The phase-locked loop as a tool for signal analysis

Abstract

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. 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), 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 present examples of the superior frequency and phase tracking provided by a PLL approach, including the extremely brief chirps produced by electric fish, and the forensic detection of editing cuts in audio samples.