AMA: An Open-source Amplitude Modulation Analysis Toolkit for Signal Processing Applications

For their analysis with conventional signal processing tools, non-stationary signals are assumed to be stationary (or at least wide-sense stationary) in short intervals. While this approach allows them to be studied, it disregards the temporal evolution of their statistics. As such, to analyze this type of signals, it is desirable to use a representation that registers and characterizes the temporal changes in the frequency content of the signals, as these changes may occur in single or multiple periodic ways. Over the last few years, the amplitude modulation approach has shown useful for the analysis and synthesis of non-stationary signals across multiple applications, including telecommunications, speech and music perception, and biological signals (e.g., electrocardiogram, electroencephalogram and respiration). Despite their usefulness, no open-source toolkits exist that are application agnostic. In this work, we fill this gap. More specifically, we present AMA, the open-source Amplitude Modulation Analysis toolkit for MATLAB, Octave and Python. The toolkit provides functions to compute forward and inverse transformations between time, frequency, time-frequency and frequency-modulation-frequency domains for single- or multi-channel signals. Additionally, a graphical user interface is provided for real-time exploration of the signals and their representations across different domains. Lastly, example data and scripts are provided. With the development of this toolkit, we hope to facilitate the study of non-stationary signals in particular for the analysis of second-order periodicities.