Complex Lags from Simple Physics
X-ray timing information produced through Fourier analysis from the variable emission of black hole X-ray binaries has been used for several decades to provide key insights into the physical setup of these systems not measurable with spectroscopy. In particular, quasi-periodic oscillations within these systems have been of particular interest and remain the source of great debate on how they come about. We investigate the timing products of simple toy models of QPO variability to provide more intuition when thinking about signals produced by these sources. We simulate simple physical setups and show how phase lags and coherence of the signals change in these different setups. We first focus on properties of QPO like signals under a single driving signal assumption. We then investigate the case of multiple oscillations in a signal. Finally, we investigate how timing products change when QPOs are produced by time dependent modulation of periodic signals. Many simple physical setups with common driving signals are able to reproduce complex non-linear phase lags that resemble those present in the data. The changes in physical setup aligns with experience in the data, such as differing power spectra but fall short of reproducing the data as expected. Multiple incoherent processes present in the signal struggle to reproduce behaviour present in the data. Coherence seems to be a more useful tool for differentiating between setups. Fourier analysis with complicated data like that produced by X-ray binaries can lead one to be tempted to invoke exotic lag mechanisms without the appropriate framing. This paper attempts to help provide tools and intuition as to how different phenomena in signals (particularly relating to QPOs) can result in non-linear phase lags with explicit structure.