Abstract

We proposed a method to use sub-bins (SBs) and the inverse matrix to reduce the spectral leakage in discrete Fourier transform (DFT) over the conventional spectral resolution. SBs were assigned between two conventional bins. Utilizing the real signal, the process reproducing complex amplitudes at each SB was described and confirmed through simulations with the pseudo-inverse matrix. In experiments, with the 256 number of data, the frequency interval of ${ k} = {107}$ and 108 was 4 divided by SBs. The single-peak spectrum at each SB frequency was measured clearly. Using the two signals with frequencies corresponding to two SBs within the conventional bin interval, the spectrum with two peaks was also measured. The linearity was confirmed for the input range from 0.1–5 V. The feasibility of this method to improve the frequency resolution has been shown for various optical applications.

© 2023 Optica Publishing Group

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

Manabu Sato, Yuuki Kimura, Junpei Masuta, Tetsuo Kosaka, and Izumi Nishidate
Appl. Opt. 60(21) 6290-6301 (2021)

Improved discrete fractional Fourier transform

Soo-Chang Pei and Min-Hung Yeh
Opt. Lett. 22(14) 1047-1049 (1997)

High-dimensional discrete Fourier transform gates with a quantum frequency processor

Hsuan-Hao Lu, Navin B. Lingaraju, Daniel E. Leaird, Andrew M. Weiner, and Joseph M. Lukens
Opt. Express 30(6) 10126-10134 (2022)

Correction of instrument line shape in Fourier transform spectrometry using matrix inversion

Raphaël Desbiens, Jérôme Genest, Pierre Tremblay, and Jean-Pierre Bouchard
Appl. Opt. 45(21) 5270-5280 (2006)

Super-resolution discrete Fourier transform spectroscopy beyond time-window size limitation using precisely periodic pulsed radiation

Takeshi Yasui, Yuki Iyonaga, Yi-Da Hsieh, Yoshiyuki Sakaguchi, Francis Hindle, Shuko Yokoyama, Tsutomu Araki, and Mamoru Hashimoto
Optica 2(5) 460-467 (2015)