{"title":"Perturbation in the Fractional Fourier Span due to Erroneous Transform Order and Window Function","authors":"Sukrit Shankar, Chetana Shanta Patsa, Jaydev Sharma","country":null,"institution":"","volume":13,"journal":"International Journal of Electronics and Communication Engineering","pagesStart":79,"pagesEnd":82,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/9355","abstract":"Fractional Fourier Transform is a generalization of the\r\nclassical Fourier Transform. The Fractional Fourier span in general\r\ndepends on the amplitude and phase functions of the signal and varies\r\nwith the transform order. However, with the development of the\r\nFractional Fourier filter banks, it is advantageous in some cases to\r\nhave different transform orders for different filter banks to achieve\r\nbetter decorrelation of the windowed and overlapped time signal. We\r\npresent an expression that is useful for finding the perturbation in the\r\nFractional Fourier span due to the erroneous transform order and the\r\npossible variation in the window shape and length. The expression is\r\nbased on the dependency of the time-Fractional Fourier span\r\nUncertainty on the amplitude and phase function of the signal. We\r\nalso show with the help of the developed expression that the\r\nperturbation of span has a varying degree of sensitivity for varying\r\ndegree of transform order and the window coefficients.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 13, 2008"}