Applications of the fractional Fourier transform to filtering, estimation and restoration
نویسندگان
چکیده
The fractional Fourier transform is more general and exible than the ordinary Fourier transform, but its optical and digital implementation is just as e cient. This underlies its potential for generalizations and improvements in every area of digital and optical signal processing. Here we consider applications of the transform to ltering, estimation and restoration. We see that the use of fractional Fourier transform based ltering con gurations allow one to exibly trade o between cost and accuracy in these applications.
منابع مشابه
Repeated filtering in consecutive fractional Fourier domains and its application to signal restoration
Filtering in a single time domain or in a single frequency domain has recently been generalized to filtering in a single fractional Fourier domain. In this correspondence, we further generalize this to repeated filtering in consecutive fractional Fourier domains and discuss its applications to signal restoration through an illustrative example.
متن کاملThe fractional Fourier transform: theory, implementation and error analysis
The fractional Fourier transform is a time–frequency distribution and an extension of the classical Fourier transform. There are several known applications of the fractional Fourier transform in the areas of signal processing, especially in signal restoration and noise removal. This paper provides an introduction to the fractional Fourier transform and its applications. These applications deman...
متن کاملFractional Fourier Transform Based OFDMA for Doubly Dispersive Channels
The performance of Orthogonal Frequency Division Multiple Access (OFDMA) system degrades significantly in doubly dispersive channels. This is due to the fact that exponential sub-carriers do not match the singular functions of this type of channels. To solve this problem, we develop a system whose sub-carriers are chirp functions. This is equivalent to exploiting Fractional Fourier Transform (F...
متن کاملApplication of FRFT Convolution Theorem in Filtering
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...
متن کاملGeneralized Parseval’s Theorem on Fractional Fourier Transform for Discrete Signals and Filtering of LFM Signals
This paper investigates the generalized Parseval’s theorem of fractional Fourier transform (FRFT) for concentrated data. Also, in the framework of multiple FRFT domains, Parseval’s theorem reduces to an inequality with lower and upper bounds associated with FRFT parameters, named as generalized Parseval’s theorem by us. These results theoretically provide potential valuable applications in filt...
متن کامل