{"title":"Quality Factor Variation with Transform Order in Fractional Fourier Domain","authors":"Sukrit Shankar, Chetana Shanta Patsa, K. Pardha Saradhi, Jaydev Sharma","country":null,"institution":"","volume":6,"journal":"International Journal of Electronics and Communication Engineering","pagesStart":1567,"pagesEnd":1571,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/9485","abstract":"Fractional Fourier Transform is a powerful tool,\nwhich is a generalization of the classical Fourier Transform. This\npaper provides a mathematical relation relating the span in Fractional\nFourier domain with the amplitude and phase functions of the signal,\nwhich is further used to study the variation of quality factor with\ndifferent values of the transform order. It is seen that with the\nincrease in the number of transients in the signal, the deviation of\naverage Fractional Fourier span from the frequency bandwidth\nincreases. Also, with the increase in the transient nature of the signal,\nthe optimum value of transform order can be estimated based on the\nquality factor variation, and this value is found to be very close to\nthat for which one can obtain the most compact representation. With\nthe entire mathematical analysis and experimentation, we consolidate\nthe fact that Fractional Fourier Transform gives more optimal\nrepresentations for a number of transform orders than Fourier\ntransform.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 6, 2007"}