a h~X @s ddlmZddlmZddlmZmZmZddlZddlm Z ddl m Z m Z m Z gdZedZe e d e d d iZeeegefd d dZeeejejddddZeddjfieddddejdddeeeeeeejejeejee d ddZeddjfieddejdddeeeejejeejee ddd Zed!d"jfiedddejddd#eeeeejejeejee d$d%d&Zed'd(jfied)ddejddd*eeeeejejeejee d+d,d-Zed.d/jfieddejdddeeeejejeejee dd0d1Z ed2d3jfieddejdddeeeejejeejee dd4d5Z!ed6d7jfieddejdddeeeejejeejee dd8d9Z"ed:d;jfieddejdddeeeejejeejee ddd?jfieddejdddeeeejejeejee d@dAdBZ$edCdDjfiedEddejdddFeeeejejeejee dGdHdIZ%edJdKjfieddejdddeeeejejeejee ddLdMZ&dS)N)Iterable)sqrt)CallableOptionalTypeVarN)Tensor)factory_common_args merge_dicts parse_kwargs) bartlettblackmancosine exponentialgaussiangeneral_cosinegeneral_hamminghamminghannkaisernuttall_Ta6 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`. Z normalizationzThe 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`.)argsreturncsttdfdd }|S)a8Adds 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): )orcsd|_|S)N)join__doc__)rrJ/var/www/auris/lib/python3.9/site-packages/torch/signal/windows/windows.py decorator8s z_add_docstr..decorator)r)rr rrr _add_docstr,s r!) function_nameMdtypelayoutrcCs\|dkrt|d||tjur6t|d||tjtjfvrXt|d|dS)aPerforms 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. rz, requires non-negative window length, got M=z/ is implemented for strided tensors only, got: z) expects float32 or float64 dtypes, got: N) ValueErrortorchstridedfloat32float64)r"r#r$r%rrr_window_function_checks?s     r+z Computes a window with an exponential waveform. Also known as Poisson window. The exponential window is defined as follows: .. math:: w_n = \exp{\left(-\frac{|n - c|}{\tau}\right)} where `c` is the ``center`` of the window. aF {normalization} Args: {M} Keyword args: center (float, optional): where the center of the window will be located. Default: `M / 2` if `sym` is `False`, else `(M - 1) / 2`. tau (float, optional): the decay value. Tau is generally associated with a percentage, that means, that the value should vary within the interval (0, 100]. If tau is 100, it is considered the uniform window. Default: 1.0. {sym} {dtype} {layout} {device} {requires_grad} Examples:: >>> # Generates a symmetric exponential window of size 10 and with a decay value of 1.0. >>> # The center will be at (M - 1) / 2, where M is 10. >>> torch.signal.windows.exponential(10) tensor([0.0111, 0.0302, 0.0821, 0.2231, 0.6065, 0.6065, 0.2231, 0.0821, 0.0302, 0.0111]) >>> # Generates a periodic exponential window and decay factor equal to .5 >>> torch.signal.windows.exponential(10, sym=False,tau=.5) tensor([4.5400e-05, 3.3546e-04, 2.4788e-03, 1.8316e-02, 1.3534e-01, 1.0000e+00, 1.3534e-01, 1.8316e-02, 2.4788e-03, 3.3546e-04]) ?TF)centertausymr$r%device requires_grad) r#r-r.r/r$r%r0r1rc Cs|durt}td||||dkr6td|d|rJ|durJtd|dkrftjd||||dS|dur|s~|dkr~|n|dd }d|}tj| || |d||||||d } tt|  S) NrrzTau must be positive, got: instead.z)Center must be None for symmetric windowsrr$r%r0r1@startendZstepsr$r%r0r1)r'get_default_dtyper+r&emptylinspaceexpabs) r#r-r.r/r$r%r0r1constantkrrrrYs09   ra 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. a {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]) r/r$r%r0r1)r#r/r$r%r0r1rc Cs|durt}td||||dkr:tjd||||dSd}tj|sV|dkrV|dn|}tj||||d||||||d}t|S)Nr rr3r4?r5r7)r'r:r+r;pir<sin r#r/r$r%r0r1r8r?r@rrrr s&2  r z Computes a window with a gaussian waveform. The gaussian window is defined as follows: .. math:: w_n = \exp{\left(-\left(\frac{n}{2\sigma}\right)^2\right)} a  {normalization} Args: {M} Keyword args: std (float, optional): the standard deviation of the gaussian. It controls how narrow or wide the window is. Default: 1.0. {sym} {dtype} {layout} {device} {requires_grad} Examples:: >>> # Generates a symmetric gaussian window with a standard deviation of 1.0. >>> torch.signal.windows.gaussian(10) tensor([4.0065e-05, 2.1875e-03, 4.3937e-02, 3.2465e-01, 8.8250e-01, 8.8250e-01, 3.2465e-01, 4.3937e-02, 2.1875e-03, 4.0065e-05]) >>> # Generates a periodic gaussian window and standard deviation equal to 0.9. >>> torch.signal.windows.gaussian(10, sym=False,std=0.9) tensor([1.9858e-07, 5.1365e-05, 3.8659e-03, 8.4658e-02, 5.3941e-01, 1.0000e+00, 5.3941e-01, 8.4658e-02, 3.8659e-03, 5.1365e-05]) )stdr/r$r%r0r1)r#rFr/r$r%r0r1rc Cs|durt}td||||dkr6td|d|dkrRtjd||||dS|sb|dkrb|n|d d}d|td }tj||||d||||||d } t| d  S) Nrrz*Standard deviation must be positive, got: r2r3r4r5r6r7)r'r:r+r&r;rr<r=) r#rFr/r$r%r0r1r8r?r@rrrrs*0  raK 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``. a {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]) g(@)betar/r$r%r0r1)r#rHr/r$r%r0r1rc Cs|durt}td||||dkr6td|d|dkrRtjd||||dS|dkrntjd||||dStj|||d }| }d ||s|n|d}t|||d|} tj|| |||||d } t t ||t | d t |S) Nrrz beta must be non-negative, got: r2r3r4r5r5)r$r0r6r7rG) r'r:r+r&r;onestensorZminimumr<Zi0rpow) r#rHr/r$r%r0r1r8r?r9r@rrrrNs61   rz 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) a {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]) cCst||||||dS)NrArr#r/r$r%r0r1rrrrs/rz Computes the Hann window. The Hann window is defined as follows: .. math:: w_n = \frac{1}{2}\ \left[1 - \cos \left( \frac{2 \pi n}{M - 1} \right)\right] = \sin^2 \left( \frac{\pi n}{M - 1} \right) a {normalization} Arguments: {M} Keyword args: {sym} {dtype} {layout} {device} {requires_grad} Examples:: >>> # Generates a symmetric Hann window. >>> torch.signal.windows.hann(10) tensor([0.0000, 0.1170, 0.4132, 0.7500, 0.9698, 0.9698, 0.7500, 0.4132, 0.1170, 0.0000]) >>> # Generates a periodic Hann window. >>> torch.signal.windows.hann(10, sym=False) tensor([0.0000, 0.0955, 0.3455, 0.6545, 0.9045, 1.0000, 0.9045, 0.6545, 0.3455, 0.0955]) c Cst|d|||||dS)NrBalphar/r$r%r0r1rMrNrrrrs.rz 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) a {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]) c Cs8|durt}td|||t|gd|||||dS)Nr )gzG?rBg{Gz?ar/r$r%r0r1)r'r:r+rrNrrrr s-r a4 Computes the Bartlett window. The Bartlett window is defined as follows: .. math:: w_n = 1 - \left| \frac{2n}{M - 1} - 1 \right| = \begin{cases} \frac{2n}{M - 1} & \text{if } 0 \leq n \leq \frac{M - 1}{2} \\ 2 - \frac{2n}{M - 1} & \text{if } \frac{M - 1}{2} < n < M \\ \end{cases} a {normalization} Arguments: {M} Keyword args: {sym} {dtype} {layout} {device} {requires_grad} Examples:: >>> # Generates a symmetric Bartlett window. >>> torch.signal.windows.bartlett(10) tensor([0.0000, 0.2222, 0.4444, 0.6667, 0.8889, 0.8889, 0.6667, 0.4444, 0.2222, 0.0000]) >>> # Generates a periodic Bartlett window. >>> torch.signal.windows.bartlett(10, sym=False) tensor([0.0000, 0.2000, 0.4000, 0.6000, 0.8000, 1.0000, 0.8000, 0.6000, 0.4000, 0.2000]) c Cs|durt}td||||dkr:tjd||||dS|dkrVtjd||||dSd}d|sd|n|d}tj|||d||||||d }dt|S) Nr rr3r4r5rIrGr7)r'r:r+r;rJr<r>rErrrr Ts./   r z Computes the general cosine window. The general cosine window is defined as follows: .. math:: w_n = \sum^{M-1}_{i=0} (-1)^i a_i \cos{ \left( \frac{2 \pi i n}{M - 1}\right)} a {normalization} Arguments: {M} Keyword args: a (Iterable): the coefficients associated to each of the cosine functions. {sym} {dtype} {layout} {device} {requires_grad} Examples:: >>> # Generates a symmetric general cosine window with 3 coefficients. >>> torch.signal.windows.general_cosine(10, a=[0.46, 0.23, 0.31], sym=True) tensor([0.5400, 0.3376, 0.1288, 0.4200, 0.9136, 0.9136, 0.4200, 0.1288, 0.3376, 0.5400]) >>> # Generates a periodic general cosine window with 2 coefficients. >>> torch.signal.windows.general_cosine(10, a=[0.5, 1 - 0.5], sym=False) tensor([0.0000, 0.0955, 0.3455, 0.6545, 0.9045, 1.0000, 0.9045, 0.6545, 0.3455, 0.0955]) )rRr/r$r%r0r1rc Cs|durt}td||||dkr:tjd||||dS|dkrVtjd||||dSt|tshtd|sttdd tj |s|n|d}tj d|d||||||d }tj d d t |D|||d } tj | jd| j| j| jd} | dt| d|dS)Nrrr3r4r5rIz!Coefficients must be a list/tuplezCoefficients cannot be emptyrGr7cSsg|]\}}d||qS)rSr).0iwrrr z"general_cosine..)r0r$r1)r$r0r1rS)r'r:r+r;rJ isinstancer TypeErrorr&rCr<rK enumerateZarangeshaper$r0r1Z unsqueezecossum) r#rRr/r$r%r0r1r?r@Za_irUrrrrsL/     rz 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)} a {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]) gHzG?rO)rPr/r$r%r0r1rc Cst||d|g|||||dS)Nr,rQr)r#rPr/r$r%r0r1rrrrs/ rz 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 :math:`z_n = \frac{2 \pi n}{M}`. a {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]) c Cst|gd|||||dS)N)gzD?g;%N?g1|?gC˅?rQr_rNrrrr;s7r)'collections.abcrmathrtypingrrrr'rZtorch._torch_docsrr r __all__rZwindow_common_argsstrr!intr$r%r+formatr(floatboolr0rr rrrrr r rrrrrrrs      1- ,#)( *0) (' )():("1