LUIZ NETO, J.; LUIZ NETO, José.
Abstract:
Fourier transforms are often used in
Numerical analysis and digital signal processing is a
indispensable tool for analyzing and synthesizing devices
such as digital filters. The evaluation of discrete
Fourier using its definition directly is a process
computationally expensive; fortunately there are algorithms that
make the process more efficient, known as
Fourier transform algorithms, which
we refer to by its initials in English FFT, of Fast Fourier
Transform. Motivated by the facts above and also by the use of FFT
in efficient convolution computation, in this work
a) we did a study of the mathematical foundations of
rapid transformations;
b) we analyzed the various formulations of
processing, in particular FFT,
Mersenne and the Chinese remainder theorem;
we study and implement the implementation of some
fast transformation algorithms to evaluate the
differences between mathematically defined algorithms
and its implementations as robust software,
efficient and portable; and
we study and implement the implementation of some
algorithms for fast computation of convolutions.
