We introduce two generalizations of the exponential function and, hence, two generalizations of the Fourier transform and series. Each generalization depends on a real, nonnegative parameter less than or equal to one, but reduces to the standard exponential function when the parameter is equal to one. For this reason, the corresponding transforms are called fractional Fourier transforms. In this talk we examine sampling theorems of bandlimited functions in these two fractional Fourier transform domains.
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