[Scipy-svn] r6411 - in trunk/doc/source: . tutorial
scipy-svn at scipy.org
scipy-svn at scipy.org
Tue May 25 00:37:20 EDT 2010
Author: warren.weckesser
Date: 2010-05-24 23:37:19 -0500 (Mon, 24 May 2010)
New Revision: 6411
Added:
trunk/doc/source/tutorial/fftpack.rst
Modified:
trunk/doc/source/fftpack.rst
trunk/doc/source/tutorial/index.rst
Log:
DOC: fftpack: Undo an undesired merger of two different rst files. Added josef's fftpack tutorial stub. Fixed rst markup of headers in the module-level rst for fftpack.
Modified: trunk/doc/source/fftpack.rst
===================================================================
--- trunk/doc/source/fftpack.rst 2010-05-24 13:12:19 UTC (rev 6410)
+++ trunk/doc/source/fftpack.rst 2010-05-25 04:37:19 UTC (rev 6411)
@@ -1,156 +1,10 @@
-=========================================
-Fourier Transforms (:mod:`scipy.fftpack`)
-=========================================
-
-.. sectionauthor:: Scipy Developers
-
-.. currentmodule:: scipy.fftpack
-
-.. warning::
-
- This is currently a stub page
-
-
-.. contents::
-
-
-Fourier analysis is fundamentally a method for expressing a function as a
-sum of periodic components, and for recovering the signal from those
-components. When both the function and its Fourier transform are
-replaced with discretized counterparts, it is called the discrete Fourier
-transform (DFT). The DFT has become a mainstay of numerical computing in
-part because of a very fast algorithm for computing it, called the Fast
-Fourier Transform (FFT), which was known to Gauss (1805) and was brought
-to light in its current form by Cooley and Tukey [CT]_. Press et al. [NR]_
-provide an accessible introduction to Fourier analysis and its
-applications.
-
-
-Fast Fourier transforms
------------------------
-
-One dimensional discrete Fourier transforms
--------------------------------------------
-
-fft, ifft, rfft, irfft
-
-
-Two and n dimensional discrete Fourier transforms
--------------------------------------------------
-
-fft in more than one dimension
-
-
-Discrete Cosine Transforms
---------------------------
-
-
-Return the Discrete Cosine Transform [Mak]_ of arbitrary type sequence ``x``.
-
-For a single dimension array ``x``, ``dct(x, norm='ortho')`` is equal to
-matlab ``dct(x)``.
-
-There are theoretically 8 types of the DCT [WP]_, only the first 3 types are
-implemented in scipy. 'The' DCT generally refers to DCT type 2, and 'the'
-Inverse DCT generally refers to DCT type 3.
-
-type I
-~~~~~~
-
-There are several definitions of the DCT-I; we use the following
-(for ``norm=None``):
-
-.. math::
- :nowrap:
-
- \[ y_k = x_0 + (-1)^k x_{N-1} + 2\sum_{n=1}^{N-2} x_n
- \cos\left({\pi nk\over N-1}\right),
- \qquad 0 \le k < N. \]
-
-Only None is supported as normalization mode for DCT-I. Note also that the
-DCT-I is only supported for input size > 1
-
-type II
-~~~~~~~
-
-There are several definitions of the DCT-II; we use the following
-(for ``norm=None``):
-
-.. math::
- :nowrap:
-
- \[ y_k = 2 \sum_{n=0}^{N-1} x_n
- \cos \left({\pi(2n+1)k \over 2N} \right)
- \qquad 0 \le k < N.\]
-
-If ``norm='ortho'``, :math:`y_k` is multiplied by a scaling factor `f`:
-
-.. math::
- :nowrap:
-
- \[f = \begin{cases} \sqrt{1/(4N)}, & \text{if $k = 0$} \\
- \sqrt{1/(2N)}, & \text{otherwise} \end{cases} \]
-
-
-Which makes the corresponding matrix of coefficients orthonormal
-(`OO' = Id`).
-
-type III
-~~~~~~~~
-
-There are several definitions, we use the following
-(for ``norm=None``):
-
-.. math::
- :nowrap:
-
- \[ y_k = x_0 + 2 \sum_{n=1}^{N-1} x_n
- \cos\left({\pi n(2k+1) \over 2N}\right)
- \qquad 0 \le k < N,\]
-
-or, for ``norm='ortho'``:
-
-.. math::
- :nowrap:
-
- \[ y_k = {x_0\over\sqrt{N}} + {1\over\sqrt{N}} \sum_{n=1}^{N-1}
- x_n \cos\left({\pi n(2k+1) \over 2N}\right)
- \qquad 0 \le k < N.\]
-
-The (unnormalized) DCT-III is the inverse of the (unnormalized) DCT-II, up
-to a factor `2N`. The orthonormalized DCT-III is exactly the inverse of the
-orthonormalized DCT-II.
-
-References
-~~~~~~~~~~
-
-.. [CT] Cooley, James W., and John W. Tukey, 1965, "An algorithm for the
- machine calculation of complex Fourier series," *Math. Comput.*
- 19: 297-301.
-
-.. [NR] Press, W., Teukolsky, S., Vetterline, W.T., and Flannery, B.P.,
- 2007, *Numerical Recipes: The Art of Scientific Computing*, ch.
- 12-13. Cambridge Univ. Press, Cambridge, UK.
-
-.. [Mak] J. Makhoul, 1980, 'A Fast Cosine Transform in One and Two Dimensions',
- `IEEE Transactions on acoustics, speech and signal processing`
- vol. 28(1), pp. 27-34, http://dx.doi.org/10.1109/TASSP.1980.1163351
-
-.. [WP] http://en.wikipedia.org/wiki/Discrete_cosine_transform
-
-
-FFT convolution
----------------
-
-scipy.fftpack.convolve performs a convolution of two one-dimensional
-arrays in frequency domain.
Fourier transforms (:mod:`scipy.fftpack`)
=========================================
.. module:: scipy.fftpack
Fast Fourier transforms
-=======================
+-----------------------
.. autosummary::
:toctree: generated/
@@ -165,7 +19,7 @@
irfft
Differential and pseudo-differential operators
-==============================================
+----------------------------------------------
.. autosummary::
:toctree: generated/
@@ -182,7 +36,7 @@
shift
Helper functions
-================
+----------------
.. autosummary::
:toctree: generated/
@@ -193,7 +47,7 @@
rfftfreq
Convolutions (:mod:`scipy.fftpack.convolve`)
-============================================
+--------------------------------------------
.. module:: scipy.fftpack.convolve
@@ -206,8 +60,8 @@
destroy_convolve_cache
-:mod:`scipy.fftpack._fftpack`
-=============================
+Other (:mod:`scipy.fftpack._fftpack`)
+-------------------------------------
.. module:: scipy.fftpack._fftpack
Added: trunk/doc/source/tutorial/fftpack.rst
===================================================================
--- trunk/doc/source/tutorial/fftpack.rst (rev 0)
+++ trunk/doc/source/tutorial/fftpack.rst 2010-05-25 04:37:19 UTC (rev 6411)
@@ -0,0 +1,145 @@
+Fourier Transforms (:mod:`scipy.fftpack`)
+=========================================
+
+.. sectionauthor:: Scipy Developers
+
+.. currentmodule:: scipy.fftpack
+
+.. warning::
+
+ This is currently a stub page
+
+
+.. contents::
+
+
+Fourier analysis is fundamentally a method for expressing a function as a
+sum of periodic components, and for recovering the signal from those
+components. When both the function and its Fourier transform are
+replaced with discretized counterparts, it is called the discrete Fourier
+transform (DFT). The DFT has become a mainstay of numerical computing in
+part because of a very fast algorithm for computing it, called the Fast
+Fourier Transform (FFT), which was known to Gauss (1805) and was brought
+to light in its current form by Cooley and Tukey [CT]_. Press et al. [NR]_
+provide an accessible introduction to Fourier analysis and its
+applications.
+
+
+Fast Fourier transforms
+-----------------------
+
+One dimensional discrete Fourier transforms
+-------------------------------------------
+
+fft, ifft, rfft, irfft
+
+
+Two and n dimensional discrete Fourier transforms
+-------------------------------------------------
+
+fft in more than one dimension
+
+
+Discrete Cosine Transforms
+--------------------------
+
+
+Return the Discrete Cosine Transform [Mak]_ of arbitrary type sequence ``x``.
+
+For a single dimension array ``x``, ``dct(x, norm='ortho')`` is equal to
+matlab ``dct(x)``.
+
+There are theoretically 8 types of the DCT [WP]_, only the first 3 types are
+implemented in scipy. 'The' DCT generally refers to DCT type 2, and 'the'
+Inverse DCT generally refers to DCT type 3.
+
+type I
+~~~~~~
+
+There are several definitions of the DCT-I; we use the following
+(for ``norm=None``):
+
+.. math::
+ :nowrap:
+
+ \[ y_k = x_0 + (-1)^k x_{N-1} + 2\sum_{n=1}^{N-2} x_n
+ \cos\left({\pi nk\over N-1}\right),
+ \qquad 0 \le k < N. \]
+
+Only None is supported as normalization mode for DCT-I. Note also that the
+DCT-I is only supported for input size > 1
+
+type II
+~~~~~~~
+
+There are several definitions of the DCT-II; we use the following
+(for ``norm=None``):
+
+.. math::
+ :nowrap:
+
+ \[ y_k = 2 \sum_{n=0}^{N-1} x_n
+ \cos \left({\pi(2n+1)k \over 2N} \right)
+ \qquad 0 \le k < N.\]
+
+If ``norm='ortho'``, :math:`y_k` is multiplied by a scaling factor `f`:
+
+.. math::
+ :nowrap:
+
+ \[f = \begin{cases} \sqrt{1/(4N)}, & \text{if $k = 0$} \\
+ \sqrt{1/(2N)}, & \text{otherwise} \end{cases} \]
+
+
+Which makes the corresponding matrix of coefficients orthonormal
+(`OO' = Id`).
+
+type III
+~~~~~~~~
+
+There are several definitions, we use the following
+(for ``norm=None``):
+
+.. math::
+ :nowrap:
+
+ \[ y_k = x_0 + 2 \sum_{n=1}^{N-1} x_n
+ \cos\left({\pi n(2k+1) \over 2N}\right)
+ \qquad 0 \le k < N,\]
+
+or, for ``norm='ortho'``:
+
+.. math::
+ :nowrap:
+
+ \[ y_k = {x_0\over\sqrt{N}} + {1\over\sqrt{N}} \sum_{n=1}^{N-1}
+ x_n \cos\left({\pi n(2k+1) \over 2N}\right)
+ \qquad 0 \le k < N.\]
+
+The (unnormalized) DCT-III is the inverse of the (unnormalized) DCT-II, up
+to a factor `2N`. The orthonormalized DCT-III is exactly the inverse of the
+orthonormalized DCT-II.
+
+References
+~~~~~~~~~~
+
+.. [CT] Cooley, James W., and John W. Tukey, 1965, "An algorithm for the
+ machine calculation of complex Fourier series," *Math. Comput.*
+ 19: 297-301.
+
+.. [NR] Press, W., Teukolsky, S., Vetterline, W.T., and Flannery, B.P.,
+ 2007, *Numerical Recipes: The Art of Scientific Computing*, ch.
+ 12-13. Cambridge Univ. Press, Cambridge, UK.
+
+.. [Mak] J. Makhoul, 1980, 'A Fast Cosine Transform in One and Two Dimensions',
+ `IEEE Transactions on acoustics, speech and signal processing`
+ vol. 28(1), pp. 27-34, http://dx.doi.org/10.1109/TASSP.1980.1163351
+
+.. [WP] http://en.wikipedia.org/wiki/Discrete_cosine_transform
+
+
+FFT convolution
+---------------
+
+scipy.fftpack.convolve performs a convolution of two one-dimensional
+arrays in frequency domain.
Modified: trunk/doc/source/tutorial/index.rst
===================================================================
--- trunk/doc/source/tutorial/index.rst 2010-05-24 13:12:19 UTC (rev 6410)
+++ trunk/doc/source/tutorial/index.rst 2010-05-25 04:37:19 UTC (rev 6411)
@@ -13,6 +13,7 @@
integrate
optimize
interpolate
+ fftpack
signal
linalg
stats
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