EXAMPLES

42c37b56-b640-4fbe-a175-92514c260bb0 131 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

http://docs.scipy.org/doc/numpy/reference/routines.fft.html

Available functions:

fft()

one-dimensional discrete Fourier Transform

ifft()

one-dimensional inverse discrete Fourier Transform

fft2()

2-dimensional discrete Fourier Transform

ifft2()

2-dimensional inverse discrete Fourier Transform

rfft()

one-dimensional discrete Fourier Transform for real input

irfft()

one-dimensional inverse discrete Fourier Transform for real input

fftfreq()

sample frequencies for a given window length

fftmagnitude()

get the magnitude of a transform. This is the built-in abs() for matrices

fftphase()

get the phase of a transform. This is the built-in arg() for matrices

fftshift()

shift the zero-frequency component to the center of the spectrum

ifftshift()

inverse of fftshift; the function differ by one sample from fftshift for odd-length dimensions

Syntax

vector fft

vector length fft

vector length normalization fft

vector

1-column vector (one-dimensional DFT, real or complex input)

2-columns matrix (one-dimensional DFT, real input, imaginary part on 2nd column)

matrix (only ftt2, real or complex input)

length

use length = 0 if you want to use normalization without changing the vector length

normalization

default normalization

x fft n el x k el e i 2 * π * k * n N / * -^* (k 0 N 1 - sum ≡

N x length :

x ifft n el 1 N / x k el e i 2 * π * k * n N / *^* (k 0 N 1 - sum * ≡

normalization =

ortho

x fft n el 1 N sqrt / x k el e i 2 * π * k * n N / * -^* (k 0 N 1 - sum * ≡

N x length :

x ifft n el 1 N sqrt / x k el e i 2 * π * k * n N / *^* (k 0 N 1 - sum * ≡

EXAMPLES

x1 1.0 2.0 1.0 1.0 - 1.5 51 mat :

x2 1.0 2.0 1.0 1.0 - 1.5 261 mat :

y1 x1 0 fft : 4.5 2.0816 1.6511 i * - 1.8316 - 1.6082 i * + 1.8316 - 1.6082 i * - 2.0816 1.6511 i * + 51 mat

y2 x2 fft : 6.5 2.75 0.433 i * + 3.25 - 0.433 i * - 0.5 3.0531 1016 -^* i * - 3.25 - 0.433 i * + 2.75 0.433 i * - 61 mat

y1 1 el x1 sum ≡

x1 sum 4.5

x2 sum 6.5

y2 ifft 1 5.0885 1017 -^* i * - 2 5.0885 1017 -^* i * + 1 5.0885 1017 -^* i * - 1 - 3.7138 1016 -^* i * + 1.5 5.0885 1017 -^* i * - 2 2.6961 1016 -^* i * - 61 mat

y1 ifft 1211 - 1.5 51 mat

010041 mat rfft 1 i - 1 - 31 mat

0010000042 mat rfft 1001 - 1 - 032 mat

1 i - 1 - 31 mat irfft 010041 mat

1 i - 1 - i 41 mat irfft 0.1667 - 0.622 0.622 0.1667 - 0.0447 0.0447 61 mat

EXAMPLES: real part on col 1, imaginary part on col 2

x4 1.0 0 2.0 0 1.0 0 1.0 - 0 1.5 02062 mat :

x3 1.0 0 2.0 0 1.0 0 1.0 - 0 1.5 052 mat :

y3 x3 fft : 4.5 0 2.0816 1.6511 - 1.8316 - 1.6082 1.8316 - 1.6082 - 2.0816 1.6511 52 mat

y4 x4 fft : 6.5 0 2.75 0.433 3.25 - 0.433 - 0.5 3.0531 1016 -^* - 3.25 - 0.433 2.75 0.433 - 62 mat

y3 ifft 1.00000000 0.00000000 2.00000000 0.00000000 1.00000000 0.00000000 1.00000000 - 0.00000000 1.50000000 0.00000000 52 mat

y4 ifft 1.00000000 5.08852220 1017 -^* - 2.00000000 5.08852220 1017 -^* 1.00000000 5.08852220 1017 -^* - 1.00000000 - 3.71379003 1016 -^* 1.50000000 5.08852220 1017 -^* - 2.00000000 2.69608559 1016 -^* - 62 mat

EXAMPLES

Ns 6412825631 mat :

number of points (N)

x 0 N 1 - (range N / :

j 029 range f j 1 + el 2 π * j 10 / * cos : 11 line for

F f N fft fftmagnitude :

x N fftfreq :

xF x fftshift F fftshift augment :

F length 256

m 12345678910111234 mat :

fft2 m fft2 : 786 - 6 i * + 6 - 6 - 6 i * - 24 - 13.8564 i * + 00024 - 13.8564 i * - 00034 mat

fft2 fftshift 0024 - 13.8564 i * - 06 - 6 - 6 i * - 786 - 6 i * + 0024 - 13.8564 i * + 034 mat