Improvement of frequency resolution using a sub-bin structure in the discrete Fourier transform

Appl Opt. 2021 Jul 20;60(21):6290-6301. doi: 10.1364/AO.426045.


To improve frequency resolution, assignments of sub-bins within the bin interval of the conventional discrete Fourier transform are proposed by decreasing the number of sampled data. The simulated and experimental results of the basic sub-bin spectrum characteristics are presented. Using a signal oscillator, digital oscilloscope, and PC, the sub-bin line spectrum between two conventional bins is measured, and nine line spectra of sub-bins corresponding to the simulated results are measured. The linearity of the sub-bin spectrum intensity for amplitudes of 0.001-10 V of the input signal is also measured. The Doppler signals from the optical interferometer using a He-Ne laser are measured using a mixer to tune the frequency. A sub-bin spectrum of 104.89 kHz between two bin frequencies of 104.49 and 105.47 kHz is measured using 256 data points at a sampling frequency of 250 kHz and an acquisition time of 1.024 ms. The precision of displacement for the acquisition time is improved by one order to 32 nm for a full displacement of 2.342 µm. The sub-bins, as a composition of bin structure, are applicable to various fields.