Phase-locked loops in acoustic analysis

Tracking of signal frequency and/or phase is made much more challenging by the presence of “rapid” frequency or phase changes in a signal—occurring in a time short compared to the amount of frequency shift: Δf×Δt << 1. In these scenarios, the usual Fourier decomposition does not provide detail sufficient to tell what is going on. Although there are time-frequency tricks one can use (such as the reassigned spectrogram, or wavelet analysis), these do not provide simple answers to the question of what is the phase as a function of time, and they do not track the instantaneous frequency as effectively as is wanted. An interesting solution from the realm of electrical engineering is provided by the phase-locked loop (PLL) detector: a construct that takes the input signal and tries to phase lock an on-board oscillator to it. It turns out that this process is surprisingly effective at tracking instantaneous frequency/phase while discarding noise if an initial estimate of the target signal frequency is known. We ...