SciPy 0.6.0 API Documentation Generated by Endo, 2007-10-17

Function summary

• fft(x, n = None, axis = -Const(1), overwrite_x = 0)
• fft2(x, shape = None, axes = (-Const(2), -Const(1)), overwrite_x = 0)
• fftn(x, shape = None, axes = None, overwrite_x = 0)
• ifft(x, n = None, axis = -Const(1), overwrite_x = 0)
• ifft2(x, shape = None, axes = (-Const(2), -Const(1)), overwrite_x = 0)
• ifftn(x, shape = None, axes = None, overwrite_x = 0)
• irfft(x, n = None, axis = -Const(1), overwrite_x = 0)
• istype(arr, typeclass)
• rfft(x, n = None, axis = -Const(1), overwrite_x = 0)
• rfftfreq(n, d = 1.0)

Functions

• fft(x, n = None, axis = -Const(1), overwrite_x = 0)

  fft(x, n=None, axis=-1, overwrite_x=0) -> y
  
  Return discrete Fourier transform of arbitrary type sequence x.
  
  The returned complex array contains
    [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).
  
  Optional input:
    n
      Defines the length of the Fourier transform. If n is not
      specified then n=x.shape[axis] is set. If n<x.shape[axis],
      x is truncated. If n>x.shape[axis], x is zero-padded.
    axis
      The transform is applied along the given axis of the input
      array (or the newly constructed array if n argument was used).
    overwrite_x
      If set to true, the contents of x can be destroyed.
  
  Notes:
    y == fft(ifft(y)) within numerical accuracy.
  

• fft2(x, shape = None, axes = (-Const(2), -Const(1)), overwrite_x = 0)

  fft2(x, shape=None, axes=(-2,-1), overwrite_x=0) -> y

  Return two-dimensional discrete Fourier transform of arbitrary type sequence x.

  See fftn.__doc__ for more information.

• 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, ...].

  Optional input:

  shape

  Defines the shape of the Fourier transform. If shape is not specified then shape=take(x.shape,axes,axis=0). If shape[i]>x.shape[i] then the i-th dimension is padded with zeros. If shape[i]<x.shape[i], then the i-th dimension is truncated to desired length shape[i].

  axes

  The transform is applied along the given axes of the input array (or the newly constructed array if shape argument was used).

  overwrite_x

  If set to true, the contents of x can be destroyed.

  Notes:

  y == fftn(ifftn(y)) within numerical accuracy.

• ifft(x, n = None, axis = -Const(1), overwrite_x = 0)

  ifft(x, n=None, axis=-1, overwrite_x=0) -> 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__

• ifft2(x, shape = None, axes = (-Const(2), -Const(1)), overwrite_x = 0)

  ifft2(x, shape=None, axes=(-2,-1), overwrite_x=0) -> y

  Return inverse two-dimensional discrete Fourier transform of arbitrary type sequence x.

  See ifftn.__doc__ for more information.

• ifftn(x, shape = None, axes = None, overwrite_x = 0)

  ifftn(x, s=None, axes=None, overwrite_x=0) -> y

  Return inverse multi-dimensional discrete Fourier transform of arbitrary type sequence x.

  The returned array contains

  y[j_1,..,j_d] = 1/p * 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), n = x.shape, and p = prod[i=1..d] n_i.

  Optional input: see fftn.__doc__

• irfft(x, n = None, axis = -Const(1), overwrite_x = 0)

  irfft(x, n=None, axis=-1, overwrite_x=0) -> y
  
  Return inverse discrete Fourier transform of real sequence x.
  The contents of x is interpreted as the output of rfft(..)
  function.
  
  The returned real array contains
    [y(0),y(1),...,y(n-1)]
  where for n is even
    y(j) = 1/n (sum[k=1..n/2-1] (x[2*k-1]+sqrt(-1)*x[2*k])
                                 * exp(sqrt(-1)*j*k* 2*pi/n)
                + c.c. + x[0] + (-1)**(j) x[n-1])
  and for n is odd
    y(j) = 1/n (sum[k=1..(n-1)/2] (x[2*k-1]+sqrt(-1)*x[2*k])
                                 * exp(sqrt(-1)*j*k* 2*pi/n)
                + c.c. + x[0])
  c.c. denotes complex conjugate of preceeding expression.
  
  Optional input: see rfft.__doc__
  

• istype(arr, typeclass)
• rfft(x, n = None, axis = -Const(1), overwrite_x = 0)

  rfft(x, n=None, axis=-1, overwrite_x=0) -> y
  
  Return discrete Fourier transform of real sequence x.
  
  The returned real arrays contains
    [y(0),Re(y(1)),Im(y(1)),...,Re(y(n/2))]              if n is even
    [y(0),Re(y(1)),Im(y(1)),...,Re(y(n/2)),Im(y(n/2))]   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).
  
  Optional input:
    n
      Defines the length of the Fourier transform. If n is not
      specified then n=x.shape[axis] is set. If n<x.shape[axis],
      x is truncated. If n>x.shape[axis], x is zero-padded.
    axis
      The transform is applied along the given axis of the input
      array (or the newly constructed array if n argument was used).
    overwrite_x
      If set to true, the contents of x can be destroyed.
  
  Notes:
    y == rfft(irfft(y)) within numerical accuracy.
  

• rfftfreq(n, d = 1.0)

  rfftfreq(n, d=1.0) -> f

  DFT sample frequencies (for usage with rfft,irfft).

  The returned float array contains the frequency bins in cycles/unit (with zero at the start) given a window length n and a sample spacing d:

  f = [0,1,1,2,2,...,n/2-1,n/2-1,n/2]/(d*n) if n is even f = [0,1,1,2,2,...,n/2-1,n/2-1,n/2,n/2]/(d*n) if n is odd

Imported Names