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 transform end points is shown to generate proper discrete-time ´analytic´ signals.