Hartley/Hilbert transform spectroscopy: absorption-mode resolution with magnitude-mode precision
Abstract
Fourier transformation (FT) of an N-point time-domain discrete signal produces, after phase correction, two independent data sets: an N/2-point absorption spectrum, A(omega), and an N/2-point dispersion spectrum, D(omega), each with the same information content. Usually only A(omega) is kept. The dispersion-mode information has conventionally been recovered in either of two ways. First, the N/2-point magnitude-mode spectrum, M(omega) = ([A(omega)]2 + [D(omega)]2)1/2, offers a square root of 2 improvement in precision compared with the original N/2-point absorption spectrum, but with poorer resolving power (factor ranging from square root of 3 to 2 for unapodized data). Alternatively, zero-filling the initial time-domain data to 2N data points prior to Fourier transformation results in an N-point absorption-mode spectrum with the same peak width and peak-height-to-noise ratio as the original N/2-point absorption spectrum, but with a square root of 2 improvement in precision. Thus, magnitude-mode display improves FT spectral precision at the expense of a loss in resolving power, whereas zero-filling improves precision at the expense of having to store twice as many data points. In this paper, we present a third method of recovering the dispersion information.(ABSTRACT TRUNCATED AT 250 WORDS)
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