Analytic signals with nonnegative instantaneous frequency

In this paper we investigate instantaneous frequency as it applies to the Hardy spaces on the disc (H p (D)), and on the upper half-plane (H p (C + )).The results obtained can then be applied to any sufficiently smooth analytic signal, as the boundary functions of elements of a Hardy space correspond naturally to analytic signals.Using only basic results from complex analysis, a more thorough understanding of instantaneous frequency is obtained.This allows the construction of analytic signals with nonnegative instantaneous frequency (ASNIFs) that have a prescribed amplitude.Resulting parallels are then drawn between the concepts of instantaneous frequency and Fourier frequency.