Abstract

A number of signal processing operations can be carried out on spectra using a digital filter based on a simple trapezoid function. The filter is applied to the Fourier transform of the spectral signal. Several signal processing examples are presented to illustrate the capabilities of this filter. These examples include filtering and diagnosis of high frequency noise on a signal, removal of fixed frequency noise, minimization of quantization noise, and differentiation and approximate deconvolution for the purpose of resolution enhancement.

Single-frame reconstruction by fractional Fourier-transform domain filtering in off-axis digital holographic microscopy

Wanying Cui, Yiwei Liu, Junjie Zhang, Yang Han, and Zhuqing Jiang
Opt. Continuum 2(12) 2500-2508 (2023)

Chirp filtering in the fractional Fourier domain

Rainer G. Dorsch, Adolf W. Lohmann, Yigal Bitran, David Mendlovic, and Haldun M. Ozaktas
Appl. Opt. 33(32) 7599-7602 (1994)

Fractional Fourier-transform filtering and reconstruction in off-axis digital holographic imaging

Yiwei Liu, Qiuya Sun, Hao Chen, and Zhuqing Jiang
Opt. Express 31(6) 10709-10719 (2023)

Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms

Haldun M. Ozaktas, Billur Barshan, David Mendlovic, and Levent Onural
J. Opt. Soc. Am. A 11(2) 547-559 (1994)

Reduction of speckle in digital holography by discrete Fourier filtering

Jonathan Maycock, Bryan M. Hennelly, John B. McDonald, Yann Frauel, Albertina Castro, Bahram Javidi, and Thomas J. Naughton
J. Opt. Soc. Am. A 24(6) 1617-1622 (2007)