  In many mechanical, electrical, and general physical systems evolving over
time or space, spectral analysis methods as Fast Fourier Transform (FFT), Short
Term Fourier Transform (STFT), Power Spectrum Density (PSD) plays a very
important role. They allow an extraction of required information content from
signals in another base by decomposing it in its spectral components for
further processing.In theory this approach is very powerful, even in some
'simple' or 'not too complicated' practical cases it has proven its utility and
efficiency. However, for real-world applications such as mechanical modal
analysis of large dimension systems including damping, noise and unpredictable
excitation those signals are often so complex that it can be almost impossible
to obtain a high-resolution spectral decomposition with these methods due to
the time-bandwidth limitation. In this paper we describe an alternative
approach for spectral analysis based on the High Order Dynamical Mode
Decomposition (HODMD) and Kernel Density Spectrum (KDS). We will show that this
method allows overcoming some limitations of the FFT and may be a promising
approach to for a much more precisely the spectral decomposition.
