scipy tutorial - Baustatik-Info-Server

SciPy Reference Guide, Release 0.8.dev
See Also:
ifft
Inverse FFT
rfft
FFT of a real sequence
Notes
with the elements:
[y(0),y(1),..,y(n/2-1),y(-n/2),...,y(-1)] if n is even [y(0),y(1),..,y((n-1)/2),y(-(n-
1)/2),...,y(-1)] if n is odd
where
y(j) = sum[k=0..n-1] x[k] * exp(-sqrt(-1)*j*k* 2*pi/n), j = 0..n-1
Note that y(-j) = y(n-j).conjugate().
The packing of the result is “standard”: If A = fft(a, n), then A[0] contains the zero-frequency term, A[1:n/2+1]
contains the positive-frequency terms, and A[n/2+1:] contains the negative-frequency terms, in order of decreasingly
negative frequency. So for an 8-point transform, the frequencies of the result are [ 0, 1, 2, 3, 4, -3, -2,
-1].
This is most efficient for n a power of two.
Examples
>>> x = np.arange(5)
>>> np.all(np.abs(x-fft(ifft(x)) y
Return inverse discrete Fourier transform of arbitrary type sequence x.
The returned complex array contains
[y(0),y(1),...,y(n-1)]
where
y(j) = 1/n sum[k=0..n-1] x[k] * exp(sqrt(-1)*j*k* 2*pi/n)
Optional input: see fft.__doc__
fftn(x, shape=None, axes=None, overwrite_x=0)
fftn(x, shape=None, axes=None, overwrite_x=0) -> y
Return multi-dimensional discrete Fourier transform of arbitrary type sequence x.
The returned array contains
y[j_1,..,j_d] = sum[k_1=0..n_1-1, ..., k_d=0..n_d-1]
x[k_1,..,k_d] * prod[i=1..d] exp(-sqrt(-1)*2*pi/n_i * j_i * k_i)
where d = len(x.shape) and n = x.shape. Note that y[..., -j_i, ...] = y[..., n_i-j_i, ...].conjugate().
Optional input:
shape
Defines the shape of the Fourier transform. If shape is not specified then
168 Chapter 3. Reference