add numpy op hanning, hamming, blackman (apache#15815)

address test file

fix test file

make default dtype is float32

python/mxnet/ndarray/numpy/_op.py

@@ -34,7 +34,7 @@
            'trunc', 'logical_not', 'arcsinh', 'arccosh', 'arctanh', 'tensordot',
            'linspace', 'expand_dims', 'tile', 'arange', 'split', 'concatenate', 'stack', 'vstack', 'mean',
            'maximum', 'minimum', 'swapaxes', 'clip', 'argmax', 'std', 'var', 'indices', 'copysign',
-           'ravel']
+           'ravel', 'hanning', 'hamming', 'blackman']
 
 
 @set_module('mxnet.ndarray.numpy')
@@ -2588,3 +2588,243 @@ def ravel(x, order='C'):
         return _npi.reshape(x, -1)
     else:
         raise TypeError('type {} not supported'.format(str(type(x))))
+
+
+@set_module('mxnet.ndarray.numpy')
+def hanning(M, dtype=_np.float32, 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 `float32`. 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.        , 0.07937324, 0.29229254, 0.5711574 , 0.8274304 ,
+           0.9797465 , 0.97974646, 0.82743025, 0.5711573 , 0.29229245,
+           0.07937312, 0.        ])
+
+    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 ctx is None:
+        ctx = current_context()
+    return _npi.hanning(M, dtype=dtype, ctx=ctx)
+
+
+@set_module('mxnet.ndarray.numpy')
+def hamming(M, dtype=_np.float32, 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 `float32`. 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([0.08000001, 0.15302339, 0.34890914, 0.6054648 , 0.841236  ,
+           0.9813669 , 0.9813668 , 0.8412359 , 0.6054647 , 0.34890908,
+           0.15302327, 0.08000001])
+
+    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 ctx is None:
+        ctx = current_context()
+    return _npi.hamming(M, dtype=dtype, ctx=ctx)
+
+
+@set_module('mxnet.ndarray.numpy')
+def blackman(M, dtype=_np.float32, 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 `float32`. 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
+    --------
+    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([-1.4901161e-08,  3.2606423e-02,  1.5990365e-01,  4.1439798e-01,
+            7.3604530e-01,  9.6704686e-01,  9.6704674e-01,  7.3604506e-01,
+            4.1439781e-01,  1.5990359e-01,  3.2606363e-02, -1.4901161e-08])
+
+    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 ctx is None:
+        ctx = current_context()
+    return _npi.blackman(M, dtype=dtype, ctx=ctx)