pracma (version 1.4.5)

ifft: Inverse Fast Fourier Transformation

Description

Performs the inverse Fast Fourier Transform.

Usage

ifft(x)
ifftshift(x)
fftshift(x)

Arguments

x

a real or complex vector

Value

• Real or complex vector of the same length.

Details

ifft returns the value of the normalized discrete, univariate, inverse Fast Fourier Transform of the values in x.

ifftshift and fftshift shift the zero-component to the center of the spectrum, that is swap the left and right half of x.

See Also

fft

Examples

x <- c(1, 2, 3, 4)
(y <- fft(x))
ifft(x)
ifft(y)

##  Compute the derivative: F(df/dt) = (1i*k) * F(f)
#   hyperbolic secans f <- sech
df <- function(x) -sech(x) * tanh(x)
d2f <- function(x) sech(x) - 2*sech(x)^3
L <- 20                                 # domain [-L/2, L/2]
N <- 128                                # number of Fourier nodes
x <- linspace(-L/2, L/2, N+1)           # domain discretization
x <- x[1:N]                             # because of periodicity
dx <- x[2] - x[1]                       # finite difference
u <- sech(x)                            # hyperbolic secans
u1d <- df(x); u2d <- d2f(x)             # first and second derivative
ut <- fft(u)                            # discrete Fourier transform
k <- (2*pi/L)*fftshift((-N/2):(N/2-1))  # shifted frequencies
u1 <- Re(ifft((1i*k) * ut))             # inverse transform
u2 <- Re(ifft(-k^2 * ut))               # first and second derivative
plot(x, u1d, type = "l", col = "blue")
points(x, u1)
grid()
figure()
plot(x, u2d, type = "l", col = "darkred")
points(x, u2)
grid()