A concise introduction to the concept of fractional Fourier transforms is followed by a discussion of their relation to chirp and wavelet transforms. The notion of fractional Fourier domains is developed in conjunction with the Wigner distribution of a signal. Convolution, filtering, and multiplexing of signals in fractional domains are discussed, revealing that under certain conditions one can...

The Fractional Fourier Transform (FRFT) is a generalization of the classical Fourier transform and has many applications in several areas including signal processing, optics and quantum mechanics. This paper presents a low pass filter, designed by using convolution theorem for FRFT. In the design of filter, Blackman window function is used and it has been observed that proposed FRFT domain filt...

The recovery of bandlimited signals with high dynamic range is a hot issue in sampling research. unlimited theory expands the recordable traditional analog-to-digital converters (ADCs) arbitrarily, and signal folded back into low measurement, avoiding saturation problem. Since non-bandlimited Fourier domain cannot be directly applied to its existing theory, may fractional domain. Therefore, thi...

It is shown that both surface tilting and translational motion can be independently estimated by use of the speckle photographic technique by capturing consecutive images in two different fractional Fourier domains. A geometric interpretation, based on use of the Wigner distribution function, is presented to describe this application of the optical fractional Fourier transform when little prior...