Amplitude measurements trajectories

Early approaches to music analysis relied on a running Fourier transform to measure sine-wave amplitude and frequency trajectories. This technique evolved into a filter-bank-based processor and ultimately to signal analysis/synthesis referred to as the phase vocoder [Flanagan and Golden, 1966], This section describes the history of the phase vocoder, its principles, and limitations that motivate sinusoidal analysis/synthesis. Other formulations and refinements of the phase vocoder are given in chapter 7. 

In order to assess magnetization transfer in a multiple-spin system, it is necessary to define a measure that reflects the efficiency of the transfer between two spins i and j. This parameter should reflect the amplitude of the ideal polarization transfer as well as the duration of the mixing process, because, in practice, Hartmann-Hahn transfer competes with relaxation. Relaxation effects result in a damping of the ideal polarization-transfer functions 7j . The damping due to relaxation depends not only on the structure and dynamics of the molecule that hosts the spin system of interest, but also on the actual trajectories of polarizations and coherences under a specific multiple-pulse Hartmann-Hahn mixing sequence (see Section IV.D). For specific sample conditions and a specific experiment, the coherence-transfer efficiency can be defined as the maximum of the damped magnetization-transfer function. 

Method of Data Processing. The amplitude of the signal pulses depends on the size of the phytoplankters, their trajectory, and their position in the measured volume because of the nonuniformity of the irradiated intensity and the characteristics of the collecting optics (Figure 6). This section presents our method to obtain size information of the particles from the raw data of the pulse-height distribution. 

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