Estudio y comparación de métodos modernos para la determinación del comportamiento en tiempo - frecuencia de una señal.

Abstract

The present study shows the most important results for the comparison of four modern methods in the analysis of signals in the time-frequency domain: Gabor Transform, Reassigned Fourier Transform, Synchronized Fourier Transform and Superlets. For this purpose, an artificial multicomponent signal will be used, whose variation of frequencies and amplitudes will result in advantages and disadvantages of each of the above-mentioned methods, both in terms of time resolution, frequency resolution, computational load and detection of very small components. This comparison will take as a reference point the ideal time-frequency diagram, this representation will be used for the 3 tests established to show the limits and characteristics of each method. The first test reflects the computational load required by each method with the use of relatively high frequencies, the second test focuses on introducing time and frequency resolution requirements and, finally, the third test introduces requirements for the detection of components with very small amplitudes. Together these three tests allow a general analysis of the use of these methods using objects or functions available in Matlab.