  Despite being the most popular methods of data analysis, Fourier-based
techniques suffer from the problem of static resolution that is currently
believed to be a fundamental limitation of the Fourier Transform. Although
alternative solutions overcome this limitation, none provide the simplicity,
versatility, and convenience of the Fourier analysis. The lack of convenience
often prevents these alternatives from replacing classical spectral methods -
even in applications that suffer from the limitation of static resolution.
  This work demonstrates that, contrary to the generally accepted belief, the
Fourier Transform can be generalized to the case of adaptive resolution. The
generalized transform provides backward compatibility with classical spectral
techniques and introduces minimal computational overhead.
