  Experiments that compare rhythmic properties across different genetic
alterations and entrainment conditions underlie some of the most important
breakthroughs in circadian biology. A robust estimation of the rhythmic
properties of the circadian signals goes hand in hand with these discoveries.
Widely applied traditional signal analysis methods such as fitting cosine
functions or Fourier transformations rely on the assumption that oscillation
periods do not change over time. However, novel high-resolution recording
techniques have shown that, most commonly, circadian signals exhibit
time-dependent changes of periods and amplitudes which cannot be captured with
the traditional approaches. In this chapter we introduce a method to determine
time-dependent properties of oscillatory signals, using the novel open-source
Python-based Biological Oscillations Analysis Toolkit (pyBOAT). We show with
examples how to detect rhythms, compute and interpret high-resolution
time-dependent spectral results, analyze the main oscillatory component and to
subsequently determine these main components time-dependent instantaneous
period, amplitude and phase. We introduce step-by-step how such an analysis can
be done by means of the easy-to-use point-and-click graphical user interface
(GUI) provided by pyBOAT or executed within a Python programming environment.
Concepts are explained using simulated signals as well as experimentally
obtained time series.
