Computing the discrete-time "analytic" signal via FFT

Starting with a real-valued N-point discrete-time signal, frequency-domain algorithms are provided for computing (1) the complex-valued standard N-point discrete-time "analytic" signal of the same sample rate; (2) the complex-valued decimated N/2-point discrete-time "analytic" signal of half the original sample rate; and (3) the complex-valued interpolated NM-point discrete-time "analytic" signal of M times the original sample rate. Special adjustment of the transform end points are shown to be necessary in order to generate proper discrete-time "analytic" signals.