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doc/intro.rst

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@@ -49,7 +49,7 @@ To install using pip::
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.. note::
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If you install Slycot using pip you'll need a development
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environment (e.g., Python development files, C, and Fortran compilers).
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environment (e.g., Python development files, C, and FORTRAN compilers).
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Pip installation can be particularly complicated for Windows.
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Many parts of `python-control` will work without `slycot`, but some
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!pip install control
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import control as ct
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Note that Google colab does not currently support Slycot, so some
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Note that Google Colab does not currently support Slycot, so some
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functionality may not be available.
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The python-control package makes use of a few naming and calling conventions:
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* Function names are written in lower case with underscores between
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words ('frequency_response').
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words (`frequency_response`).
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* Class names use camel case ('StateSpace', 'ControlPlot', etc) and
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instances of the class are created with "factory functions" ('ss')
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or as the output of an operation ('bode_plot').
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* Class names use camel case (`StateSpace`, `ControlPlot`, etc) and
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instances of the class are created with "factory functions" (`ss`)
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or as the output of an operation (`bode_plot`).
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* Functions that return multiple values use either objects (with
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elements for each return value) or tuples. For those functions that
@@ -105,10 +105,10 @@ The python-control package makes use of a few naming and calling conventions:
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K, _, _ = lqr(sys)
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* Python-control supports both single-input, single-output (SISO)
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systems and mullti-input, multi-output (MIMO) systems, including
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systems and multi-input, multi-output (MIMO) systems, including
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time and frequency responses. By default, SISO systems will
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typically generate objects that have the input and output dimensions
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supressed (using the NumPy :func:`~numpy.squeeze` function). The
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suppressed (using the NumPy :func:`~numpy.squeeze` function). The
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`squeeze` keyword can be set to `False` to force functions to return
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objects that include the input and output dimensions.
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@@ -136,7 +136,7 @@ some things to keep in mind:
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* Functions that in MATLAB would return variable numbers of values
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will have a parameter of the form `return_<val>` that is used to
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return additional data. (These functions usually return an object of
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a class that has attributpes that can be used to access the
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a class that has attributes that can be used to access the
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information and this is the preferred usage pattern.)
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* You cannot use braces for collections; use tuples instead.
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* Time series data have time as the final index (see

doc/iosys.rst

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@@ -8,7 +8,7 @@ Interconnected I/O Systems
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Input/output systems can be interconnected in a variety of ways,
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including operator overloading, block diagram algebra functions, and
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using the :func:`interconnect` function to build a hiearchical system
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using the :func:`interconnect` function to build a hierarchical system
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description. This chapter provides more detailed information on
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operator overloading and block diagram algebra, as well as a
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description of the :class:`InterconnectedSystem` class, which can be
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:header-rows: 1
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* - Operation
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- Desription
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- Description
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- Equivalent command
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* - `sys1 + sys2`
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- Add the outputs of two systems receiving the same input
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`outputs` keywords, as described in the :class:`InputOutputSystem`
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class. For state space systems, the names of the states can also be
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given, but caution should be used since the order of states in the
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combined system is not gauranteed.
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combined system is not guaranteed.
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Signal-based interconnection
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the signal range. Note that despite the similarity to slice notation,
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negative indices and step specifications are not supported.
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Using these various forms can simplfy the specification of
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Using these various forms can simplify the specification of
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interconnections. For example, consider a process with inputs 'u' and
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'v', each of dimension 2, and two outputs 'w' and 'y', each of
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'v', each of dimension 2, and two outputs 'w' and 'y', each of
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dimension 2::
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P = ct.rss(
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as well as the controller input `u`.
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This collection of systems can be combined in a variety of ways. The
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most explict would specify every signal::
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most explicit would specify every signal::
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clsys1 = ct.interconnect(
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[C, P, sumblk],
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A reference gain controller can be created with the command::
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ctrl, clsys = ct.create_statefbk_iosystem(sys, K, kf, feedfwd_pattern='refgain')
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ctrl, clsys = ct.create_statefbk_iosystem(
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sys, K, kf, feedfwd_pattern='refgain')
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This reference gain design pattern is described in more detail in
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Section 7.2 of `Feedback Systems <http://fbsbook.org>`_ (Stabilization

doc/linear.rst

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@@ -64,7 +64,7 @@ operations as well as the :func:`feedback`, :func:`parallel`, and
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:ref:`function-ref`.
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The :func:`rss` function can be used to create a random state space
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system with a desired numbef or inputs, outputs, and states::
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system with a desired number or inputs, outputs, and states::
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sys = ct.rss(states=4, outputs=1, inputs=1], strictly_proper=True)
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Multi-input, multi-output (MIMO) systems
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----------------------------------------
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Multi-input, multi-output (MIMO) sytems are created by providing
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Multi-input, multi-output (MIMO) systems are created by providing
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parameters of the appropriate dimensions to the relevant factory
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function. For transfer functions, this is done by providing a 2D list
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of numerator and denominator polynomials to the :func:`tf` function,
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e.g.::
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sys = ct.tf(
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[[num11, num12], [num21, num22]],
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[[den11, den12], [den21, denm22]])
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[[den11, den12], [den21, den22]])
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Similarly, MIMO frequency response data (FRD) systems are created by
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providing the :func:`frd` function with a 3D array of response
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changing the value of `config.defaults['control.default_dt']`.
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Functions operating on LTI systems will take into account whether a
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system is continous time or discrete time when carrying out operations
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system is continuous time or discrete time when carrying out operations
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that depend on this difference. For example, the :func:`rss` function
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will place all system eigenvalues within the unit circle when called
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using `dt` corresponding to a discrete time system::
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==============================
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A variety of functions are available to manipulate LTI systems,
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including functions for convering between state space and frequency
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including functions for converting between state space and frequency
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domain, sampling systems in time and frequency domain, and creating
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reduced order models.
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operate on LTI systems will work on any subclass.
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To explicitly convert a state space system into a transfer function
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represetation, the state space system can be passed as an argument to
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representation, the state space system can be passed as an argument to
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the :func:`tf` factory functions::
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sys_ss = ct.rss(4, 2, 2, name='sys_ss')
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Time sampling
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-------------
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Continous time systems can be converted to discrete time systems using
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Continuous time systems can be converted to discrete time systems using
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the :func:`sample_system` function and specifying a sampling time::
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>> csys = ct.rss(4, 2, 2, name='csys')
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Note that the system name for the discrete time system is the name of
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the origal system with the string '$sampled' appended.
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the original system with the string '$sampled' appended.
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Discrete time systems can also be created using the
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:func:`StateSpace.sample` or :func:`TransferFunction.sample` methods
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The :func:`minimal_realization` function eliminates uncontrollable or
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unobservable states in state space models or cancels pole-zero pairs
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in transfer functions. The resuling output system has minimal order
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in transfer functions. The resulting output system has minimal order
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and the same input/output response characteristics as the original
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model system. Unlike the :func:`balanced_reduction` function, the
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:func:`minimal_realization` eliminates all uncontrollable and/or
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D = [[-0. 0.]
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[ 0. 0.]]
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For a more compact represention, LTI objects can be evaluated directly
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For a more compact representation, LTI objects can be evaluated directly
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to return a summary of the system input/output properties::
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>>> sys = ct.rss(4, 2, 2, name='sys_2x2')

doc/nlsys.rst

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updfcn(t, x, u, params) -> array
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where `x` is a 1-D array with shape (n,), `u` is a 1-D array
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with shape (m,), `t` is a float representing the currrent time,
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with shape (m,), `t` is a float representing the current time,
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and `params` is a dict containing the values of parameters used by the
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function. The dynamics of the system can be in continuous or discrete
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time (use the `dt` keyword to create a discrte time system).
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time (use the `dt` keyword to create a discrete time system).
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The output function `outfcn` is used to specify the outputs of the
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system and has the same calling signature as `updfcn`. If it is not
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More complex operating points can be found by specifying which states,
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inputs, or outputs should be used in computing the operating point, as
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well as desired values of the states, inputs, outputs, or state
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updates. See the :func:`find_operating_point` documentation for more deatils.
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updates. See the :func:`find_operating_point` documentation for more
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details.
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Simulations and plotting

doc/optimal.rst

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plt.xlabel("t [sec]")
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plt.ylabel("u2 [rad/s]")
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plt.suptitle("Lane change manuever")
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plt.suptitle("Lane change maneuver")
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plt.tight_layout()
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plt.show()
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doc/stochastic.rst

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==================
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A stochastic signal is a representation of the output of a random
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process. NumPy and SciPy have a number of functions to calculate the
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covariance and correlation of random signals:
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* :func:`numpy.cov` - returns the sample variance of vector random
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variable :math:`X \in \mathbb{R}^n` where the input argument
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represents samples of :math:`X`.
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* :func:`numpy.cov` - returns the (cross-)covariance of the
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variables :math:`X` and :math:`Y` where the input arguments
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represent samples of the given random variables.
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process. NumPy and SciPy have a functions to calculate the covariance
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and correlation of random signals:
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* :func:`numpy.cov` - with a single argument, returns the sample
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variance of a vector random variable :math:`X \in \mathbb{R}^n`
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where the input argument represents samples of :math:`X`. With
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two arguments, returns the (cross-)covariance of random variables
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:math:`X` and :math:`Y` where the input arguments represent
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samples of the given random variables.
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* :func:`scipy.signal.correlate` - the "cross-correlation" between two
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random (1D) sequences. If these sequences came from a random

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