Metadata-Version: 1.1
Name: audiolazy
Version: 0.5
Summary: Real-Time Expressive Digital Signal Processing (DSP) Package for Python!
Home-page: http://github.com/danilobellini/audiolazy
Author: Danilo de Jesus da Silva Bellini
Author-email: danilo [dot] bellini [at] gmail [dot] com
License: GPLv3
Description: 
        AudioLazy
        =========
        
        Laziness and object representation
        ----------------------------------
        
        There are several tools and packages that let the Python use and
        expressiveness look like languages such as MatLab and Octave. However, the
        eager evaluation done by most of these tools make it difficult, perhaps
        impossible, to use them for real time audio processing. To avoid such
        eagerness, one can make the calculations only when data is requested, not
        when the path to the data is given. This is the core idea in laziness that
        allows:
        
        - Real-time application (you don't need to wait until all data is
          processed to have a result);
        - Endless data sequence representation;
        - Data-flow representation;
        - Task elimination when a reverse task is done: instead of doing something
          to then undo, nothing needs to be done, and no conscious optimization
          need to be done for that.
        
        Another difficulty concerns expressive code creation for audio processing in
        blocks through indexes and vectors. Sometimes, that's unavoidable, or at
        least such avoidance would limit the power of the system that works with
        sequence data.
        
        Block sequences can be found from sample sequences being both objects, where
        the latter can be the result of a method or function over the former. The
        information needed for such is the block size and where would start the next
        block. Although one can think about the last block and the exact index where
        it would start, most of the time spent in steps like this one happens to be
        an implementation issue that just keep the focus away from the problem being
        worked on. To allow a thing like an endless data sequence, there should be
        no need to know when something stops.
        
        Probably an engineer would find the use of equations and structures from
        electrical engineering theory much cleaner to understand than storing
        everything into data arrays, mainly when common operations are done to these
        representations. What is the product of the filter with numerator
        ``[1, 7, 2]`` and denominator ``[1, 0.5, 0.2]`` as its system equation with
        the one that has the arrays reversed like ``[2, 7, 1]``? That might be simple,
        and the reversed would avoid questions like "what comes first, the zero or the
        [minus] two exponent?", but maybe we could get more efficient ourselves if we
        had something easier: multiplication could be written once and for all and
        with a representation programmers are used to see. This would be even more
        expressive if we could get rid from the asymmetry of a method call like
        ``filt1.multiply_by(filt2)``, since multiplication in this case should be
        commutative. The use of natural operators is possible in a language that
        allows operator overloading, but for such we need to describe
        those equations and structures as objects and object relationships.
        
        The name ``Hz`` can be a number that would allow conversion to a default DSP
        internal rad/samples unit, so one can write things like ``freq = 440 * Hz``.
        This isn't difficult in probably any language, but can help in expressiveness,
        already. If (almost) everything would need data in "samples" or "rad/sample"
        units, constants for converting these from "second" and "hertz" would help
        with the code expressiveness. A comb filter ``comb.tau(delay=30*s, tau=40*s)``
        can represent a comb filter with the given delay and time constant, both in
        samples, but with a more clear meaning for the reader than it would have with
        an expression like ``[1] + [0] * 239999 + [alpha]``. Would it be needed to
        store all those zeros while just using the filter to get a frequency response
        plot?
        
        It's possible to avoid some of these problems with well-chosen constants,
        duck typing, overloaded operators, functions as first-class citizens, object
        oriented together with functional style programming, etc.., resources
        that the Python language gives us for free.
        
        What does it do?
        ----------------
        
        Prioritizing code expressiveness, clarity and simplicity, without precluding
        the lazy evaluation, and aiming to be used together with Numpy, Scipy and
        Matplotlib as well as default Python structures like lists and generators,
        AudioLazy is a package written in pure Python proposing digital audio signal
        processing (DSP), featuring:
        
        - A ``Stream`` class for finite and endless signals representation with
          elementwise operators (auto-broadcast with non-iterables) in a common
          Python iterable container accepting heterogeneous data;
        - Strongly sample-based representation (Stream class) with easy conversion
          to block representation using the ``Stream.blocks(size, hop)`` method;
        - Sample-based interactive processing with ``ControlStream``;
        - ``Streamix`` mixer for iterables given their starting time deltas;
        - Multi-thread audio I/O integration with PyAudio;
        - Linear filtering with Z-transform filters directly as equations (e.g.
          ``filt = 1 / (1 - .3 * z ** -1)``), including linear time variant filters
          (i.e., the ``a`` in ``a * z ** k`` can be a Stream instance), cascade
          filters (behaves as a list of filters), resonators, etc.. Each
          ``LinearFilter`` instance is compiled just in time when called;
        - Zeros and poles plots and frequency response plotting integration with
          MatPlotLib;
        - Linear Predictive Coding (LPC) directly to ``ZFilter`` instances, from
          which you can find PARCOR coeffs and LSFs;
        - Both sample-based (e.g., zero-cross rate, envelope, moving average,
          clipping, unwrapping) and block-based (e.g., window functions, DFT,
          autocorrelation, lag matrix) analysis and processing tools;
        - A simple synthesizer (Table lookup, Karplus-Strong) with processing tools
          (Linear ADSR envelope, fade in/out, fixed duration line stream) and basic
          wave data generation (sinusoid, white noise, impulse);
        - Biological auditory periphery modeling (ERB and gammatone filter models);
        - Multiple implementation organization as ``StrategyDict`` instances:
          callable dictionaries that allows the same name to have several different
          implementations (e.g. ``erb``, ``gammatone``, ``lowpass``, ``resonator``,
          ``lpc``, ``window``);
        - Converters among MIDI pitch numbers, strings like "F#4" and frequencies;
        - Polynomials, Stream-based functions from itertools, math, cmath, and more!
          Go try yourself! =)
        
        Installing
        ----------
        
        The package works both on Linux and on Windows. You can find the last stable
        version at `PyPI <http://pypi.python.org/pypi/audiolazy>`_ and install it with
        the usual Python installing mechanism::
        
          python setup.py install
        
        If you have pip, you can go directly (use ``-U`` for update or reinstall)::
        
          pip install audiolazy
        
        for downloading (from PyPI) and installing the package for you, or::
        
          pip install -U .
        
        To install from a path that has the ``setup.py`` file and the package data
        uncompressed previously.
        
        For the *bleeding-edge* version, you can install directly from the github
        repository (requires ``git`` for cloning)::
        
          pip install -U git+git://github.com/danilobellini/audiolazy.git
        
        For older versions, you can install from the PyPI link or directly from the
        github repository, based on the repository tags. For example, to install the
        version 0.04 (requires ``git`` for cloning)::
        
          pip install -U git+git://github.com/danilobellini/audiolazy.git@v0.04
        
        The package doesn't have any strong dependency for its core besides the Python
        itself (versions 2.7, 3.2 or newer) as well as its standard library, but you
        might need:
        
        - PyAudio: needed for playing and recording audio (``AudioIO`` class);
        - NumPy: needed for doing some maths, such as finding the LSFs from a filter
          or roots from a polynomial;
        - MatPlotLib: needed for all default plotting, like in ``LinearFilter.plot``
          method and several examples;
        - SciPy (testing and examples only): used as an oracle for LTI filter testing
          and for the Butterworth filter example;
        - pytest, pytest-cov and pytest-timeout (testing only): runs test suite and
          shows code coverage status;
        - wxPython (example only): used by one example with FM synthesis in an
          interactive GUI;
        - Tkinter (example only): needed for the pitch follower based on the
          zero-crossing rate example GUI;
        - Music21 (example only): there's one example that gets the Bach chorals from
          that package corpora for synthesizing and playing;
        - Sphinx (documentation only): it can create the software documentation in
          several different file formats.
        
        Beside examples and tests, only the filter plotting with ``plot`` and
        ``zplot`` methods needs MatPlotLib. Also, the routines that needs NumPy up to
        now are:
        
        - Root finding with ``zeros`` and ``poles`` properties (filter classes) or
          with ``roots`` property (Poly class);
        - Some Linear Predictive Coding (``lpc``) strategies: ``nautocor``,
          ``autocor`` and ``covar``;
        - Line Spectral Frequencies ``lsf`` and ``lsf_stable`` functions.
        
        Getting started
        ---------------
        
        Before all examples below, it's easier to get everything from audiolazy
        namespace:
        
        .. code-block:: python
        
          from audiolazy import *
        
        All modules starts with "lazy\_", but their data is already loaded in the main
        namespace. These two lines of code do the same thing:
        
        .. code-block:: python
        
          from audiolazy.lazy_stream import Stream
          from audiolazy import Stream
        
        Endless iterables with operators (be careful with loops through an endless
        iterator!):
        
        .. code-block:: python
        
          >>> a = Stream(2, -2, -1) # Periodic
          >>> b = Stream(3, 7, 5, 4) # Periodic
          >>> c = a + b # Elementwise sum, periodic
          >>> c.take(15) # First 15 elements from the Stream object
          [5, 5, 4, 6, 1, 6, 7, 2, 2, 9, 3, 3, 5, 5, 4]
        
        And also finite iterators (you can think on any Stream as a generator with
        elementwise operators):
        
        .. code-block:: python
        
          >>> a = Stream([1, 2, 3, 2, 1]) # Finite, since it's a cast from an iterable
          >>> b = Stream(3, 7, 5, 4) # Periodic
          >>> c = a + b # Elementwise sum, finite
          >>> list(c)
          [4, 9, 8, 6, 4]
        
        LTI Filtering from system equations (Z-transform). After this, try summing,
        composing, multiplying ZFilter objects:
        
        .. code-block:: python
        
          >>> filt = 1 - z ** -1 # Diff between a sample and the previous one
          >>> filt
          1 - z^-1
          >>> data = filt([.1, .2, .4, .3, .2, -.1, -.3, -.2]) # Past memory has 0.0
          >>> data # This should have internally [.1, .1, .2, -.1, -.1, -.3, -.2, .1]
          <audiolazy.lazy_stream.Stream object at ...>
          >>> data *= 10 # Elementwise gain
          >>> [int(round(x)) for x in data] # Streams are iterables
          [1, 1, 2, -1, -1, -3, -2, 1]
          >>> data_int = filt([1, 2, 4, 3, 2, -1, -3, -2], zero=0) # Now zero is int
          >>> list(data_int)
          [1, 1, 2, -1, -1, -3, -2, 1]
        
        LTI Filter frequency response plot (needs MatPlotLib):
        
        .. code-block:: python
        
          (1 + z ** -2).plot().show()
        
        .. image:: https://raw.github.com/danilobellini/audiolazy/master/images/filt_plot.png
        
        The ``matplotlib.figure.Figure.show`` method won't work unless you're
        using a newer version of MatPlotLib (works on MatPlotLib 1.2.0), but you still
        can save the above plot directly to a PDF, PNG, etc. with older versions
        (e.g. MatPlotLib 1.0.1):
        
        .. code-block:: python
        
          (1 + z ** -2).plot().savefig("my_plot.pdf")
        
        On the other hand, you can always show the figure using MatPlotLib directly:
        
        .. code-block:: python
        
          from matplotlib import pyplot as plt # Or "import pylab as plt"
          filt = 1 + z ** -2
          fig1 = filt.plot(plt.figure()) # Argument not needed on the first figure
          fig2 = filt.zplot(plt.figure()) # The argument ensures a new figure
          plt.show()
        
        CascadeFilter instances and ParallelFilter instances are lists of filters with
        the same operator behavior as a list, and also works for plotting linear
        filters. Constructors accepts both a filter and an iterable with filters.
        For example, a zeros and poles plot (needs MatPlotLib):
        
        .. code-block:: python
        
          filt1 = CascadeFilter(0.2 - z ** -3) # 3 zeros
          filt2 = CascadeFilter(1 / (1 -.8 * z ** -1 + .6 * z ** -2)) # 2 poles
          # Here __add__ concatenates and __mul__ by an integer make reference copies
          filt = (filt1 * 5 + filt2 * 10) # 15 zeros and 20 poles
          filt.zplot().show()
        
        .. image:: https://raw.github.com/danilobellini/audiolazy/master/images/cascade_plot.png
        
        Linear Predictive Coding (LPC) autocorrelation method analysis filter
        frequency response plot (needs MatPlotLib):
        
        .. code-block:: python
        
          lpc([1, -2, 3, -4, -3, 2, -3, 2, 1], order=3).plot().show()
        
        .. image:: https://raw.github.com/danilobellini/audiolazy/master/images/lpc_plot.png
        
        Linear Predictive Coding covariance method analysis and synthesis filter,
        followed by the frequency response plot together with block data DFT
        (MatPlotLib):
        
        .. code-block:: python
        
          >>> data = Stream(-1., 0., 1., 0.) # Periodic
          >>> blk = data.take(200)
          >>> analysis_filt = lpc.covar(blk, 4)
          >>> analysis_filt
          1 + 0.5 * z^-2 - 0.5 * z^-4
          >>> residual = list(analysis_filt(blk))
          >>> residual[:10]
          [-1.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
          >>> synth_filt = 1 / analysis_filt
          >>> synth_filt(residual).take(10)
          [-1.0, 0.0, 1.0, 0.0, -1.0, 0.0, 1.0, 0.0, -1.0, 0.0]
          >>> amplified_blk = list(Stream(blk) * -200) # For alignment w/ DFT
          >>> synth_filt.plot(blk=amplified_blk).show()
        
        .. image:: https://raw.github.com/danilobellini/audiolazy/master/images/dft_lpc_plot.png
        
        AudioLazy doesn't need any audio card to process audio, but needs PyAudio to
        play some sound:
        
        .. code-block:: python
        
          rate = 44100 # Sampling rate, in samples/second
          s, Hz = sHz(rate) # Seconds and hertz
          ms = 1e-3 * s
          note1 = karplus_strong(440 * Hz) # Pluck "digitar" synth
          note2 = zeros(300 * ms).append(karplus_strong(880 * Hz))
          notes = (note1 + note2) * .5
          sound = notes.take(int(2 * s)) # 2 seconds of a Karplus-Strong note
          with AudioIO(True) as player: # True means "wait for all sounds to stop"
            player.play(sound, rate=rate)
        
        See also the docstrings and the "examples" directory at the github repository
        for more help. Also, the huge test suite might help you understanding how the
        package works and how to use it.
        
        ..
          This file is part of AudioLazy, the signal processing Python package.
          Copyright (C) 2012-2013 Danilo de Jesus da Silva Bellini
        
          AudioLazy is free software: you can redistribute it and/or modify
          it under the terms of the GNU General Public License as published by
          the Free Software Foundation, version 3 of the License.
        
          This program is distributed in the hope that it will be useful,
          but WITHOUT ANY WARRANTY; without even the implied warranty of
          MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
          GNU General Public License for more details.
        
          You should have received a copy of the GNU General Public License
          along with this program. If not, see <http://www.gnu.org/licenses/>.
        
          danilo [dot] bellini [at] gmail [dot] com
        
        AudioLazy changes history
        -------------------------
        
        *** Version 0.05 (Python 2 & 3, more examples, refactoring, polinomials) ***
        
        + examples:
        
          - Pitch follower via zero-crossing rate with Tkinter GUI
          - Pi with Madhava-Gregory-Leibniz series and Machin formula using Stream
          - LPC plot with DFT, showing two formants (magnitude peaks)
          - A somehow disturbing example based on Shepard "going higher" tone
          - Linear Periodically Time Variant filter example
          - Now the Bach choral player can play in loop
          - New DFT-based pitch follower (guitar tuner like) and better ZCR-based
            pitch follower by using a simple limiter
          - Butterworth filter from SciPy as a ZFilter instance, with plots
        
        + general:
        
          - Now with 82% code coverage in tests
          - Mock testing for audio output
          - Bugfixes (``envelope.abs``, ``midi2str``, ``StreamTeeHub.blocks``, etc.)
          - Extended domain for some functions by using ``inf`` and ``nan``
          - Removed deprecated ``Stream.tee()`` method
          - Constants ``DEFAULT_CHUNK_SIZE`` and ``LATEX_PI_SYMBOL`` were removed:
            the default values are now changeable and inside ``chunks`` and
            ``float_str``, respectively (see docstrings for more details)
          - No more distinction between ``__div__`` and ``__truediv__`` (Python 2.7)
          - Now AudioLazy works with Python 3.2 and 3.3!
          - Test skipping for tests that depends upon something that is Python
            version-specific
          - Test "xfail" using XFailer classes when depending package (e.g. pyaudio)
            is unavailable in the testing environment
        
        + lazy_compat (*new!*):
        
          - Module for Python 2.x and 3.x compatibility resources (constants
            and functions) without AudioLazy dependencies (i.e., no Stream here)
          - Common place for iterable-based version of itertools/built-ins in both
            Python 2 and 3 starting with "x": ``xmap``, ``xfilter``, ``xzip``,
            ``xrange``, ``xzip_longest``. Versions with "i" are kept in lazy_itertools
            module to return Stream instances (``imap``, ``izip``, ``izip.longest``,
            etc.), and Python 2 list-based behaviour of ``range`` is kept as
            ``orange`` (a fruitful name)
          - New ``meta`` function for creating metaclasses always in a "Python 3
            look-alike" style, keeping the semantics (including the inheritance
            hierarchy, which won't have any extra "dummy" class)
        
        + lazy_core:
        
          - New ``OpMethod`` class with 33 operator method instances and querying
          - Changed ``AbstractOperatorOverloaderMeta`` to the new OpMethod-based
            interface
          - Now StrategyDict changes the module ``__test__`` so that doctests from
            strategies are found by the doctest finder.
        
        + lazy_filters:
        
          - ZFilter instances are now better prepared for Stream coeffs and
            operator-based filter creation, as well as a new copy helper method
          - Filters are now hashable (e.g., they can be used in sets)
        
        + lazy_io:
        
          - New RecStream class for recording Stream instances with a ``stop`` method
          - Now chunks is a StrategyDict here, instead of two lazy_misc functions
          - Now the default chunk size is stored in chunks.size, and can be changed
        
        + lazy_itertools:
        
          - New ``accumulate`` itertool from Python 3, available also in Python 2
            yielding a Stream. This is a new StrategyDict with one more strategy in
            Python 3
          - Strategy ``chain.from_iterable`` is now available (Stream version
            itertool), and ``chain`` is now a StrategyDict
          - Now ``izip`` is a StrategyDict, with ``izip.smallest`` (default) and
            ``izip.longest`` strategies
        
        + lazy_misc:
        
          - New ``rint`` for "round integer" operations as well as other higher step
            integer quantization
          - Now ``almost_eq`` is a single StrategyDict with both ``bits`` (default,
            comparison by significand/mantissa bits) and ``diff`` (absolute value
            difference) strategies
        
        + lazy_poly:
        
          - New ``x`` Poly object (to be used like the ``z`` ZFilter instance)
          - Waring-Lagrange polynomial interpolator StrategyDict
          - General resample based on Waring-Lagrange interpolators, working with
            time-varying sample rate
          - New methods ``Poly.is_polynomial()`` and ``Poly.is_laurent()``
          - New property ``Poly.order`` for common polynomials
          - Now ``Poly.integrate()`` and ``Poly.diff()`` methods returns Poly
            instances, and the ``zero`` from the caller Poly is always kept in
            result (this includes many bugfixes)
          - Poly instances are now better prepared for Stream coeffs and evaluation,
            including a helper ``Poly.copy()`` method
          - Poly is now hashable and have __setitem__ (using both isn't allowed for
            the same instance)
        
        + lazy_stream:
        
          - Stream.take now accepts floats, so with first ``sHz`` output as
            ``s`` (for second) you can now use ``my_stream.take(20 * s)`` directly,
            as well as a "take all" feature ``my_stream.take(inf)``
          - New ``Stream.peek()`` method, allowing taking items while keeping them
            as the next to be yielded by the Stream or StreamTeeHub
          - New ``Stream.skip()`` method for neglecting the leading items without
            storing them
          - New ``Stream.limit()`` method, to enforce a maximum "length"
          - StreamTeeHub methods ``skip()``, ``limit()``, ``append()``, ``map()`` and
            ``filter()`` returns the modified copy as a Stream instance (i.e., works
            like ``Stream(my_stream_tee_hub).method_name()``)
          - Control over the module name in ``tostream`` (needed for lazy_itertools)
        
        + lazy_synth:
        
          - Input "dur" in ``ones()``, ``zeros()``, ``white_noise()`` and
            ``impulse()`` now can be inf (besides None)
          - Impulse now have ``one=1.`` and ``zero=0.`` arguments
          - New ``gauss_noise`` for Normal / Gaussian-distributed noise
          - White-noise limits parametrization
        
        + lazy_text (*new!*):
        
         - Got all text/string formatting functions from lazy_misc.
         - Namespace clean-up: new StrategyDict ``float_str`` embraces older
           rational/pi/auto formatters in one instance
        
        *** Version 0.04 (Documentation, LPC, Plots!) ***
        
        + examples:
        
          - Random Bach Choral playing example (needs Music21 corpus)
        
        + general:
        
          - Sphinx documentation!
          - Self-generated package and module summary at the docstring
          - Integration with NumPy (tested on 1.5.0, 1.6.1 and 1.6.2) and MatPlotLib
            (tested on 1.0.1 and 1.2.0)
          - More docstrings and doctests, besides lots of corrections
          - Itemized package description, installation instructions and getting
            started examples with plots in README.rst
          - Now with 5400+ tests and 75% code coverage
        
        + lazy_analysis:
        
          - One-dimensional autocorrelation function with ``acorr`` and lag
            "covariance" (due to lpc.covar) with ``lag_matrix``
          - DFT for any frequency, given a block
          - Three envelope filtering strategies (time domain)
          - Three moving average filter strategies
          - Signal clipping function
          - Signal unwrap, defaults to the ``2 * pi`` radians range but configurable
            to other units and max signal difference allowed
          - New AMDF algorithm as a non-linear filter
        
        + lazy_core:
        
          - StrategyDict instances now are singletons of a new class, which have
            lazy non-memoized docstrings based on their contents
        
        + lazy_filters:
        
          - ZFilter composition/substitution, e.g., ``(1 + z ** -1)(1 / z)`` results
            to the ZFilter instance ``1 + z``
          - New LinearFilter.plot() directly plots the frequency response of a LTI
            filter to a MatPlotLib figure. Configurable:
        
            * Linear (default) or logarithmic frequency scale
            * Linear, squared or dB (default) magnitude scale
            * Plots together the DFT of a given block, if needed. Useful for LPC
            * Phase unwrapping (defaults to True)
            * Allows frequency in Hz and in rad/sample. When using radians units,
              the tick locator is based on ``pi``, as well as the formatter
        
          - New LinearFilter.zplot() for plotting the zero-pole plane of a LTI filter
            directly into a MatPlotLib figure
          - New LinearFilterProperties read-only properties ``numpolyz`` and
            ``denpolyz`` returning polynomials based on ``x = z`` instead of the
            polynomials based on ``x = z ** -1`` returned from ``numpoly`` and
            ``denpoly``
          - New LinearFilter properties ``poles`` and ``zeros``, based on NumPy
          - New class ``FilterList`` for filter grouping with a ``callables``
            property, for casting from lists with constant gain values as filters.
            It is an instance of ``FilterListMeta`` (old CascadeFilterMeta), and
            CascadeFilter now inherits from this FilterList
          - More LinearFilter behaviour into FilterList: Plotting (``plot`` and
            ``zplot``), ``poles``, ``zeros``, ``is_lti`` and ``is_causal``
          - New ``ParallelFilter`` class, inheriting from FilterList
          - Now comb is a StrategyDict too, with 3 strategies:
        
            * ``comb.fb`` (default): Feedback comb filter (IIR or time variant)
            * ``comb.tau``: Same to the feedback strategy, but with a time decay
              ``tau`` parameter (time in samples up to ``1/e`` amplitude, or
              -8.686 dB) instead of a gain ``alpha``
            * ``comb.ff``: Feed-forward comb filter (FIR or time variant)
        
        + lazy_lpc (*new!*):
        
          - Linear Predictive Coding (LPC) coefficients as a ZFilter from:
        
            * ``lpc.autocor`` (default): Auto-selects autocorrelation implementation
              (Faster)
            * ``lpc.nautocor``: Autocorrelation, with linear system solved by NumPy
              (Safer)
            * ``lpc.kautocor``: Autocorrelation, using the Levinson-Durbin algorithm
            * ``lpc.covar`` or ``lpc.ncovar``: Covariance, with linear system solved
              by NumPy
            * ``lpc.kcovar``: Covariance, slower. Mainly for those without NumPy
            * ``levinson_durbin``: Same to the ``lpc.kautocor``, but with the
              autocorrelation vector as the input, not the signal data
        
          - Toeplitz matrix as a list of lists
          - Partial correlation coefficients (PARCOR) or reflection coefficients
          - Line Spectral Frequencies (LSF)
          - Stability testers for filters with LSF and PARCOR
        
        + lazy_math:
        
          - New ``sign`` gets the sign of a given sequence.
        
        + lazy_midi:
        
          - Completed converters between frequency (in hertz), string and MIDI pitch
            numbers
          - New ``octaves`` for finding all octaves in a frequency range given one
            frequency
        
        + lazy_misc:
        
          - New ``rational_formatter``: casts floats to strings, perhaps with a symbol
            string as multiplier
          - New ``pi_formatter``: same to ``rational_formatter``, but with the symbol
            fixed to pi, mainly for use in MatPlotLib labels
        
        + lazy_poly:
        
          - New Poly.roots property, based on NumPy
        
        + lazy_stream:
        
          - Streamix class for mixing Streams based on delta starting times,
            automatically managing the need for multiple "tracks"
        
        + lazy_synth:
        
          - Karplus-Strong algorithm now uses ``tau`` time decay constant instead of
            the comb filter ``alpha`` gain.
        
        
        *** Version 0.03 (Time variant filters, examples, etc.. Major changes!) ***
        
        + examples (*new!*):
        
          - Gammatone frequency and impulse response plots example
          - FM synthesis example for benchmarking with CPython and PyPy
          - Simple I/O wire example, connecting the input directly to the output
          - Modulo Counter graphics w/ FM synthesis audio in a wxPython application
          - Window functions plot example (all window strategies)
        
        + general:
        
          - Namespace cleanup with __all__
          - Lots of optimization and refactoring, also on tests and setup.py
          - Better docstrings and README.rst
          - Doctests (with pytest) and code coverage (needs pytest-cov)
          - Now with 5200+ tests and 79% code coverage
        
        + lazy_analysis (*new!*):
        
          - New ``window`` StrategyDict instance, with:
        
            * Hamming (default)
            * Hann
            * Rectangular
            * Bartlett (triangular with zero endpoints)
            * Triangular (without zeros)
            * Blackman
        
        + lazy_auditory (*new!*):
        
          - Two ERB (Equivalent Rectangular Bandwidth) models (both by Glasberg and
            Moore)
          - Function to find gammatone bandwidth from ERB for any gammatone order
          - Three gammatone filter implementations: sampled impulse response, Slaney,
            Klapuri
        
        + lazy_core:
        
          - MultiKeyDict: an "inversible" dict (i.e., a dict whose values must be
            hashable) that may have several keys for each value
          - StrategyDict: callable dict to store multiple function implementations
            in. Inherits from MultiKeyDict, so the same strategy may have multiple
            names. It's also an iterable on its values (functions)
        
        + lazy_filters:
        
          - LTI and LTIFreq no longer exists! They were renamed to LinearFilter and
            ZFilter since filters now can have Streams as coefficients (they don't
            need to be "Time Invariant" anymore)
          - Linear filters are now iterables, allowing:
        
            * Comparison with almost_eq like ``assert almost_eq(filt1, filt2)``
            * Expression like ``numerator_data, denominator_data = filt``, where
              each data is a list of pairs that can be used as input for Poly,
              LinearFilter or ZFilter
        
          - LinearFilterProperties class, implementing numlist, denlist, numdict and
            dendict, besides numerator and denominator, from numpoly and denpoly
          - Comparison "==" and "!=" are now strict
          - CascadeFilter: list of filters that behave as a filter
          - LinearFilter.__call__ now has the "zero" optional argument (allows
            non-float)
          - LinearFilter.__call__ memory input can be a function or a Stream
          - LinearFilter.linearize: linear interpolated delay-line from fractional
            delays
          - Feedback comb filter
          - 4 resonator filter models with 2-poles with exponential approximation
            for finding the radius from the bandwidth
          - Simple one pole lowpass and highpass filters
        
        + lazy_io:
        
          - AudioIO.record method, creating audio Stream instances from device data
        
        + lazy_itertools:
        
          - Now with a changed tee function that allows not-iterable inputs,
            helpful to let the same code work with Stream instances and constants
        
        + lazy_math (*new!*):
        
          - dB10, dB20 functions for converting amplitude (squared or linear,
            respectively) to logarithmic dB (power) values from complex-numbers
            (like the ones returned by LinearFilter.freq_response)
          - Most functions from math module, but working decorated with elementwise
            (``sin``, ``cos``, ``sqrt``, etc.), and the constants ``e`` and ``pi``
          - Other functions: ``factorial``, ``ln`` (the ``log`` from math), ``log2``,
            ``cexp`` (the ``exp`` from cmath) and ``phase`` (from cmath)
        
        + lazy_midi:
        
          - MIDI pitch numbers and Hz frequency converters from strings like "C#4"
        
        + lazy_misc:
        
          - Elementwise decorator now based on both argument keyword and position
        
        + lazy_poly:
        
          - Horner-like scheme for Poly.__call__ evaluation
          - Poly now can have Streams as coefficients
          - Comparison "==" and "!=" are now strict
        
        + lazy_stream:
        
          - Methods and attributes from Stream elements can be used directly,
            elementwise, like ``my_stream.imag`` and ``my_stream.conjugate()`` in a
            stream with complex numbers
          - New thub() function and StreamTeeHub class: tee (or "T") hub auto-copier
            to help working with Stream instances *almost* the same way as you do with
            numbers
        
        + lazy_synth:
        
          - Karplus-Strong synthesis algorithm
          - ADSR envelope
          - Impulse, ones, zeros/zeroes and white noise Stream generator
          - Faster sinusoid not based on the TableLookup class
        
        
        *** Version 0.02 (Interactive Stream objects & Table lookup synthesis!) ***
        
        + general:
        
          - 10 new tests
        
        + lazy_midi (*new!*):
        
          - MIDI to frequency (Hz) conversor
        
        + lazy_misc:
        
          - sHz function for explicit time (s) and frequency (Hz) units conversion
        
        + lazy_stream:
        
          - Interactive processing with ControlStream instances
          - Stream class now allows inheritance
        
        + lazy_synth (*new!*):
        
          - TableLookup class, with sinusoid and sawtooth instances
          - Endless counter with modulo, allowing Stream inputs, mainly created for
            TableLookup instances
          - Line, fade in, fade out, ADS attack with endless sustain
        
        
        *** Version 0.01 (First "pre-alpha" version!) ***
        
        + general:
        
          - 4786 tests (including parametrized tests), based on pytest
        
        + lazy_core:
        
          - AbstractOperatorOverloaderMeta class to help massive operator
            overloading as needed by Stream, Poly and LTIFreq (now ZFilter) classes
        
        + lazy_filters:
        
          - LTI filters, callable objects with operators and derivatives, returning
            Stream instances
          - Explicit filter formulas with the ``z`` object, e.g.
            ``filt = 1 / (.5 + z ** -1)``
        
        + lazy_io:
        
          - Multi-thread audio playing (based on PyAudio), with context manager
            interface
        
        + lazy_itertools:
        
          - Stream-based version of all itertools
        
        + lazy_misc:
        
          - Block-based processing, given size and (optionally) hop
          - Simple zero padding generator
          - Elementwise decorator for functions
          - Bit-based and diff-based "almost equal" comparison function for floats
            and iterables with floats. Also works with (finite) generators
        
        + lazy_poly:
        
          - Poly: polynomials based on dictionaries, with list interface and
            operators
        
        + lazy_stream:
        
          - Stream: each instance is basically a generator with elementwise
            operators
          - Decorator ``tostream`` so generator functions can return Stream objects
        
Platform: UNKNOWN
Classifier: Development Status :: 3 - Alpha
Classifier: Intended Audience :: Developers
Classifier: Intended Audience :: Education
Classifier: Intended Audience :: Science/Research
Classifier: Intended Audience :: Other Audience
Classifier: License :: OSI Approved :: GNU General Public License v3 (GPLv3)
Classifier: Operating System :: Microsoft :: Windows
Classifier: Operating System :: POSIX :: Linux
Classifier: Operating System :: MacOS
Classifier: Operating System :: OS Independent
Classifier: Programming Language :: Python
Classifier: Programming Language :: Python :: 2
Classifier: Programming Language :: Python :: 2.7
Classifier: Programming Language :: Python :: 3
Classifier: Programming Language :: Python :: 3.2
Classifier: Programming Language :: Python :: 3.3
Classifier: Topic :: Artistic Software
Classifier: Topic :: Multimedia :: Sound/Audio
Classifier: Topic :: Multimedia :: Sound/Audio :: Analysis
Classifier: Topic :: Multimedia :: Sound/Audio :: Capture/Recording
Classifier: Topic :: Multimedia :: Sound/Audio :: Players
Classifier: Topic :: Multimedia :: Sound/Audio :: Sound Synthesis
Classifier: Topic :: Scientific/Engineering
Classifier: Topic :: Software Development
Classifier: Topic :: Software Development :: Libraries
Classifier: Topic :: Software Development :: Libraries :: Python Modules
