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The analysis of the time-frequency content of a signal is a classical problemin signal processing, with a broad number of applications in real life. Manydifferent approaches have been developed over the decades, which providealternative time-frequency representations of a signal each with its advantagesand limitations. In this work, following the success of nonlinear methods forthe decomposition of signals into intrinsic mode functions (IMFs), we firstprovide more theoretical insights into the so-called Iterative Filteringdecomposition algorithm, proving an energy conservation result for the deriveddecompositions. Furthermore, we present a new time-frequency representationmethod based on the IMF decomposition of a signal, which is called IMFogram. Weprove theoretical results regarding this method, including its convergence tothe spectrogram representation for a certain class of signals, and we present afew examples of applications, comparing results with some of the most well knowapproaches available in the literature.

New theoretical insights in the decomposition and time-frequency representation of nonstationary signals: the IMFogram algorithm