral smoothing. STRAIGHT attempts to obtain a more accurate spectral estimation and a use more sophisticated soiuce model than simple impulses. A comparison of STRAIGHT and standard cepstral analysis is showen in Figure 15.17. 

Figure 3-14. Experimental and simulatedstatic NMR spectra of (a) as-made TiOz nanoparticles and then after heat treatment at (b) 400°C, (c) 650°Cand (d) 700° C compared to (e) bulk polycrystalUne anatase. The average particle size and spectral smoothing required are indicated Gervais et al (2001) with permission of the American Chemical Society.

All pole model of sound production mechanism (common method for speech analysis and synthesis). Good if signal has strong resonant structure (e.g. humans, birds) can also be used for spectral smoothing (Kondoz, 2004). 

J, Computer Processing of Measured Spectra 6J2.1 Spectral Smoothing... 

Attention should be paid to the fact that, as spectral noise tends to be amplified in derivative spectra, false peaks may appear in derivative spectra, especially from a poor S/N ratio original spectrum. Therefore, it is advisable to apply appropriate spectral smoothing to a noisy spectrum before computing its derivative spectra. 

It is worth pointing out that reconstruction of spectra using the basis factors in Equation (7.18) is useful for noise reduction. This noise-reduction technique is much better than spectral smoothing, as chemical information contained in original spectra is not lost, if the number of basis factors is appropriately determined. 

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