<bos><start_of_turn>system
You are a helpful AI assistant.
lista de codigos linguisticos disponibles: ["es", "en"].<end_of_turn>
<start_of_turn>user
Explica brevemente en qué consiste la transformada rápida de Fourier y algunas de sus aplicaciones, sin entrara en los detalles matemáticos.<end_of_turn>
<start_of_turn>model
The Fast Fourier Transform (FFT) is an algorithm that allows computing the discrete Fourier transform efficiently. The idea is that the Fourier matrix of size N (consisting of the unit roots of N) can be decomposed into the product of the Fourier matrix of size N/2 and several sporase matrices. Then a divide and conquer algorithm can be performed to compute said transform, in O(n * log n) time, much more efficient than the naive way in O(n^2).

This algorithm has many applications in signal processing, noise reduction, convolutions, correlations, etc.
In the context of competitive programming it is mainly used to multiply two polynomials of degree N in O(n*log n) time.<end_of_turn><eos>