add numpy op hanning, hamming, blackman

python/mxnet/ndarray/numpy/_op.py

@@ -27,7 +27,8 @@
 from ..ndarray import NDArray
 
 __all__ = ['zeros', 'ones', 'add', 'subtract', 'multiply', 'divide', 'mod', 'power', 'tensordot',
-           'linspace', 'expand_dims', 'tile', 'arange', 'split', 'concatenate', 'stack']
+           'linspace', 'expand_dims', 'tile', 'arange', 'split', 'concatenate', 'stack', 'hanning',
+           'hamming', 'blackman']
 
 
 @set_module('mxnet.ndarray.numpy')
@@ -732,3 +733,275 @@ def get_list(arrays):
 
     arrays = get_list(arrays)
     return _npi.stack(*arrays, axis=axis, out=out)
+
+
+@set_module('mxnet.ndarray.numpy')
+def hanning(M, dtype=_np.float64, ctx=None):
+    r"""Return the Hanning window.
+
+    The Hanning window is a taper formed by using a weighted cosine.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero or less, an
+        empty array is returned.
+    dtype : str or numpy.dtype, optional
+        An optional value type. Default is `numpy.float64`. Note that you need
+        select numpy.float32 or float64 in this operator.
+    ctx : Context, optional
+        An optional device context (default is the current default context).
+
+    Returns
+    -------
+    out : ndarray, shape(M,)
+        The window, with the maximum value normalized to one (the value
+        one appears only if `M` is odd).
+
+    See Also
+    --------
+    blackman, hamming
+
+    Notes
+    -----
+    The Hanning window is defined as
+
+    .. math::  w(n) = 0.5 - 0.5cos\left(\frac{2\pi{n}}{M-1}\right)
+               \qquad 0 \leq n \leq M-1
+
+    The Hanning was named for Julius von Hann, an Austrian meteorologist.
+    It is also known as the Cosine Bell. Some authors prefer that it be
+    called a Hann window, to help avoid confusion with the very similar
+    Hamming window.
+
+    Most references to the Hanning window come from the signal processing
+    literature, where it is used as one of many windowing functions for
+    smoothing values.  It is also known as an apodization (which means
+    "removing the foot", i.e. smoothing discontinuities at the beginning
+    and end of the sampled signal) or tapering function.
+
+    References
+    ----------
+    .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power
+           spectra, Dover Publications, New York.
+    .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics",
+           The University of Alberta Press, 1975, pp. 106-108.
+    .. [3] Wikipedia, "Window function",
+           http://en.wikipedia.org/wiki/Window_function
+    .. [4] W.H. Press,  B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
+           "Numerical Recipes", Cambridge University Press, 1986, page 425.
+
+    Examples
+    --------
+    >>> np.hanning(12)
+    array([0.00000000e+00, 7.93732437e-02, 2.92292528e-01, 5.71157416e-01,
+           8.27430424e-01, 9.79746513e-01, 9.79746489e-01, 8.27430268e-01,
+           5.71157270e-01, 2.92292448e-01, 7.93731320e-02, 1.06192832e-13], dtype=float64)
+
+    Plot the window and its frequency response:
+
+    >>> import matplotlib.pyplot as plt
+    >>> window = np.hanning(51)
+    >>> plt.plot(window.asnumpy())
+    [<matplotlib.lines.Line2D object at 0x...>]
+    >>> plt.title("Hann window")
+    Text(0.5, 1.0, 'Hann window')
+    >>> plt.ylabel("Amplitude")
+    Text(0, 0.5, 'Amplitude')
+    >>> plt.xlabel("Sample")
+    Text(0.5, 0, 'Sample')
+    >>> plt.show()
+    """
+    if dtype is None:
+        dtype = _np.float64
+    if ctx is None:
+        ctx = current_context()
+    return _npi.hanning(M, dtype=dtype, ctx=ctx)
+
+
+@set_module('mxnet.ndarray.numpy')
+def hamming(M, dtype=_np.float64, ctx=None):
+    r"""Return the hamming window.
+
+    The hamming window is a taper formed by using a weighted cosine.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero or less, an
+        empty array is returned.
+    dtype : str or numpy.dtype, optional
+        An optional value type. Default is `numpy.float64`. Note that you need
+        select numpy.float32 or float64 in this operator.
+    ctx : Context, optional
+        An optional device context (default is the current default context).
+
+    Returns
+    -------
+    out : ndarray, shape(M,)
+        The window, with the maximum value normalized to one (the value
+        one appears only if `M` is odd).
+
+    See Also
+    --------
+    blackman, hanning
+
+    Notes
+    -----
+    The Hamming window is defined as
+
+    .. math::  w(n) = 0.54 - 0.46cos\left(\frac{2\pi{n}}{M-1}\right)
+               \qquad 0 \leq n \leq M-1
+
+    The Hamming was named for R. W. Hamming, an associate of J. W. Tukey
+    and is described in Blackman and Tukey. It was recommended for
+    smoothing the truncated autocovariance function in the time domain.
+    Most references to the Hamming window come from the signal processing
+    literature, where it is used as one of many windowing functions for
+    smoothing values.  It is also known as an apodization (which means
+    "removing the foot", i.e. smoothing discontinuities at the beginning
+    and end of the sampled signal) or tapering function.
+
+    References
+    ----------
+    .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power
+           spectra, Dover Publications, New York.
+    .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The
+           University of Alberta Press, 1975, pp. 109-110.
+    .. [3] Wikipedia, "Window function",
+           https://en.wikipedia.org/wiki/Window_function
+    .. [4] W.H. Press,  B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
+           "Numerical Recipes", Cambridge University Press, 1986, page 425.
+
+    Examples
+    --------
+    >>> np.hamming(12)
+    array([0.08      , 0.15302338, 0.34890913, 0.60546482, 0.84123599,
+           0.98136679, 0.98136677, 0.84123585, 0.60546469, 0.34890905,
+           0.15302328, 0.08      ], dtype=float64)
+
+    Plot the window and its frequency response:
+
+    >>> import matplotlib.pyplot as plt
+    >>> window = np.hamming(51)
+    >>> plt.plot(window.asnumpy())
+    [<matplotlib.lines.Line2D object at 0x...>]
+    >>> plt.title("hamming window")
+    Text(0.5, 1.0, 'hamming window')
+    >>> plt.ylabel("Amplitude")
+    Text(0, 0.5, 'Amplitude')
+    >>> plt.xlabel("Sample")
+    Text(0.5, 0, 'Sample')
+    >>> plt.show()
+    """
+    if dtype is None:
+        dtype = _np.float64
+    if ctx is None:
+        ctx = current_context()
+    return _npi.hamming(M, dtype=dtype, ctx=ctx)
+
+
+@set_module('mxnet.ndarray.numpy')
+def blackman(M, dtype=_np.float64, ctx=None):
+    r"""Return the Blackman window.
+
+    The Blackman window is a taper formed by using the first three
+    terms of a summation of cosines. It was designed to have close to the
+    minimal leakage possible.  It is close to optimal, only slightly worse
+    than a Kaiser window.
+
+    Parameters
+    ----------
+    M : int
+        Number of points in the output window. If zero or less, an
+        empty array is returned.
+    dtype : str or numpy.dtype, optional
+        An optional value type. Default is `numpy.float64`. Note that you need
+        select numpy.float32 or float64 in this operator.
+    ctx : Context, optional
+        An optional device context (default is the current default context).
+
+    Returns
+    -------
+    out : ndarray
+        The window, with the maximum value normalized to one (the value one
+        appears only if the number of samples is odd).
+
+    See Also
+    --------
+    bartlett, hamming, hanning, kaiser
+
+    Notes
+    -----
+    The Blackman window is defined as
+
+    .. math::  w(n) = 0.42 - 0.5 \cos(2\pi n/{M-1}) + 0.08 \cos(4\pi n/{M-1})
+
+    Most references to the Blackman window come from the signal processing
+    literature, where it is used as one of many windowing functions for
+    smoothing values.  It is also known as an apodization (which means
+    "removing the foot", i.e. smoothing discontinuities at the beginning
+    and end of the sampled signal) or tapering function. It is known as a
+    "near optimal" tapering function, almost as good (by some measures)
+    as the kaiser window.
+
+    References
+    ----------
+    Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra,
+    Dover Publications, New York.
+
+    Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing.
+    Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471.
+
+    See Also
+    --------
+    hamming, hanning
+
+    Notes
+    -----
+    The Blackman window is defined as
+
+    .. math::  w(n) = 0.42 - 0.5 \cos(2\pi n/{M-1}) + 0.08 \cos(4\pi n/{M-1})
+
+    Most references to the Blackman window come from the signal processing
+    literature, where it is used as one of many windowing functions for
+    smoothing values.  It is also known as an apodization (which means
+    "removing the foot", i.e. smoothing discontinuities at the beginning
+    and end of the sampled signal) or tapering function. It is known as a
+    "near optimal" tapering function, almost as good (by some measures)
+    as the kaiser window.
+
+    References
+    ----------
+    Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra,
+    Dover Publications, New York.
+
+    Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing.
+    Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471.
+
+    Examples
+    --------
+    >>> np.blackman(12)
+    array([-1.38777878e-17,  3.26064393e-02,  1.59903660e-01,  4.14397978e-01,
+            7.36045260e-01,  9.67046812e-01,  9.67046772e-01,  7.36045039e-01,
+            4.14397819e-01,  1.59903601e-01,  3.26063877e-02,  3.82194276e-14], dtype=float64)
+
+    Plot the window and its frequency response:
+
+    >>> import matplotlib.pyplot as plt
+    >>> window = np.blackman(51)
+    >>> plt.plot(window.asnumpy())
+    [<matplotlib.lines.Line2D object at 0x...>]
+    >>> plt.title("blackman window")
+    Text(0.5, 1.0, 'blackman window')
+    >>> plt.ylabel("Amplitude")
+    Text(0, 0.5, 'Amplitude')
+    >>> plt.xlabel("Sample")
+    Text(0.5, 0, 'Sample')
+    >>> plt.show()
+    """
+    if dtype is None:
+        dtype = _np.float64
+    if ctx is None:
+        ctx = current_context()
+    return _npi.blackman(M, dtype=dtype, ctx=ctx)