# Discrete Fourier Transform Formula

Use the DFT formula to manually perform the Discrete Fourier Series (DFT). It is a tool used to convert the finite sequence of equally-spaced samples of any function into an equivalent-length sequence. It transforms a sequence of complex numbers into another sequence of complex numbers. The Discrete Fourier transform formula is derived from the Euler's formula. To derive the discrete fourier series, compute the nth value series and number of period (N) in the formula.

# DFT Formula

#### DFT Formula:

N-1
X(k) = ∑ x(n) e -j2πnk / N

n=0

Where,

n - nth value series
k - iterative value
N - number of period

#### Related Calculator:

Fourier analysis is a technique used in mathematics. It is generally used for decomposing signals into sinusoids. Discrete Fourier series is a part of discrete fourier transform but it uses digitized signals. Discrete fourier transform (DFT) formula is also used to efficiently solve partial differential equations, and to perform other operations such as convolutions or multiplying large integers.