the filter window (i.e., the number of coefficients).
    If `mode` is 'interp', `window_length` must be less than or equal
    to the size of `x`.
polyorder : int
    The order of the polynomial used to fit the samples.
    `polyorder` must be less than `window_length`.
deriv : int, optional
    The order of the derivative to compute. This must be a
    nonnegative integer. The default is 0, which means to filter
    the data without differentiating.
delta : float, optional
    The spacing of the samples to which the filter will be applied.
    This is only used if deriv > 0. Default is 1.0.
axis : int, optional
    The axis of the array `x` along which the filter is to be applied.
    Default is -1.
mode : str, optional
    Must be 'mirror', 'constant', 'nearest', 'wrap' or 'interp'. This
    determines the type of extension to use for the padded signal to
    which the filter is applied.  When `mode` is 'constant', the padding
    value is given by `cval`.  See the Notes for more details on 'mirror',
    'constant', 'wrap', and 'nearest'.
    When the 'interp' mode is selected (the default), no extension
    is used.  Instead, a degree `polyorder` polynomial is fit to the
    last `window_length` values of the edges, and this polynomial is
    used to evaluate the last `window_length // 2` output values.
cval : scalar, optional
    Value to fill past the edges of the input if `mode` is 'constant'.
    Default is 0.0.

Returns
-------
y : ndarray, same shape as `x`
    The filtered data.

See Also
--------
savgol_coeffs

Notes
-----
Details on the `mode` options:

    'mirror':
        Repeats the values at the edges in reverse order. The value
        closest to the edge is not included.
    'nearest':
        The extension contains the nearest input value.
    'constant':
        The extension contains the value given by the `cval` argument.
    'wrap':
        The extension contains the values from the other end of the array.

For example, if the input is [1, 2, 3, 4, 5, 6, 7, 8], and
`window_length` is 7, the following shows the extended data for
the various `mode` options (assuming `cval` is 0)::

    mode       |   Ext   |         Input          |   Ext
    -----------+---------+------------------------+---------
    'mirror'   | 4  3  2 | 1  2  3  4  5  6  7  8 | 7  6  5
    'nearest'  | 1  1  1 | 1  2  3  4  5  6  7  8 | 8  8  8
    'constant' | 0  0  0 | 1  2  3  4  5  6  7  8 | 0  0  0
    'wrap'     | 6  7  8 | 1  2  3  4  5  6  7  8 | 1  2  3

.. versionadded:: 0.14.0

Examples
--------
>>> import numpy as np
>>> from scipy.signal import savgol_filter
>>> np.set_printoptions(precision=2)  # For compact display.
>>> x = np.array([2, 2, 5, 2, 1, 0, 1, 4, 9])

Filter with a window length of 5 and a degree 2 polynomial.  Use
the defaults for all other parameters.

>>> savgol_filter(x, 5, 2)
array([1.66, 3.17, 3.54, 2.86, 0.66, 0.17, 1.  , 4.  , 9.  ])

Note that the last five values in x are samples of a parabola, so
when mode='interp' (the default) is used with polyorder=2, the last
three values are unchanged. Compare that to, for example,
`mode='nearest'`:

>>> savgol_filter(x, 5, 2, mode='nearest')
array([1.74, 3.03, 3.54, 2.86, 0.66, 0.17, 1.  , 4.6 , 7.97])

)