کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
562646 | 875425 | 2012 | 7 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: On uncertainty principle for signal concentrations with fractional Fourier transform On uncertainty principle for signal concentrations with fractional Fourier transform](/preview/png/562646.png)
The fractional Fourier transform (FRFT) – a generalized form of the classical Fourier transform – has been shown to be a powerful analyzing tool in signal processing. This paper investigates the uncertainty principle for signal concentrations associated with the FRFT. It is shown that if the fraction of a nonzero signal's energy on a finite interval in one fractional domain with a certain angle αα is specified, then the fraction of its energy on a finite interval in other fractional domain with any angle ββ(β≠α)(β≠α) must remain below a certain maximum. This is a generalization of the fact that any nonzero signal cannot have arbitrarily large proportions of energy in both a finite time duration and a finite frequency bandwidth. The signals which are the best in achieving simultaneous concentration in two arbitrary fractional domains are derived. Moreover, some applications of the derived theory are presented.
► We derive an uncertainty principle for signal concentrations in fractional domains.
► A nonzero signal's energy cannot be arbitrarily large in any two fractional domains.
► We present signals that are best concentrated in any two fractional domains.
► Applications of the derived result in signal and filter design are presented.
Journal: Signal Processing - Volume 92, Issue 12, December 2012, Pages 2830–2836