A convolution and product theorem for the fractional Fourier transform 论文

详细信息

发表期刊/会议

IEEE Signal Processing Letters

发表日期

1998-04-01

发表年份

1998

摘要

The fractional Fourier transform (FRFT), which is a generalization of the Fourier transform, has many applications in several areas, including signal processing and optics. Almeida (see ibid., vol.4, p.15-17, 1997) and Mendlovic et al. (see Appl. Opt., vol.34, p.303-9, 1995) derived fractional Fourier transforms of a product and of a convolution of two functions. Unfortunately, their convolution formulas do not generalize very well the classical result for the Fourier transform, which states that the Fourier transform of the convolution of two functions is the product of their Fourier transforms. This paper introduces a new convolution structure for the FRFT that preserves the convolution theorem for the Fourier transform and is also easy to implement in the designing of filters.