A fast Fourier transform (FFT) algorithm computes the discrete Fourier transform (DFT) of a sequence, or its inverse. Fourier analysis converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa. An FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse (mostly zero) factors. As a result, it manages to reduce the complexity of computing the DFT from , which arises if one simply applies the definition of DFT, to
, where
is the data size.
Fast Fourier transforms are widely used for many applications in engineering, science, and mathematics. The basic ideas were popularized in 1965, but some algorithms had been derived as early as 1805. In 1994 Gilbert Strang described the FFT as "the most important numerical algorithm of our lifetime" and it was included in Top 10 Algorithms of 20th Century by the IEEE journal Computing in Science & Engineering.
There are many different FFT algorithms involving a wide range of mathematics, from simple complex-number arithmetic to group theory and number theory; this article gives an overview of the available techniques and some of their general properties, while the specific algorithms are described in subsidiary articles linked below.
FFT is a fast Fourier transform.
FFT may also refer to:
For Those Who Have Heart is the second studio album by American rock band A Day to Remember, and their first for Victory. It was released on January 22, 2007 by Victory. For the album, the band had a line-up change swapping drummer Bobby Scruggs for Alex Shelnutt. It charted at number 17 on the Heatseekers Album Chart in the U.S. The music video for "The Plot to Bomb the Panhandle" was released a month later. Several of the album's songs appeared on the band's MySpace profile before the release. Recorded and mixed at Zing Studios by producer Eric Arena, the album was re-released in February 2008, with additional tracks and a bonus DVD. The DVD featured a performance of the band live at The Capitol, in the band's hometown, Ocala, Florida. The music video for "The Danger in Starting a Fire" was released in the same month, and the music video for "Since U Been Gone", which had been streamed on the band's MySpace previously, was released in July. For Those Who Have Heart was generally well received by music critics.
sitting in my room the thoughts
are flying through my head
tast inside my brain is tart
the contract's on my bed
smell the smell of cigar smoke
and i know who it is
ideas are dumb the doors are shut
the messages are his
my buddly al drove off a cliff
and ran into a nail
he licks his wounds and wonders
how the tooth drove him to fail
he hates to park his car
downtown on 16th avenue
sometimes her eyes are green
and other times i think they're blue
my sister is a mother
and my mother is a chore
my brother is a junkie
for the c.o. music boards
i knew this guy who was so lazy
and he was so dumb
he slept all day and lost his job