`ifft`

Inverse discrete Fourier transform.

Category: Mathematics > Fourier Analysis and Filtering

Syntax

X = ifft(Y)

Inverse transform along the first non-singleton dimension.

X = ifft(Y, n)

Pads or truncates Y to length n first.

X = ifft(Y, n, dim)

Operates along dimension dim.

Description

ifft(fft(x)) returns x. The inverse uses the opposite sign in the exponent and divides by the transform length. When the input has the conjugate symmetry that the spectrum of a real signal has, the tiny imaginary parts from rounding are dropped and the result is real.

Padding in the frequency domain with n larger than the input length adds zeros at the end of the spectrum, not at the middle, so it does not behave as interpolation.

Input arguments

Y: Frequency-domain data, usually from fft.
n: Transform length.
dim: Dimension to operate along.

Output arguments

X: Time-domain data. It is real when Y is conjugate symmetric.

Example

Round trip

x = [1 2 3 4];
ifft(fft(x))
ifft([10, -2+2i, -2, -2-2i])

Output

ans = 1×4

     1     2     3     4
ans = 1×4

     1     2     3     4

ifft