Repeated filtering in consecutive fractional Fourier domains and its application to signal restoration
نویسندگان
چکیده
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.
منابع مشابه
Repeated fractional Fourier domain filtering is equivalent to repeated time and frequency domain filtering
Any system consisting of a sequence of multiplicative filters inserted between several fractional Fourier transform stages, is equivalent to a system composed of an appropriately chosen sequence of multiplicative filters inserted between appropriately scaled ordinary Fourier transform stages. Thus every operation that can be accomplished by repeated filtering in fractional Fourier domains can a...
متن کاملSynthesis of general linear systems with repeated filtering in consecutive fractional Fourier domains
The optical and digital implementations of general linear systems are costly. Through several examples we show that either exact realizations or useful approximations of these systems may be implemented in the form of repeated-filtering operations in consecutive fractional Fourier domains. These implementations are much cheaper than direct implementations of general linear systems. Thus we may ...
متن کاملApplications of the fractional Fourier transform to filtering, estimation and restoration
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 fract...
متن کاملEvery Fourier optical system is equivalent to consecutive fractional-Fourier-domain filtering.
We consider optical systems composed of an arbitrary number of lenses and filters, separated by arbitrary distances, under the standard approximations of Fourier optics. We show that every such system is equivalent to (i) consecutive filtering operations in several fractional Fourier domains and (ii) consecutive filtering operations alternately in the space and the frequency domains.
متن کاملApplication of Single-Frequency Time-Space Filtering Technique for Seismic Ground Roll and Random Noise Attenuation
Time-frequency filtering is an acceptable technique for attenuating noise in 2-D (time-space) and 3-D (time-space-space) reflection seismic data. The common approach for this purpose is transforming each seismic signal from 1-D time domain to a 2-D time-frequency domain and then denoising the signal by a designed filter and finally transforming back the filtered signal to original time domain. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- IEEE Trans. Signal Processing
دوره 47 شماره
صفحات -
تاریخ انتشار 1999