The analysis of the time-frequency content of a signal is a classical problem in signal processing, with a broad number of applications in real life. Many different approaches have been developed over the decades, which provide alternative time-frequency representations of a signal each with its advantages and limitations. In this work, following the success of nonlinear methods for the decomposition of signals into intrinsic mode functions (IMFs), we first provide more theoretical insights into the so-called Iterative Filtering decomposition algorithm, proving an energy conservation result for the derived decompositions. Furthermore, we present a new time-frequency representation method based on the IMF decomposition of a signal, which is called IMFogram. We prove theoretical results regarding this method, including its convergence to the spectrogram representation for a certain class of signals, and we present a few examples of applications, comparing results with some of the most well know approaches available in the literature.
翻译:对信号的时间-频率内容的分析是信号处理的一个典型问题,在现实生活中应用了多种应用。几十年来,我们制定了许多不同的方法,这些方法为每个信号提供了替代的时间-频率表示及其优点和局限性。在这项工作中,在成功采用非线性方法将信号分解成内在模式功能(IMFs)之后,我们首先对所谓的“循环过滤分解算法”提供更多的理论见解,证明衍生分解的节能结果。此外,我们提出了一种新的时间-频率代表法,其依据是IMF对信号的分解,即IMF图。我们证明了关于这种方法的理论结果,包括它与某类信号的光谱代表的趋同,我们提出了几个应用实例,将结果与文献中最熟悉的一些方法进行比较。