[Scipy-svn] r6883 - trunk/scipy/fftpack
scipy-svn at scipy.org
scipy-svn at scipy.org
Sun Nov 14 04:58:14 EST 2010
Author: rgommers
Date: 2010-11-14 03:58:13 -0600 (Sun, 14 Nov 2010)
New Revision: 6883
Modified:
trunk/scipy/fftpack/__init__.py
trunk/scipy/fftpack/basic.py
trunk/scipy/fftpack/realtransforms.py
Log:
DOC: merge wiki edits for fftpack module.
Modified: trunk/scipy/fftpack/__init__.py
===================================================================
--- trunk/scipy/fftpack/__init__.py 2010-11-14 09:57:53 UTC (rev 6882)
+++ trunk/scipy/fftpack/__init__.py 2010-11-14 09:58:13 UTC (rev 6883)
@@ -1,3 +1,57 @@
+"""
+Home of discrete Fourier transform algorithms
+
+Modules
+=======
+
+.. autosummary::
+ :toctree: generated/
+
+ basic - Basic discrete Fourier transform operators
+ convolve - Convolution functions
+ helper - TODO
+ pseudo_diffs - Differential and pseudo-differential operators
+ realtransforms - Real spectrum tranforms (DCT, DST, MDCT)
+
+Functions
+=========
+
+Fast Fourier Transforms (FFTs)
+------------------------------
+
+.. autosummary::
+ :toctree: generated/
+
+ fft - Fast (discrete) Fourier Transform (FFT)
+ ifft - Inverse FFT
+ fft2 - Two dimensional FFT
+ ifft2 - Two dimensional inverse FFT
+ fftn - n-dimensional FFT
+ ifftn - n-dimensional inverse FFT
+ rfft - FFT of strictly real-valued sequence
+ irfft - Inverse of rfft
+ rfftfreq - DFT sample frequencies (specific to rfft and irfft)
+ dct - Discrete cosine transform
+ idct - Inverse discrete cosine transform
+
+Differential and pseudo-differential operators
+----------------------------------------------
+
+.. autosummary::
+ :toctree: generated/
+
+ diff - Differentiation and integration of periodic sequences
+ tilbert - Tilbert transform: cs_diff(x,h,h)
+ itilbert - Inverse Tilbert transform: sc_diff(x,h,h)
+ hilbert - Hilbert transform: cs_diff(x,inf,inf)
+ ihilbert - Inverse Hilbert transform: sc_diff(x,inf,inf)
+ cs_diff - cosh/sinh pseudo-derivative of periodic sequences
+ sc_diff - sinh/cosh pseudo-derivative of periodic sequences
+ ss_diff - sinh/sinh pseudo-derivative of periodic sequences
+ cc_diff - cosh/cosh pseudo-derivative of periodic sequences
+ shift - Shift periodic sequences
+
+"""
#
# fftpack - Discrete Fourier Transform algorithms.
#
Modified: trunk/scipy/fftpack/basic.py
===================================================================
--- trunk/scipy/fftpack/basic.py 2010-11-14 09:57:53 UTC (rev 6882)
+++ trunk/scipy/fftpack/basic.py 2010-11-14 09:58:13 UTC (rev 6883)
@@ -219,17 +219,27 @@
return swapaxes(tmp, axis, -1)
def ifft(x, n=None, axis=-1, overwrite_x=0):
- """ ifft(x, n=None, axis=-1, overwrite_x=0) -> y
+ """
+ Return discrete inverse Fourier transform of real or complex sequence.
- Return inverse discrete Fourier transform of arbitrary type
- sequence x.
+ The returned complex array contains ``y(0), y(1),..., y(n-1)`` where
- 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)
+ ``y(j) = (x * exp(2*pi*sqrt(-1)*j*np.arange(n)/n)).mean()``.
- Optional input: see fft.__doc__
+ Parameters
+ ----------
+ x : array_like
+ Transformed data to invert.
+ n : int, optional
+ Length of the inverse Fourier transform. If ``n < x.shape[axis]``,
+ `x` is truncated. If ``n > x.shape[axis]``, `x` is zero-padded.
+ The default results in ``n = x.shape[axis]``.
+ axis : int, optional
+ Axis along which the ifft's are computed; the default is over the
+ last axis (i.e., ``axis=-1``).
+ overwrite_x : bool, optional
+ If True the contents of `x` can be destroyed; the default is False.
+
"""
tmp = _asfarray(x)
@@ -263,31 +273,45 @@
def rfft(x, n=None, axis=-1, overwrite_x=0):
- """ rfft(x, n=None, axis=-1, overwrite_x=0) -> y
+ """
+ Discrete Fourier transform of a real sequence.
- Return discrete Fourier transform of real sequence x.
+ The returned real arrays contains::
- 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)
+ ::
+
+ 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().
- 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.
+ Note that ``y(-j) == y(n-j).conjugate()``.
- Notes:
- y == rfft(irfft(y)) within numerical accuracy.
+ Parameters
+ ----------
+ x : array_like, real-valued
+ The data to tranform.
+ n : int, optional
+ Defines the length of the Fourier transform. If `n` is not specified
+ (the default) then ``n = x.shape[axis]``. If ``n < x.shape[axis]``,
+ `x` is truncated, if ``n > x.shape[axis]``, `x` is zero-padded.
+ axis : int, optional
+ The axis along which the transform is applied. The default is the
+ last axis.
+ overwrite_x : bool, optional
+ If set to true, the contents of `x` can be overwritten. Default is
+ False.
+
+ See also
+ --------
+ fft, irfft, scipy.fftpack.basic
+
+ Notes
+ -----
+ Within numerical accuracy, ``y == rfft(irfft(y))``.
+
"""
tmp = _asfarray(x)
@@ -479,11 +503,17 @@
def ifft2(x, shape=None, axes=(-2,-1), overwrite_x=0):
- """ ifft2(x, shape=None, axes=(-2,-1), overwrite_x=0) -> y
+ """
+ 2-D discrete inverse Fourier transform of real or complex sequence.
Return inverse two-dimensional discrete Fourier transform of
arbitrary type sequence x.
- See ifftn.__doc__ for more information.
+ See `ifft` for more information.
+
+ See also
+ --------
+ fft2, ifft
+
"""
return ifftn(x,shape,axes,overwrite_x)
Modified: trunk/scipy/fftpack/realtransforms.py
===================================================================
--- trunk/scipy/fftpack/realtransforms.py 2010-11-14 09:57:53 UTC (rev 6882)
+++ trunk/scipy/fftpack/realtransforms.py 2010-11-14 09:58:13 UTC (rev 6883)
@@ -19,7 +19,7 @@
Parameters
----------
- x : array-like
+ x : array_like
The input array.
type : {1, 2, 3}, optional
Type of the DCT (see Notes). Default type is 2.
@@ -42,7 +42,7 @@
Notes
-----
For a single dimension array ``x``, ``dct(x, norm='ortho')`` is equal to
- matlab ``dct(x)``.
+ MATLAB ``dct(x)``.
There are theoretically 8 types of the DCT, only the first 3 types are
implemented in scipy. 'The' DCT generally refers to DCT type 2, and 'the'
@@ -115,11 +115,11 @@
def idct(x, type=2, n=None, axis=-1, norm=None):
"""
- Return the Inverse Discrete Cosine Transform of arbitrary type sequence x.
+ Return the Inverse Discrete Cosine Transform of an arbitrary type sequence.
Parameters
----------
- x : array-like
+ x : array_like
The input array.
type : {1, 2, 3}, optional
Type of the DCT (see Notes). Default type is 2.
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