| from typing import Optional, Iterable |
| |
| import torch |
| from math import sqrt |
| |
| from torch import Tensor |
| from torch._torch_docs import factory_common_args, parse_kwargs, merge_dicts |
| |
| __all__ = [ |
| 'bartlett', |
| 'blackman', |
| 'cosine', |
| 'exponential', |
| 'gaussian', |
| 'general_cosine', |
| 'general_hamming', |
| 'hamming', |
| 'hann', |
| 'kaiser', |
| 'nuttall', |
| ] |
| |
| window_common_args = merge_dicts( |
| parse_kwargs( |
| """ |
| M (int): the length of the window. |
| In other words, the number of points of the returned window. |
| sym (bool, optional): If `False`, returns a periodic window suitable for use in spectral analysis. |
| If `True`, returns a symmetric window suitable for use in filter design. Default: `True`. |
| """ |
| ), |
| factory_common_args, |
| { |
| "normalization": "The window is normalized to 1 (maximum value is 1). However, the 1 doesn't appear if " |
| ":attr:`M` is even and :attr:`sym` is `True`.", |
| } |
| ) |
| |
| |
| def _add_docstr(*args): |
| r"""Adds docstrings to a given decorated function. |
| |
| Specially useful when then docstrings needs string interpolation, e.g., with |
| str.format(). |
| REMARK: Do not use this function if the docstring doesn't need string |
| interpolation, just write a conventional docstring. |
| |
| Args: |
| args (str): |
| """ |
| |
| def decorator(o): |
| o.__doc__ = "".join(args) |
| return o |
| |
| return decorator |
| |
| |
| def _window_function_checks(function_name: str, M: int, dtype: torch.dtype, layout: torch.layout) -> None: |
| r"""Performs common checks for all the defined windows. |
| This function should be called before computing any window. |
| |
| Args: |
| function_name (str): name of the window function. |
| M (int): length of the window. |
| dtype (:class:`torch.dtype`): the desired data type of returned tensor. |
| layout (:class:`torch.layout`): the desired layout of returned tensor. |
| """ |
| if M < 0: |
| raise ValueError(f'{function_name} requires non-negative window length, got M={M}') |
| if layout is not torch.strided: |
| raise ValueError(f'{function_name} is implemented for strided tensors only, got: {layout}') |
| if dtype not in [torch.float32, torch.float64]: |
| raise ValueError(f'{function_name} expects float32 or float64 dtypes, got: {dtype}') |
| |
| |
| @_add_docstr( |
| r""" |
| Computes a window with an exponential waveform. |
| Also known as Poisson window. |
| |
| The exponential window is defined as follows: |
| |
| .. math:: |
| w_n = \exp{\left(-\frac{|n - c|}{\tau}\right)} |
| |
| where `c` is the ``center`` of the window. |
| """, |
| r""" |
| |
| {normalization} |
| |
| Args: |
| {M} |
| |
| Keyword args: |
| center (float, optional): where the center of the window will be located. |
| Default: `M / 2` if `sym` is `False`, else `(M - 1) / 2`. |
| tau (float, optional): the decay value. |
| Tau is generally associated with a percentage, that means, that the value should |
| vary within the interval (0, 100]. If tau is 100, it is considered the uniform window. |
| Default: 1.0. |
| {sym} |
| {dtype} |
| {layout} |
| {device} |
| {requires_grad} |
| |
| Examples:: |
| |
| >>> # Generates a symmetric exponential window of size 10 and with a decay value of 1.0. |
| >>> # The center will be at (M - 1) / 2, where M is 10. |
| >>> torch.signal.windows.exponential(10) |
| tensor([0.0111, 0.0302, 0.0821, 0.2231, 0.6065, 0.6065, 0.2231, 0.0821, 0.0302, 0.0111]) |
| |
| >>> # Generates a periodic exponential window and decay factor equal to .5 |
| >>> torch.signal.windows.exponential(10, sym=False,tau=.5) |
| tensor([4.5400e-05, 3.3546e-04, 2.4788e-03, 1.8316e-02, 1.3534e-01, 1.0000e+00, 1.3534e-01, 1.8316e-02, 2.4788e-03, 3.3546e-04]) |
| """.format( |
| **window_common_args |
| ), |
| ) |
| def exponential( |
| M: int, |
| *, |
| center: Optional[float] = None, |
| tau: float = 1.0, |
| sym: bool = True, |
| dtype: Optional[torch.dtype] = None, |
| layout: torch.layout = torch.strided, |
| device: Optional[torch.device] = None, |
| requires_grad: bool = False |
| ) -> Tensor: |
| if dtype is None: |
| dtype = torch.get_default_dtype() |
| |
| _window_function_checks('exponential', M, dtype, layout) |
| |
| if tau <= 0: |
| raise ValueError(f'Tau must be positive, got: {tau} instead.') |
| |
| if sym and center is not None: |
| raise ValueError('Center must be None for symmetric windows') |
| |
| if M == 0: |
| return torch.empty((0,), dtype=dtype, layout=layout, device=device, requires_grad=requires_grad) |
| |
| if center is None: |
| center = (M if not sym and M > 1 else M - 1) / 2.0 |
| |
| constant = 1 / tau |
| |
| k = torch.linspace(start=-center * constant, |
| end=(-center + (M - 1)) * constant, |
| steps=M, |
| dtype=dtype, |
| layout=layout, |
| device=device, |
| requires_grad=requires_grad) |
| |
| return torch.exp(-torch.abs(k)) |
| |
| |
| @_add_docstr( |
| r""" |
| Computes a window with a simple cosine waveform, following the same implementation as SciPy. |
| This window is also known as the sine window. |
| |
| The cosine window is defined as follows: |
| |
| .. math:: |
| w_n = \sin\left(\frac{\pi (n + 0.5)}{M}\right) |
| |
| This formula differs from the typical cosine window formula by incorporating a 0.5 term in the numerator, |
| which shifts the sample positions. This adjustment results in a window that starts and ends with non-zero values. |
| |
| """, |
| r""" |
| |
| {normalization} |
| |
| Args: |
| {M} |
| |
| Keyword args: |
| {sym} |
| {dtype} |
| {layout} |
| {device} |
| {requires_grad} |
| |
| Examples:: |
| |
| >>> # Generates a symmetric cosine window. |
| >>> torch.signal.windows.cosine(10) |
| tensor([0.1564, 0.4540, 0.7071, 0.8910, 0.9877, 0.9877, 0.8910, 0.7071, 0.4540, 0.1564]) |
| |
| >>> # Generates a periodic cosine window. |
| >>> torch.signal.windows.cosine(10, sym=False) |
| tensor([0.1423, 0.4154, 0.6549, 0.8413, 0.9595, 1.0000, 0.9595, 0.8413, 0.6549, 0.4154]) |
| """.format( |
| **window_common_args, |
| ), |
| ) |
| def cosine( |
| M: int, |
| *, |
| sym: bool = True, |
| dtype: Optional[torch.dtype] = None, |
| layout: torch.layout = torch.strided, |
| device: Optional[torch.device] = None, |
| requires_grad: bool = False |
| ) -> Tensor: |
| if dtype is None: |
| dtype = torch.get_default_dtype() |
| |
| _window_function_checks('cosine', M, dtype, layout) |
| |
| if M == 0: |
| return torch.empty((0,), dtype=dtype, layout=layout, device=device, requires_grad=requires_grad) |
| |
| start = 0.5 |
| constant = torch.pi / (M + 1 if not sym and M > 1 else M) |
| |
| k = torch.linspace(start=start * constant, |
| end=(start + (M - 1)) * constant, |
| steps=M, |
| dtype=dtype, |
| layout=layout, |
| device=device, |
| requires_grad=requires_grad) |
| |
| return torch.sin(k) |
| |
| |
| @_add_docstr( |
| r""" |
| Computes a window with a gaussian waveform. |
| |
| The gaussian window is defined as follows: |
| |
| .. math:: |
| w_n = \exp{\left(-\left(\frac{n}{2\sigma}\right)^2\right)} |
| """, |
| r""" |
| |
| {normalization} |
| |
| Args: |
| {M} |
| |
| Keyword args: |
| std (float, optional): the standard deviation of the gaussian. It controls how narrow or wide the window is. |
| Default: 1.0. |
| {sym} |
| {dtype} |
| {layout} |
| {device} |
| {requires_grad} |
| |
| Examples:: |
| |
| >>> # Generates a symmetric gaussian window with a standard deviation of 1.0. |
| >>> torch.signal.windows.gaussian(10) |
| tensor([4.0065e-05, 2.1875e-03, 4.3937e-02, 3.2465e-01, 8.8250e-01, 8.8250e-01, 3.2465e-01, 4.3937e-02, 2.1875e-03, 4.0065e-05]) |
| |
| >>> # Generates a periodic gaussian window and standard deviation equal to 0.9. |
| >>> torch.signal.windows.gaussian(10, sym=False,std=0.9) |
| tensor([1.9858e-07, 5.1365e-05, 3.8659e-03, 8.4658e-02, 5.3941e-01, 1.0000e+00, 5.3941e-01, 8.4658e-02, 3.8659e-03, 5.1365e-05]) |
| """.format( |
| **window_common_args, |
| ), |
| ) |
| def gaussian( |
| M: int, |
| *, |
| std: float = 1.0, |
| sym: bool = True, |
| dtype: Optional[torch.dtype] = None, |
| layout: torch.layout = torch.strided, |
| device: Optional[torch.device] = None, |
| requires_grad: bool = False |
| ) -> Tensor: |
| if dtype is None: |
| dtype = torch.get_default_dtype() |
| |
| _window_function_checks('gaussian', M, dtype, layout) |
| |
| if std <= 0: |
| raise ValueError(f'Standard deviation must be positive, got: {std} instead.') |
| |
| if M == 0: |
| return torch.empty((0,), dtype=dtype, layout=layout, device=device, requires_grad=requires_grad) |
| |
| start = -(M if not sym and M > 1 else M - 1) / 2.0 |
| |
| constant = 1 / (std * sqrt(2)) |
| |
| k = torch.linspace(start=start * constant, |
| end=(start + (M - 1)) * constant, |
| steps=M, |
| dtype=dtype, |
| layout=layout, |
| device=device, |
| requires_grad=requires_grad) |
| |
| return torch.exp(-k ** 2) |
| |
| |
| @_add_docstr( |
| r""" |
| Computes the Kaiser window. |
| |
| The Kaiser window is defined as follows: |
| |
| .. math:: |
| w_n = I_0 \left( \beta \sqrt{1 - \left( {\frac{n - N/2}{N/2}} \right) ^2 } \right) / I_0( \beta ) |
| |
| where ``I_0`` is the zeroth order modified Bessel function of the first kind (see :func:`torch.special.i0`), and |
| ``N = M - 1 if sym else M``. |
| """, |
| r""" |
| |
| {normalization} |
| |
| Args: |
| {M} |
| |
| Keyword args: |
| beta (float, optional): shape parameter for the window. Must be non-negative. Default: 12.0 |
| {sym} |
| {dtype} |
| {layout} |
| {device} |
| {requires_grad} |
| |
| Examples:: |
| |
| >>> # Generates a symmetric gaussian window with a standard deviation of 1.0. |
| >>> torch.signal.windows.kaiser(5) |
| tensor([4.0065e-05, 2.1875e-03, 4.3937e-02, 3.2465e-01, 8.8250e-01, 8.8250e-01, 3.2465e-01, 4.3937e-02, 2.1875e-03, 4.0065e-05]) |
| >>> # Generates a periodic gaussian window and standard deviation equal to 0.9. |
| >>> torch.signal.windows.kaiser(5, sym=False,std=0.9) |
| tensor([1.9858e-07, 5.1365e-05, 3.8659e-03, 8.4658e-02, 5.3941e-01, 1.0000e+00, 5.3941e-01, 8.4658e-02, 3.8659e-03, 5.1365e-05]) |
| """.format( |
| **window_common_args, |
| ), |
| ) |
| def kaiser( |
| M: int, |
| *, |
| beta: float = 12.0, |
| sym: bool = True, |
| dtype: Optional[torch.dtype] = None, |
| layout: torch.layout = torch.strided, |
| device: Optional[torch.device] = None, |
| requires_grad: bool = False |
| ) -> Tensor: |
| if dtype is None: |
| dtype = torch.get_default_dtype() |
| |
| _window_function_checks('kaiser', M, dtype, layout) |
| |
| if beta < 0: |
| raise ValueError(f'beta must be non-negative, got: {beta} instead.') |
| |
| if M == 0: |
| return torch.empty((0,), dtype=dtype, layout=layout, device=device, requires_grad=requires_grad) |
| |
| if M == 1: |
| return torch.ones((1,), dtype=dtype, layout=layout, device=device, requires_grad=requires_grad) |
| |
| # Avoid NaNs by casting `beta` to the appropriate dtype. |
| beta = torch.tensor(beta, dtype=dtype, device=device) |
| |
| start = -beta |
| constant = 2.0 * beta / (M if not sym else M - 1) |
| end = torch.minimum(beta, start + (M - 1) * constant) |
| |
| k = torch.linspace(start=start, |
| end=end, |
| steps=M, |
| dtype=dtype, |
| layout=layout, |
| device=device, |
| requires_grad=requires_grad) |
| |
| return torch.i0(torch.sqrt(beta * beta - torch.pow(k, 2))) / torch.i0(beta) |
| |
| |
| @_add_docstr( |
| r""" |
| Computes the Hamming window. |
| |
| The Hamming window is defined as follows: |
| |
| .. math:: |
| w_n = \alpha - \beta\ \cos \left( \frac{2 \pi n}{M - 1} \right) |
| """, |
| r""" |
| |
| {normalization} |
| |
| Arguments: |
| {M} |
| |
| Keyword args: |
| {sym} |
| alpha (float, optional): The coefficient :math:`\alpha` in the equation above. |
| beta (float, optional): The coefficient :math:`\beta` in the equation above. |
| {dtype} |
| {layout} |
| {device} |
| {requires_grad} |
| |
| Examples:: |
| |
| >>> # Generates a symmetric Hamming window. |
| >>> torch.signal.windows.hamming(10) |
| tensor([0.0800, 0.1876, 0.4601, 0.7700, 0.9723, 0.9723, 0.7700, 0.4601, 0.1876, 0.0800]) |
| |
| >>> # Generates a periodic Hamming window. |
| >>> torch.signal.windows.hamming(10, sym=False) |
| tensor([0.0800, 0.1679, 0.3979, 0.6821, 0.9121, 1.0000, 0.9121, 0.6821, 0.3979, 0.1679]) |
| """.format( |
| **window_common_args |
| ), |
| ) |
| def hamming(M: int, |
| *, |
| sym: bool = True, |
| dtype: Optional[torch.dtype] = None, |
| layout: torch.layout = torch.strided, |
| device: Optional[torch.device] = None, |
| requires_grad: bool = False) -> Tensor: |
| return general_hamming(M, sym=sym, dtype=dtype, layout=layout, device=device, requires_grad=requires_grad) |
| |
| |
| @_add_docstr( |
| r""" |
| Computes the Hann window. |
| |
| The Hann window is defined as follows: |
| |
| .. math:: |
| w_n = \frac{1}{2}\ \left[1 - \cos \left( \frac{2 \pi n}{M - 1} \right)\right] = |
| \sin^2 \left( \frac{\pi n}{M - 1} \right) |
| """, |
| r""" |
| |
| {normalization} |
| |
| Arguments: |
| {M} |
| |
| Keyword args: |
| {sym} |
| {dtype} |
| {layout} |
| {device} |
| {requires_grad} |
| |
| Examples:: |
| |
| >>> # Generates a symmetric Hann window. |
| >>> torch.signal.windows.hann(10) |
| tensor([0.0000, 0.1170, 0.4132, 0.7500, 0.9698, 0.9698, 0.7500, 0.4132, 0.1170, 0.0000]) |
| |
| >>> # Generates a periodic Hann window. |
| >>> torch.signal.windows.hann(10, sym=False) |
| tensor([0.0000, 0.0955, 0.3455, 0.6545, 0.9045, 1.0000, 0.9045, 0.6545, 0.3455, 0.0955]) |
| """.format( |
| **window_common_args |
| ), |
| ) |
| def hann(M: int, |
| *, |
| sym: bool = True, |
| dtype: Optional[torch.dtype] = None, |
| layout: torch.layout = torch.strided, |
| device: Optional[torch.device] = None, |
| requires_grad: bool = False) -> Tensor: |
| return general_hamming(M, |
| alpha=0.5, |
| sym=sym, |
| dtype=dtype, |
| layout=layout, |
| device=device, |
| requires_grad=requires_grad) |
| |
| |
| @_add_docstr( |
| r""" |
| Computes the Blackman window. |
| |
| The Blackman window is defined as follows: |
| |
| .. math:: |
| w_n = 0.42 - 0.5 \cos \left( \frac{2 \pi n}{M - 1} \right) + 0.08 \cos \left( \frac{4 \pi n}{M - 1} \right) |
| """, |
| r""" |
| |
| {normalization} |
| |
| Arguments: |
| {M} |
| |
| Keyword args: |
| {sym} |
| {dtype} |
| {layout} |
| {device} |
| {requires_grad} |
| |
| Examples:: |
| |
| >>> # Generates a symmetric Blackman window. |
| >>> torch.signal.windows.blackman(5) |
| tensor([-1.4901e-08, 3.4000e-01, 1.0000e+00, 3.4000e-01, -1.4901e-08]) |
| |
| >>> # Generates a periodic Blackman window. |
| >>> torch.signal.windows.blackman(5, sym=False) |
| tensor([-1.4901e-08, 2.0077e-01, 8.4923e-01, 8.4923e-01, 2.0077e-01]) |
| """.format( |
| **window_common_args |
| ), |
| ) |
| def blackman(M: int, |
| *, |
| sym: bool = True, |
| dtype: Optional[torch.dtype] = None, |
| layout: torch.layout = torch.strided, |
| device: Optional[torch.device] = None, |
| requires_grad: bool = False) -> Tensor: |
| if dtype is None: |
| dtype = torch.get_default_dtype() |
| |
| _window_function_checks('blackman', M, dtype, layout) |
| |
| return general_cosine(M, a=[0.42, 0.5, 0.08], sym=sym, dtype=dtype, layout=layout, device=device, |
| requires_grad=requires_grad) |
| |
| |
| @_add_docstr( |
| r""" |
| Computes the Bartlett window. |
| |
| The Bartlett window is defined as follows: |
| |
| .. math:: |
| w_n = 1 - \left| \frac{2n}{M - 1} - 1 \right| = \begin{cases} |
| \frac{2n}{M - 1} & \text{if } 0 \leq n \leq \frac{M - 1}{2} \\ |
| 2 - \frac{2n}{M - 1} & \text{if } \frac{M - 1}{2} < n < M \\ \end{cases} |
| """, |
| r""" |
| |
| {normalization} |
| |
| Arguments: |
| {M} |
| |
| Keyword args: |
| {sym} |
| {dtype} |
| {layout} |
| {device} |
| {requires_grad} |
| |
| Examples:: |
| |
| >>> # Generates a symmetric Bartlett window. |
| >>> torch.signal.windows.bartlett(10) |
| tensor([0.0000, 0.2222, 0.4444, 0.6667, 0.8889, 0.8889, 0.6667, 0.4444, 0.2222, 0.0000]) |
| |
| >>> # Generates a periodic Bartlett window. |
| >>> torch.signal.windows.bartlett(10, sym=False) |
| tensor([0.0000, 0.2000, 0.4000, 0.6000, 0.8000, 1.0000, 0.8000, 0.6000, 0.4000, 0.2000]) |
| """.format( |
| **window_common_args |
| ), |
| ) |
| def bartlett(M: int, |
| *, |
| sym: bool = True, |
| dtype: Optional[torch.dtype] = None, |
| layout: torch.layout = torch.strided, |
| device: Optional[torch.device] = None, |
| requires_grad: bool = False) -> Tensor: |
| if dtype is None: |
| dtype = torch.get_default_dtype() |
| |
| _window_function_checks('bartlett', M, dtype, layout) |
| |
| if M == 0: |
| return torch.empty((0,), dtype=dtype, layout=layout, device=device, requires_grad=requires_grad) |
| |
| if M == 1: |
| return torch.ones((1,), dtype=dtype, layout=layout, device=device, requires_grad=requires_grad) |
| |
| start = -1 |
| constant = 2 / (M if not sym else M - 1) |
| |
| k = torch.linspace(start=start, |
| end=start + (M - 1) * constant, |
| steps=M, |
| dtype=dtype, |
| layout=layout, |
| device=device, |
| requires_grad=requires_grad) |
| |
| return 1 - torch.abs(k) |
| |
| |
| @_add_docstr( |
| r""" |
| Computes the general cosine window. |
| |
| The general cosine window is defined as follows: |
| |
| .. math:: |
| w_n = \sum^{M-1}_{i=0} (-1)^i a_i \cos{ \left( \frac{2 \pi i n}{M - 1}\right)} |
| """, |
| r""" |
| |
| {normalization} |
| |
| Arguments: |
| {M} |
| |
| Keyword args: |
| a (Iterable): the coefficients associated to each of the cosine functions. |
| {sym} |
| {dtype} |
| {layout} |
| {device} |
| {requires_grad} |
| |
| Examples:: |
| |
| >>> # Generates a symmetric general cosine window with 3 coefficients. |
| >>> torch.signal.windows.general_cosine(10, a=[0.46, 0.23, 0.31], sym=True) |
| tensor([0.5400, 0.3376, 0.1288, 0.4200, 0.9136, 0.9136, 0.4200, 0.1288, 0.3376, 0.5400]) |
| |
| >>> # Generates a periodic general cosine window wit 2 coefficients. |
| >>> torch.signal.windows.general_cosine(10, a=[0.5, 1 - 0.5], sym=False) |
| tensor([0.0000, 0.0955, 0.3455, 0.6545, 0.9045, 1.0000, 0.9045, 0.6545, 0.3455, 0.0955]) |
| """.format( |
| **window_common_args |
| ), |
| ) |
| def general_cosine(M, *, |
| a: Iterable, |
| sym: bool = True, |
| dtype: Optional[torch.dtype] = None, |
| layout: torch.layout = torch.strided, |
| device: Optional[torch.device] = None, |
| requires_grad: bool = False) -> Tensor: |
| if dtype is None: |
| dtype = torch.get_default_dtype() |
| |
| _window_function_checks('general_cosine', M, dtype, layout) |
| |
| if M == 0: |
| return torch.empty((0,), dtype=dtype, layout=layout, device=device, requires_grad=requires_grad) |
| |
| if M == 1: |
| return torch.ones((1,), dtype=dtype, layout=layout, device=device, requires_grad=requires_grad) |
| |
| if not isinstance(a, Iterable): |
| raise TypeError("Coefficients must be a list/tuple") |
| |
| if not a: |
| raise ValueError("Coefficients cannot be empty") |
| |
| constant = 2 * torch.pi / (M if not sym else M - 1) |
| |
| k = torch.linspace(start=0, |
| end=(M - 1) * constant, |
| steps=M, |
| dtype=dtype, |
| layout=layout, |
| device=device, |
| requires_grad=requires_grad) |
| |
| a_i = torch.tensor([(-1) ** i * w for i, w in enumerate(a)], device=device, dtype=dtype, requires_grad=requires_grad) |
| i = torch.arange(a_i.shape[0], dtype=a_i.dtype, device=a_i.device, requires_grad=a_i.requires_grad) |
| return (a_i.unsqueeze(-1) * torch.cos(i.unsqueeze(-1) * k)).sum(0) |
| |
| |
| @_add_docstr( |
| r""" |
| Computes the general Hamming window. |
| |
| The general Hamming window is defined as follows: |
| |
| .. math:: |
| w_n = \alpha - (1 - \alpha) \cos{ \left( \frac{2 \pi n}{M-1} \right)} |
| """, |
| r""" |
| |
| {normalization} |
| |
| Arguments: |
| {M} |
| |
| Keyword args: |
| alpha (float, optional): the window coefficient. Default: 0.54. |
| {sym} |
| {dtype} |
| {layout} |
| {device} |
| {requires_grad} |
| |
| Examples:: |
| |
| >>> # Generates a symmetric Hamming window with the general Hamming window. |
| >>> torch.signal.windows.general_hamming(10, sym=True) |
| tensor([0.0800, 0.1876, 0.4601, 0.7700, 0.9723, 0.9723, 0.7700, 0.4601, 0.1876, 0.0800]) |
| |
| >>> # Generates a periodic Hann window with the general Hamming window. |
| >>> torch.signal.windows.general_hamming(10, alpha=0.5, sym=False) |
| tensor([0.0000, 0.0955, 0.3455, 0.6545, 0.9045, 1.0000, 0.9045, 0.6545, 0.3455, 0.0955]) |
| """.format( |
| **window_common_args |
| ), |
| ) |
| def general_hamming(M, |
| *, |
| alpha: float = 0.54, |
| sym: bool = True, |
| dtype: Optional[torch.dtype] = None, |
| layout: torch.layout = torch.strided, |
| device: Optional[torch.device] = None, |
| requires_grad: bool = False) -> Tensor: |
| return general_cosine(M, |
| a=[alpha, 1. - alpha], |
| sym=sym, |
| dtype=dtype, |
| layout=layout, |
| device=device, |
| requires_grad=requires_grad) |
| |
| |
| @_add_docstr( |
| r""" |
| Computes the minimum 4-term Blackman-Harris window according to Nuttall. |
| |
| .. math:: |
| w_n = 1 - 0.36358 \cos{(z_n)} + 0.48917 \cos{(2z_n)} - 0.13659 \cos{(3z_n)} + 0.01064 \cos{(4z_n)} |
| |
| where ``z_n = 2 π n/ M``. |
| """, |
| """ |
| |
| {normalization} |
| |
| Arguments: |
| {M} |
| |
| Keyword args: |
| {sym} |
| {dtype} |
| {layout} |
| {device} |
| {requires_grad} |
| |
| References:: |
| |
| - A. Nuttall, “Some windows with very good sidelobe behavior,” |
| IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 29, no. 1, pp. 84-91, |
| Feb 1981. https://doi.org/10.1109/TASSP.1981.1163506 |
| |
| - Heinzel G. et al., “Spectrum and spectral density estimation by the Discrete Fourier transform (DFT), |
| including a comprehensive list of window functions and some new flat-top windows”, |
| February 15, 2002 https://holometer.fnal.gov/GH_FFT.pdf |
| |
| Examples:: |
| |
| >>> # Generates a symmetric Nutall window. |
| >>> torch.signal.windows.general_hamming(5, sym=True) |
| tensor([3.6280e-04, 2.2698e-01, 1.0000e+00, 2.2698e-01, 3.6280e-04]) |
| |
| >>> # Generates a periodic Nuttall window. |
| >>> torch.signal.windows.general_hamming(5, sym=False) |
| tensor([3.6280e-04, 1.1052e-01, 7.9826e-01, 7.9826e-01, 1.1052e-01]) |
| """.format( |
| **window_common_args |
| ), |
| ) |
| def nuttall( |
| M: int, |
| *, |
| sym: bool = True, |
| dtype: Optional[torch.dtype] = None, |
| layout: torch.layout = torch.strided, |
| device: Optional[torch.device] = None, |
| requires_grad: bool = False |
| ) -> Tensor: |
| return general_cosine(M, |
| a=[0.3635819, 0.4891775, 0.1365995, 0.0106411], |
| sym=sym, |
| dtype=dtype, |
| layout=layout, |
| device=device, |
| requires_grad=requires_grad) |
