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paddlepaddle--paddle/python/paddle/audio/functional/window.py
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# Copyright (c) 2022 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
from __future__ import annotations
import math
import warnings
from typing import TYPE_CHECKING
import numpy as np
import paddle
if TYPE_CHECKING:
from paddle import Tensor
from paddle._typing import PlaceLike
from ..features.layers import _WindowLiteral
from paddle.base.framework import (
_current_expected_place,
_get_paddle_place,
_to_pinned_place,
in_dynamic_or_pir_mode,
)
class WindowFunctionRegister:
def __init__(self):
self._functions_dict = {}
def register(self, func=None):
def add_subfunction(func):
name = func.__name__
self._functions_dict[name] = func
return func
return add_subfunction
def get(self, name):
return self._functions_dict[name]
window_function_register = WindowFunctionRegister()
@window_function_register.register()
def _cat(x: list[Tensor], data_type: str) -> Tensor:
l = []
for t in x:
if np.isscalar(t) and not isinstance(t, str):
l.append(paddle.to_tensor([t], data_type))
else:
l.append(paddle.to_tensor(t, data_type))
return paddle.concat(l)
@window_function_register.register()
def _bartlett(M: int, sym: bool = True, dtype: str = 'float64') -> Tensor:
"""
Computes the Bartlett window.
This function is consistent with scipy.signal.windows.bartlett().
"""
if _len_guards(M):
return paddle.ones((M,), dtype=dtype)
M, needs_trunc = _extend(M, sym)
n = paddle.arange(0, M, dtype=dtype)
M = paddle.to_tensor(M, dtype=dtype)
w = paddle.where(
paddle.less_equal(n, (M - 1) / 2.0),
2.0 * n / (M - 1),
2.0 - 2.0 * n / (M - 1),
)
return _truncate(w, needs_trunc)
@window_function_register.register()
def _kaiser(
M: int, beta: float, sym: bool = True, dtype: str = 'float64'
) -> Tensor:
"""Compute the Kaiser window.
This function is consistent with scipy.signal.windows.kaiser().
"""
if _len_guards(M):
return paddle.ones((M,), dtype=dtype)
M, needs_trunc = _extend(M, sym)
beta = paddle.to_tensor(beta, dtype=dtype)
n = paddle.arange(0, M, dtype=dtype)
M = paddle.to_tensor(M, dtype=dtype)
alpha = (M - 1) / 2.0
w = paddle.i0(
beta * paddle.sqrt(1 - ((n - alpha) / alpha) ** 2.0)
) / paddle.i0(beta)
return _truncate(w, needs_trunc)
@window_function_register.register()
def _nuttall(M: int, sym: bool = True, dtype: str = 'float64') -> Tensor:
"""Nuttall window.
This function is consistent with scipy.signal.windows.nuttall().
"""
a = paddle.to_tensor(
[0.3635819, 0.4891775, 0.1365995, 0.0106411], dtype=dtype
)
return _general_cosine(M, a=a, sym=sym, dtype=dtype)
@window_function_register.register()
def _acosh(x: 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))
@window_function_register.register()
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
@window_function_register.register()
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
@window_function_register.register()
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
@window_function_register.register()
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)
@window_function_register.register()
def _general_cosine(
M: int, a: list[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)
@window_function_register.register()
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, 1.0 - alpha], sym, dtype=dtype)
@window_function_register.register()
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.
"""
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)):
number = 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] = number / denom
def W(n):
return 1 + 2 * paddle.matmul(
Fm.unsqueeze(0),
paddle.cos(2 * math.pi * ma.unsqueeze(1) * (n - M / 2.0 + 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)
@window_function_register.register()
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.
"""
return _general_hamming(M, 0.54, sym, dtype=dtype)
@window_function_register.register()
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.
"""
return _general_hamming(M, 0.5, sym, dtype=dtype)
@window_function_register.register()
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.
"""
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)
@window_function_register.register()
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).
"""
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)
@window_function_register.register()
def _exponential(
M: int, center=None, tau=1.0, sym: bool = True, dtype: str = 'float64'
) -> Tensor:
"""Compute an exponential (or Poisson) window."""
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)
@window_function_register.register()
def _triang(M: int, sym: bool = True, dtype: str = 'float64') -> Tensor:
"""Compute a triangular window."""
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)
@window_function_register.register()
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.
"""
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)
@window_function_register.register()
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.
"""
return _general_cosine(M, [0.42, 0.50, 0.08], sym, dtype=dtype)
@window_function_register.register()
def _cosine(M: int, sym: bool = True, dtype: str = 'float64') -> Tensor:
"""Compute a window with a simple cosine shape."""
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) + 0.5))
return _truncate(w, needs_trunc)
def get_window(
window: _WindowLiteral | tuple[_WindowLiteral, float],
win_length: int,
fftbins: bool = True,
dtype: str | None = 'float64',
) -> Tensor:
"""Return a window of a given length and type.
Args:
window (Union[str, Tuple[str, float]]): The window function applied to the signal before the Fourier transform. Supported window functions: 'hamming', 'hann', 'gaussian', 'general_gaussian', 'exponential', 'triang', 'bohman', 'blackman', 'cosine', 'tukey', 'taylor', 'bartlett', 'kaiser', 'nuttall'.
win_length (int): Number of samples.
fftbins (bool, optional): If True, create a "periodic" window. Otherwise, create a "symmetric" window, for use in filter design. Defaults to True.
dtype (str, optional): The data type of the return window. Defaults to 'float64'.
Returns:
Tensor: The window represented as a tensor.
Examples:
.. code-block:: pycon
>>> import paddle
>>> n_fft = 512
>>> cosine_window = paddle.audio.functional.get_window('cosine', n_fft)
>>> std = 7
>>> gaussian_window = paddle.audio.functional.get_window(('gaussian', std), n_fft)
"""
if dtype is None:
dtype = 'float32'
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', 'kaiser']:
raise ValueError(
"The '" + window + "' window needs one or "
"more parameters -- pass a tuple."
)
else:
winstr = window
else:
raise ValueError(f"{type(window)} as window type is not supported.")
try:
winfunc = window_function_register.get('_' + 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)
def _apply_window_postprocess(
w: Tensor,
*,
layout: str | None = None,
device: PlaceLike | None = None,
pin_memory: bool = False,
requires_grad: bool = False,
) -> Tensor:
if layout not in (None, 'strided'):
raise RuntimeError(
"Window functions only support layout='strided' or None"
)
if layout is not None:
warnings.warn("layout only supports 'strided' in Paddle; ignored")
if in_dynamic_or_pir_mode():
device = (
_get_paddle_place(device)
if device is not None
else _current_expected_place()
)
if pin_memory and paddle.in_dynamic_mode() and device is not None:
device = _to_pinned_place(device)
w = w.to(device=device)
if pin_memory and paddle.in_dynamic_mode():
w = w.pin_memory()
if requires_grad is True:
w.stop_gradient = False
return w
def hamming_window(
window_length: int,
periodic: bool = True,
alpha: float = 0.54,
beta: float = 0.46,
*,
dtype: str = 'float32',
layout: str | None = None,
device: PlaceLike | None = None,
pin_memory: bool = False,
requires_grad: bool = False,
):
"""
Compute a generalized Hamming window.
Args:
window_length (int): The size of the returned window. Must be positive.
periodic (bool, optional): If True, returns a window for use as a periodic function; if False, returns a symmetric window. Defaults to True.
alpha (float, optional): The coefficient α in the equation above. Defaults to 0.54.
beta (float, optional): The coefficient β in the equation above. Defaults to 0.46.
dtype (str, optional): The data type of the returned tensor. Defaults to 'float32'.
layout (str, optional): Only included for API consistency with PyTorch; ignored in Paddle. Defaults to None.
device(PlaceLike|None, optional): The desired device of returned tensor.
if None, uses the current device for the default tensor type (see paddle.device.set_device()).
device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types. Default: None.
pin_memory(bool, optional): If set, return tensor would be allocated in the pinned memory. Works only for CPU tensors. Default: False
requires_grad(bool, optional): If autograd should record operations on the returned tensor. Default: False.
Returns:
Tensor: A 1-D tensor of shape `(window_length,)` containing the Hamming window.
Examples:
.. code-block:: pycon
>>> import paddle
>>> win = paddle.hamming_window(400, requires_grad=True)
>>> win = paddle.hamming_window(256, alpha=0.5, beta=0.5)
"""
w0 = get_window('hamming', window_length, fftbins=periodic, dtype=dtype)
alpha0, beta0 = 0.54, 0.46
B = beta / beta0
A = alpha - B * alpha0
w = A + B * w0
return _apply_window_postprocess(
w,
layout=layout,
device=device,
pin_memory=pin_memory,
requires_grad=requires_grad,
)
def hann_window(
window_length: int,
periodic: bool = True,
*,
dtype: str = 'float32',
layout: str | None = None,
device: PlaceLike | None = None,
pin_memory: bool = False,
requires_grad: bool = False,
):
"""
Compute a Hann window.
Args:
window_length (int): The size of the returned window. Must be positive.
periodic (bool, optional): If True, returns a window for use as a periodic function; if False, returns a symmetric window. Defaults to True.
dtype (str, optional): The data type of the returned tensor. Defaults to 'float32'.
layout (str, optional): Only included for API consistency with PyTorch; ignored in Paddle. Defaults to None.
device(PlaceLike|None, optional): The desired device of returned tensor.
if None, uses the current device for the default tensor type (see paddle.device.set_device()).
device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types. Default: None.
pin_memory(bool, optional): If set, return tensor would be allocated in the pinned memory. Works only for CPU tensors. Default: False
requires_grad(bool, optional): If autograd should record operations on the returned tensor. Default: False.
Returns:
Tensor: A 1-D tensor of shape `(window_length,)` containing the Hann window.
Examples:
.. code-block:: pycon
>>> import paddle
>>> win = paddle.hann_window(512)
>>> win = paddle.hann_window(512, requires_grad=True)
"""
w = get_window('hann', window_length, fftbins=periodic, dtype=dtype)
return _apply_window_postprocess(
w,
layout=layout,
device=device,
pin_memory=pin_memory,
requires_grad=requires_grad,
)
def kaiser_window(
window_length: int,
periodic: bool = True,
beta: float = 12.0,
*,
dtype: str | None = 'float32',
layout: str | None = None,
device: PlaceLike | None = None,
pin_memory: bool = False,
requires_grad: bool = False,
out: Tensor | None = None,
):
"""
Compute a Kaiser window.
Args:
window_length (int): The size of the returned window. Must be positive.
periodic (bool, optional): If True, returns a window for use as a periodic function; if False, returns a symmetric window. Defaults to True.
beta (float, optional): Shape parameter for the window. Defaults to 12.0.
dtype (str, optional): The data type of the returned tensor. Defaults to 'float32'.
layout (str, optional): Only included for API consistency with PyTorch; ignored in Paddle. Defaults to None.
device(PlaceLike|None, optional): The desired device of returned tensor.
if None, uses the current device for the default tensor type (see paddle.device.set_device()).
device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types. Default: None.
pin_memory(bool, optional): If set, return tensor would be allocated in the pinned memory. Works only for CPU tensors. Default: False
requires_grad(bool, optional): If autograd should record operations on the returned tensor. Default: False.
out(Tensor|None, optional): The output tensor. Default: None.
Returns:
Tensor: A 1-D tensor of shape `(window_length,)` containing the Kaiser window.
Examples:
.. code-block:: pycon
>>> import paddle
>>> win = paddle.kaiser_window(400, beta=8.6)
>>> win = paddle.kaiser_window(400, requires_grad=True)
"""
w = get_window(
('kaiser', beta), window_length, fftbins=periodic, dtype=dtype
)
w = _apply_window_postprocess(
w,
layout=layout,
device=device,
pin_memory=pin_memory,
requires_grad=requires_grad,
)
return paddle.assign(w, out) if out is not None else w
def blackman_window(
window_length: int,
periodic: bool = True,
*,
dtype: str = 'float32',
layout: str | None = None,
device: PlaceLike | None = None,
pin_memory: bool = False,
requires_grad: bool = False,
):
"""
Compute a Blackman window.
Args:
window_length (int): The size of the returned window. Must be positive.
periodic (bool, optional): If True, returns a window for use as a periodic function; if False, returns a symmetric window. Defaults to True.
dtype (str, optional): The data type of the returned tensor. Defaults to 'float32'.
layout (str, optional): Only included for API consistency with PyTorch; ignored in Paddle. Defaults to None.
device(PlaceLike|None, optional): The desired device of returned tensor.
if None, uses the current device for the default tensor type (see paddle.device.set_device()).
device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types. Default: None.
pin_memory(bool, optional): If set, return tensor would be allocated in the pinned memory. Works only for CPU tensors. Default: False
requires_grad(bool, optional): If autograd should record operations on the returned tensor. Default: False.
Returns:
Tensor: A 1-D tensor of shape `(window_length,)` containing the Blackman window.
Examples:
.. code-block:: pycon
>>> import paddle
>>> win = paddle.blackman_window(256)
>>> win = paddle.blackman_window(256, requires_grad=True)
"""
w = get_window('blackman', window_length, fftbins=periodic, dtype=dtype)
return _apply_window_postprocess(
w,
layout=layout,
device=device,
pin_memory=pin_memory,
requires_grad=requires_grad,
)
def bartlett_window(
window_length: int,
periodic: bool = True,
*,
dtype: str = 'float32',
layout: str | None = None,
device: PlaceLike | None = None,
pin_memory: bool = False,
requires_grad: bool = False,
):
"""
Compute a Bartlett window.
Args:
window_length (int): The size of the returned window. Must be positive.
periodic (bool, optional): If True, returns a window for use as a periodic function; if False, returns a symmetric window. Defaults to True.
dtype (str, optional): The data type of the returned tensor. Defaults to 'float32'.
layout (str, optional): Only included for API consistency with PyTorch; ignored in Paddle. Defaults to None.
device(PlaceLike|None, optional): The desired device of returned tensor.
if None, uses the current device for the default tensor type (see paddle.device.set_device()).
device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types. Default: None.
pin_memory(bool, optional): If set, return tensor would be allocated in the pinned memory. Works only for CPU tensors. Default: False
requires_grad(bool, optional): If autograd should record operations on the returned tensor. Default: False.
Returns:
Tensor: A 1-D tensor of shape `(window_length,)` containing the Bartlett window.
Examples:
.. code-block:: pycon
>>> import paddle
>>> n_fft = 512
>>> win = paddle.bartlett_window(n_fft)
>>> win = paddle.bartlett_window(n_fft, requires_grad=True)
"""
w = get_window('bartlett', window_length, fftbins=periodic, dtype=dtype)
return _apply_window_postprocess(
w,
layout=layout,
device=device,
pin_memory=pin_memory,
requires_grad=requires_grad,
)