Dispersion vs absorption (DISPA): Effects of digitization, noise, truncation of free induction decay, and zero-filling

Abstract A plot of dispersion vs absorption (DISPA) for a single Lorentzian line gives a semicircle, and the direction and magnitude of the displacement of an experimental DISPA curve from its reference semicircle can be diagnostic for several line-broadening mechanisms (A. G. Marshall and D. C. Roe, Anal. Chem. 50, 756, 764 (1978)) . Four important practical aspects in application of DISPA plots are considered. First, since absorption and dispersion are most conveniently obtained in digitized form by Fourier transformation of a free induction decay (FID), it is shown that the position of the first digitized point can be spurious and may be ignored if below the abscissa. Second, by plotting DISPA curves for Lorentzians with varying signal-to-noise ratio, it is found that a minimal working signal-to-noise ratio of about 20:1 is needed for reliable interpretation. Third, truncation of the FID can produce marked distortion in theoretical DISPA plots, but will not matter in practice, since the number of data points in a DISPA plot constructed from a truncated decay would be too small for useful analysis. Fourth, the addition of N zeroes to an N-point FID yields a resultant DISPA plot with improved signal-to-noise ratio, while addition of further zeroes simply results in interpolation of subsequent DISPA points between previous points.