# Copyright (c) 2021 PaddlePaddle Authors. All Rights Reserved
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
import math
from typing import List
from typing import Tuple
from typing import Union
import paddle
from paddle import Tensor
__all__ = [
'get_window',
]
def _cat(a: List[Tensor], data_type: str) -> Tensor:
l = [paddle.to_tensor(_a, data_type) for _a in a]
return paddle.concat(l)
def _acosh(x: Union[Tensor, float]) -> Tensor:
if isinstance(x, float):
return math.log(x + math.sqrt(x**2 - 1))
return paddle.log(x + paddle.sqrt(paddle.square(x) - 1))
def _extend(M: int, sym: bool) -> bool:
"""Extend window by 1 sample if needed for DFT-even symmetry"""
if not sym:
return M + 1, True
else:
return M, False
def _len_guards(M: int) -> bool:
"""Handle small or incorrect window lengths"""
if int(M) != M or M < 0:
raise ValueError('Window length M must be a non-negative integer')
return M <= 1
def _truncate(w: Tensor, needed: bool) -> Tensor:
"""Truncate window by 1 sample if needed for DFT-even symmetry"""
if needed:
return w[:-1]
else:
return w
def general_gaussian(M: int, p, sig, sym: bool=True,
dtype: str='float64') -> Tensor:
"""Compute a window with a generalized Gaussian shape.
This function is consistent with scipy.signal.windows.general_gaussian().
"""
if _len_guards(M):
return paddle.ones((M, ), dtype=dtype)
M, needs_trunc = _extend(M, sym)
n = paddle.arange(0, M, dtype=dtype) - (M - 1.0) / 2.0
w = paddle.exp(-0.5 * paddle.abs(n / sig)**(2 * p))
return _truncate(w, needs_trunc)
def general_hamming(M: int, alpha: float, sym: bool=True,
dtype: str='float64') -> Tensor:
"""Compute a generalized Hamming window.
This function is consistent with scipy.signal.windows.general_hamming()
"""
return general_cosine(M, [alpha, 1. - alpha], sym, dtype=dtype)
def taylor(M: int,
nbar=4,
sll=30,
norm=True,
sym: bool=True,
dtype: str='float64') -> Tensor:
"""Compute a Taylor window.
The Taylor window taper function approximates the Dolph-Chebyshev window's
constant sidelobe level for a parameterized number of near-in sidelobes.
Parameters:
M(int): window size
nbar, sil, norm: the window-specific parameter.
sym(bool)：whether to return symmetric window.
The default value is True
dtype(str): the datatype of returned tensor.
Returns:
Tensor: the window tensor
"""
if _len_guards(M):
return paddle.ones((M, ), dtype=dtype)
M, needs_trunc = _extend(M, sym)
# Original text uses a negative sidelobe level parameter and then negates
# it in the calculation of B. To keep consistent with other methods we
# assume the sidelobe level parameter to be positive.
B = 10**(sll / 20)
A = _acosh(B) / math.pi
s2 = nbar**2 / (A**2 + (nbar - 0.5)**2)
ma = paddle.arange(1, nbar, dtype=dtype)
Fm = paddle.empty((nbar - 1, ), dtype=dtype)
signs = paddle.empty_like(ma)
signs[::2] = 1
signs[1::2] = -1
m2 = ma * ma
for mi in range(len(ma)):
numer = signs[mi] * paddle.prod(1 - m2[mi] / s2 / (A**2 + (ma - 0.5)**2
))
if mi == 0:
denom = 2 * paddle.prod(1 - m2[mi] / m2[mi + 1:])
elif mi == len(ma) - 1:
denom = 2 * paddle.prod(1 - m2[mi] / m2[:mi])
else:
denom = 2 * paddle.prod(1 - m2[mi] / m2[:mi]) * paddle.prod(1 - m2[
mi] / m2[mi + 1:])
Fm[mi] = numer / denom
def W(n):
return 1 + 2 * paddle.matmul(
Fm.unsqueeze(0),
paddle.cos(2 * math.pi * ma.unsqueeze(1) * (n - M / 2. + 0.5) / M))
w = W(paddle.arange(0, M, dtype=dtype))
# normalize (Note that this is not described in the original text [1])
if norm:
scale = 1.0 / W((M - 1) / 2)
w *= scale
w = w.squeeze()
return _truncate(w, needs_trunc)
def general_cosine(M: int, a: float, sym: bool=True,
dtype: str='float64') -> Tensor:
"""Compute a generic weighted sum of cosine terms window.
This function is consistent with scipy.signal.windows.general_cosine().
"""
if _len_guards(M):
return paddle.ones((M, ), dtype=dtype)
M, needs_trunc = _extend(M, sym)
fac = paddle.linspace(-math.pi, math.pi, M, dtype=dtype)
w = paddle.zeros((M, ), dtype=dtype)
for k in range(len(a)):
w += a[k] * paddle.cos(k * fac)
return _truncate(w, needs_trunc)
def hamming(M: int, sym: bool=True, dtype: str='float64') -> Tensor:
"""Compute a Hamming window.
The Hamming window is a taper formed by using a raised cosine with
non-zero endpoints, optimized to minimize the nearest side lobe.
Parameters:
M(int): window size
sym(bool)：whether to return symmetric window.
The default value is True
dtype(str): the datatype of returned tensor.
Returns:
Tensor: the window tensor
"""
return general_hamming(M, 0.54, sym, dtype=dtype)
def hann(M: int, sym: bool=True, dtype: str='float64') -> Tensor:
"""Compute a Hann window.
The Hann window is a taper formed by using a raised cosine or sine-squared
with ends that touch zero.
Parameters:
M(int): window size
sym(bool)：whether to return symmetric window.
The default value is True
dtype(str): the datatype of returned tensor.
Returns:
Tensor: the window tensor
"""
return general_hamming(M, 0.5, sym, dtype=dtype)
def tukey(M: int, alpha=0.5, sym: bool=True, dtype: str='float64') -> Tensor:
"""Compute a Tukey window.
The Tukey window is also known as a tapered cosine window.
Parameters:
M(int): window size
sym(bool)：whether to return symmetric window.
The default value is True
dtype(str): the datatype of returned tensor.
Returns:
Tensor: the window tensor
"""
if _len_guards(M):
return paddle.ones((M, ), dtype=dtype)
if alpha <= 0:
return paddle.ones((M, ), dtype=dtype)
elif alpha >= 1.0:
return hann(M, sym=sym)
M, needs_trunc = _extend(M, sym)
n = paddle.arange(0, M, dtype=dtype)
width = int(alpha * (M - 1) / 2.0)
n1 = n[0:width + 1]
n2 = n[width + 1:M - width - 1]
n3 = n[M - width - 1:]
w1 = 0.5 * (1 + paddle.cos(math.pi * (-1 + 2.0 * n1 / alpha / (M - 1))))
w2 = paddle.ones(n2.shape, dtype=dtype)
w3 = 0.5 * (1 + paddle.cos(math.pi * (-2.0 / alpha + 1 + 2.0 * n3 / alpha /
(M - 1))))
w = paddle.concat([w1, w2, w3])
return _truncate(w, needs_trunc)
def kaiser(M: int, beta: float, sym: bool=True, dtype: str='float64') -> Tensor:
"""Compute a Kaiser window.
The Kaiser window is a taper formed by using a Bessel function.
Parameters:
M(int): window size.
beta(float): the window-specific parameter.
sym(bool)：whether to return symmetric window.
The default value is True
Returns:
Tensor: the window tensor
"""
raise NotImplementedError()
def gaussian(M: int, std: float, sym: bool=True,
dtype: str='float64') -> Tensor:
"""Compute a Gaussian window.
The Gaussian widows has a Gaussian shape defined by the standard deviation(std).
Parameters:
M(int): window size.
std(float): the window-specific parameter.
sym(bool)：whether to return symmetric window.
The default value is True
dtype(str): the datatype of returned tensor.
Returns:
Tensor: the window tensor
"""
if _len_guards(M):
return paddle.ones((M, ), dtype=dtype)
M, needs_trunc = _extend(M, sym)
n = paddle.arange(0, M, dtype=dtype) - (M - 1.0) / 2.0
sig2 = 2 * std * std
w = paddle.exp(-n**2 / sig2)
return _truncate(w, needs_trunc)
def exponential(M: int,
center=None,
tau=1.,
sym: bool=True,
dtype: str='float64') -> Tensor:
"""Compute an exponential (or Poisson) window.
Parameters:
M(int): window size.
tau(float): the window-specific parameter.
sym(bool)：whether to return symmetric window.
The default value is True
dtype(str): the datatype of returned tensor.
Returns:
Tensor: the window tensor
"""
if sym and center is not None:
raise ValueError("If sym==True, center must be None.")
if _len_guards(M):
return paddle.ones((M, ), dtype=dtype)
M, needs_trunc = _extend(M, sym)
if center is None:
center = (M - 1) / 2
n = paddle.arange(0, M, dtype=dtype)
w = paddle.exp(-paddle.abs(n - center) / tau)
return _truncate(w, needs_trunc)
def triang(M: int, sym: bool=True, dtype: str='float64') -> Tensor:
"""Compute a triangular window.
Parameters:
M(int): window size.
sym(bool)：whether to return symmetric window.
The default value is True
dtype(str): the datatype of returned tensor.
Returns:
Tensor: the window tensor
"""
if _len_guards(M):
return paddle.ones((M, ), dtype=dtype)
M, needs_trunc = _extend(M, sym)
n = paddle.arange(1, (M + 1) // 2 + 1, dtype=dtype)
if M % 2 == 0:
w = (2 * n - 1.0) / M
w = paddle.concat([w, w[::-1]])
else:
w = 2 * n / (M + 1.0)
w = paddle.concat([w, w[-2::-1]])
return _truncate(w, needs_trunc)
def bohman(M: int, sym: bool=True, dtype: str='float64') -> Tensor:
"""Compute a Bohman window.
The Bohman window is the autocorrelation of a cosine window.
Parameters:
M(int): window size.
sym(bool)：whether to return symmetric window.
The default value is True
dtype(str): the datatype of returned tensor.
Returns:
Tensor: the window tensor
"""
if _len_guards(M):
return paddle.ones((M, ), dtype=dtype)
M, needs_trunc = _extend(M, sym)
fac = paddle.abs(paddle.linspace(-1, 1, M, dtype=dtype)[1:-1])
w = (1 - fac) * paddle.cos(math.pi * fac) + 1.0 / math.pi * paddle.sin(
math.pi * fac)
w = _cat([0, w, 0], dtype)
return _truncate(w, needs_trunc)
def blackman(M: int, sym: bool=True, dtype: str='float64') -> Tensor:
"""Compute a 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): window size.
sym(bool)：whether to return symmetric window.
The default value is True
dtype(str): the datatype of returned tensor.
Returns:
Tensor: the window tensor
"""
return general_cosine(M, [0.42, 0.50, 0.08], sym, dtype=dtype)
def cosine(M: int, sym: bool=True, dtype: str='float64') -> Tensor:
"""Compute a window with a simple cosine shape.
Parameters:
M(int): window size.
sym(bool)：whether to return symmetric window.
The default value is True
dtype(str): the datatype of returned tensor.
Returns:
Tensor: the window tensor
"""
if _len_guards(M):
return paddle.ones((M, ), dtype=dtype)
M, needs_trunc = _extend(M, sym)
w = paddle.sin(math.pi / M * (paddle.arange(0, M, dtype=dtype) + .5))
return _truncate(w, needs_trunc)
def get_window(window: Union[str, Tuple[str, float]],
win_length: int,
fftbins: bool=True,
dtype: str='float64') -> Tensor:
"""Return a window of a given length and type.
Parameters:
window(str|(str,float)): the type of window to create.
win_length(int): the number of samples in the window.
fftbins(bool): If True, create a "periodic" window. Otherwise,
create a "symmetric" window, for use in filter design.
Returns:
The window represented as a tensor.
"""
sym = not fftbins
args = ()
if isinstance(window, tuple):
winstr = window[0]
if len(window) > 1:
args = window[1:]
elif isinstance(window, str):
if window in ['gaussian', 'exponential']:
raise ValueError("The '" + window + "' window needs one or "
"more parameters -- pass a tuple.")
else:
winstr = window
else:
raise ValueError("%s as window type is not supported." %
str(type(window)))
try:
winfunc = eval(winstr)
except KeyError as e:
raise ValueError("Unknown window type.") from e
params = (win_length, ) + args
kwargs = {'sym': sym}
return winfunc(*params, dtype=dtype, **kwargs)