Spectra in Time

Chapter 2. Inspecting the spectrogram allows us to see the individual phonemes. Vowels III, /U/, /a/, etc., exhibit harmonics (parallel horizontal stripes), while consonants /s/, /th/, and /z/ show as vertical clouds of high-frequency fuzz. 

In this chapter (and in the prior chapter on the Fourier transform) we ve seen that lots of interesting information can be gleaned by transforming waveforms into the frequency domain. The appearance of a spectral plot can often be directly related to the sonic quality of the auditory experience of hearing that sound. In future chapters, we will return to the spectrum often to observe characteristics of sounds and the vibrations of physical systems. 

Robert J. McAulay and Thomas Quatieri. Speech Analysis/Synthesis Based on a Sinusoidal Representation. IEEE Transactions Acoustics, Speech, and Signal 

Xavier Serra and Julius O. Smith. Spectral Modeling Synthesis A Sound Analysis/ Synthesis System Based on a Deterministic Plus Stochastic Decomposition. Computer Music Journal 14(4) 12-24 (1990). 

Tony Verma and Teresa Meng. An Analysis/Synthesis Tool for Transient Signals that Allows aFlexible Sines -i- Transients -i- Noise Model for Audio. IEEE ICASSP-98. (1998). 

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The best tool for observation of these phenomena is time-resolved spectroscopy [42, 43] that makes it possible to observe the excitation-wavelength-dependent evolution of the spectra in time. The steady-state observations can be complicated by the existence of ground-state heterogeneity [44] that originates not only from the presence of different dyes but also from the same dyes participating in different (e.g., H-bonding) interactions. 

Simulations of NRS time spectra (left column) and Mossbauer emission energy spectra (right column) for an immobile probe atom in a surface layer when an adatom is jumping on top of the surface layer. The essential difference to the spectra of Fig. 1.27 is the much gentler decay of the NRS spectra in time with the decay completely vanishing for fast adatom Jumps. This corresponds to the motional narrowing of the Mossbauer spectra. (Reproduced from Ref. 98 with permission of the American Physical Society.)... 

For the sake of illustration, a TOF analyzer could be likened to a camera taking snapshots of the m/z values of an assembly (beam) of ions the faster the repetition rate at which the camera shutter is clicked, the greater is the number of mass spectra that can be taken in a very short time. For TOF analyzers, it is not uncommon to measure several thousand mass spectra in one second All such spectra can be added to each other digitally, a process that improves the signal-to-noise ratio in the final accumulated total. 

When a mass spectrum has been acquired by the spectrometer/computer system, it is already in digital form as m/z values versus peak heights (ion abundances), and it is a simple matter for the computer to compare each spectrum in the library with that of the unknown until it finds a match. The shortened search is carried out first, and the computer reports the best fits or matches between the unknown and spectra in the library. A search of even 60,000 to 70,000 spectra takes only a few seconds, particularly if transputers are used, thus saving the operator a great deal of time. Even a partial match can be valuable because, although the required structure may not have been found in the library, it is more than likely that some of the library compounds will have stractural pieces that can be recognized from a partial fit and so provide information on at least part of the structure of the unknown. 

Conceptually, the problem of going from the time domain spectra in Figures 3.7(a)-3.9(a) to the frequency domain spectra in Figures 3.7(b)-3.9(b) is straightforward, at least in these cases because we knew the result before we started. Nevertheless, we can still visualize the breaking down of any time domain spectrum, however complex and irregular in appearance, into its component waves, each with its characteristic frequency and amplitude. Although we can visualize it, the process of Fourier transformation which actually carries it out is a mathematically complex operation. The mathematical principles will be discussed only briefly here. 

The significance of the magic number 32 found in the experiment may also be stated in a different manner. If a cluster containing Ba and a fuUerene molecule will be stable and, thus, result in a clearly discernible structure in the mass spectra every time there is exactly one Ba-atom situated on each of the rings of the ful-lerene molecule, this property might be used to count the rings of a fullerene. Of course, such a proposal has to be verified using other fullerenes, for example, C70 which is available in sufficient quantity and purity for such an experiment. 

FT-NMR (Section 13.4) Fourier-transform NMR a rapid technique for recording XMR spectra in wrhich all magnetic nuclei absorb at the same time. 

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