Effect of Sampling Rate on Fourier Transform Spectra: Oversampling is Overrated

Abstract

In Fourier transform spectrometry, an analog time-domain signal is sampled at equally spaced intervals and subjected to a discrete Fourier transform to yield a discrete frequency-domain spectrum. Round-off errors in the sampling process can generate quantization “noise” even for a noiseless time-domain analog signal. Oversampling refers to sampling a time-domain analog signal at a rate faster than that required by the Nyquist limit. Oversampling has been applied in a wide variety of fields, including image, speech, and audio spectral analysis. It has been variously claimed that oversampling can increase the effective number of analog-to-digital converter (ADC) bits, increase signal-to-noise ratio and/or resolution, allow for improved phase and/or magnitude linearity, and reduce quantization “noise” in the bandwidth of interest. In this paper, we explain and demonstrate the effects of oversampling in Fourier transform spectrometry. For Fourier transform interferometry, magnetic resonance, or ion cyclotron resonance mass spectrometry conducted with an ADC of at least 12 bit/word, we conclude that quantization “noise” is negligible; oversampling thus has little effect on FT spectral signal-to-noise ratio, dynamic range, or resolution. Oversampling can, however, improve phase and magnitude linearity by eliminating the need for a sharp cutoff in the passband of the analog filter. Finally, autocorrelation analysis of simulated time-domain signals shows that quantization “noise” is random and essentially independent of frequency (i.e., “white”) at practically attainable sampling rates.