U ʹjY @sddlmZmZddlZddlmZddlmZddlmZm Z m Z dddd d d d d dddg Z e e deddiZ ddZ eeejejddddZe ddjfe ddddejdddeeeeeeejejeejeed d d Ze d!d"jfe ddejddd#eeeejejeejeed$d%dZe d&d'jfe dddejddd(eeeeejejeejeed)d*d Ze d+d,jfe d-ddejddd.eeeeejejeejeed/d0dZe d1d2jfe ddejddd#eeeejejeejeed$d3d Ze d4d5jfe ddejddd#eeeejejeejeed$d6dZe d7d8jfe ddejddd#eeeejejeejeed$d9dZe d:d;jfe ddejddd#eeeejejeejeed$djfe ddejddd#eeeejejeejeed?d@d Z e dAdBjfe dCddejdddDeeeejejeejeedEdFd Z!e dGdHjfe ddejddd#eeeejejeejeed$dIdZ"dS)J)OptionalIterableN)sqrt)Tensor)factory_common_args parse_kwargs merge_dictsbartlettblackmancosine exponentialgaussiangeneral_cosinegeneral_hamminghamminghannkaisernuttalla6 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`.csfdd}|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): csd|_|S)N)join__doc__)oargs[/var/www/html/bwave/python/venv/lib/python3.8/site-packages/torch/signal/windows/windows.py decorator4s z_add_docstr..decoratorr)rrrrr _add_docstr(s r) function_nameMdtypelayoutreturncCs\|dkrt|d||tjk r6t|d||tjtjfkrXt|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) ValueErrortorchstridedZfloat32Zfloat64)rrr 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) rr(r)r*r r!r+r,r"c Cs|dkrt}td||||dkr6td|d|rJ|dk rJtd|dkrftjd||||dS|dkr|s~|dkr~|n|dd }d|}tj| || |d||||||d } tt|  S) Nr rzTau must be positive, got: instead.z)Center must be None for symmetric windowsrr r!r+r,@startendZstepsr r!r+r,)r$get_default_dtyper&r#emptylinspaceexpabs) rr(r)r*r r!r+r,constantkrrrr Ms*9  z Computes a window with a simple cosine waveform. Also known as the sine window. The cosine window is defined as follows: .. math:: w_n = \cos{\left(\frac{\pi n}{M} - \frac{\pi}{2}\right)} = \sin{\left(\frac{\pi n}{M}\right)} a {normalization} Args: {M} Keyword args: {sym} {dtype} {layout} {device} {requires_grad} Examples:: >>> # Generates a symmetric cosine window. >>> torch.signal.windows.cosine(10) tensor([0.1564, 0.4540, 0.7071, 0.8910, 0.9877, 0.9877, 0.8910, 0.7071, 0.4540, 0.1564]) >>> # Generates a periodic cosine window. >>> torch.signal.windows.cosine(10, sym=False) tensor([0.1423, 0.4154, 0.6549, 0.8413, 0.9595, 1.0000, 0.9595, 0.8413, 0.6549, 0.4154]) r*r r!r+r,)rr*r r!r+r,r"c Cs|dkrt}td||||dkr:tjd||||dSd}tj|sV|dkrV|dn|}tj||||d||||||d}t|S)Nr rr.r/?r0r2)r$r5r&r6pir7sin rr*r r!r+r,r3r:r;rrrr s . 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!r+r,)rrAr*r r!r+r,r"c Cs|dkrt}td||||dkr6td|d|dkrRtjd||||dS|sb|dkrb|n|d d}d|td }tj||||d||||||d } t| d  S) Nr rz*Standard deviation must be positive, got: r-r.r/r0r1r2)r$r5r&r#r6rr7r8) rrAr*r r!r+r,r3r:r;rrrr s$0 aK Computes the Kaiser window. The Kaiser window is defined as follows: .. math:: w_n = I_0 \left( \beta \sqrt{1 - \left( {\frac{n - N/2}{N/2}} \right) ^2 } \right) / I_0( \beta ) where ``I_0`` is the zeroth order modified Bessel function of the first kind (see :func:`torch.special.i0`), and ``N = M - 1 if sym else M``. a {normalization} Args: {M} Keyword args: beta (float, optional): shape parameter for the window. Must be non-negative. Default: 12.0 {sym} {dtype} {layout} {device} {requires_grad} Examples:: >>> # Generates a symmetric gaussian window with a standard deviation of 1.0. >>> torch.signal.windows.kaiser(5) tensor([4.0065e-05, 2.1875e-03, 4.3937e-02, 3.2465e-01, 8.8250e-01, 8.8250e-01, 3.2465e-01, 4.3937e-02, 2.1875e-03, 4.0065e-05]) >>> # Generates a periodic gaussian window and standard deviation equal to 0.9. >>> torch.signal.windows.kaiser(5, sym=False,std=0.9) tensor([1.9858e-07, 5.1365e-05, 3.8659e-03, 8.4658e-02, 5.3941e-01, 1.0000e+00, 5.3941e-01, 8.4658e-02, 3.8659e-03, 5.1365e-05]) g(@)betar*r r!r+r,)rrCr*r r!r+r,r"c Cs|dkrt}td||||dkr6td|d|dkrRtjd||||dS|dkrntjd||||dS| }d ||s|n|d}tj|||d||||||d } tt||t | d ttj ||d S) Nrrz beta must be non-negative, got: r-r.r/r0r0r1r2rB)r+) r$r5r&r#r6onesr7Zi0rpowtensor) rrCr*r r!r+r,r3r:r;rrrr2s(1z 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)Nr<rrr*r r!r+r,rrrrs-z 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)Nr=alphar*r r!r+r,rHrIrrrrs,z 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 Cs:|dkrt}td|||t|dddg|||||dS)Nr gzG?r=g{Gz?ar*r r!r+r,)r$r5r&rrIrrrr s +a4 Computes the Bartlett window. The Bartlett window is defined as follows: .. math:: w_n = 1 - \left| \frac{2n}{M - 1} - 1 \right| = \begin{cases} \frac{2n}{M - 1} & \text{if } 0 \leq n \leq \frac{M - 1}{2} \\ 2 - \frac{2n}{M - 1} & \text{if } \frac{M - 1}{2} < n < M \\ \end{cases} a {normalization} Arguments: {M} Keyword args: {sym} {dtype} {layout} {device} {requires_grad} Examples:: >>> # Generates a symmetric Bartlett window. >>> torch.signal.windows.bartlett(10) tensor([0.0000, 0.2222, 0.4444, 0.6667, 0.8889, 0.8889, 0.6667, 0.4444, 0.2222, 0.0000]) >>> # Generates a periodic Bartlett window. >>> torch.signal.windows.bartlett(10, sym=False) tensor([0.0000, 0.2000, 0.4000, 0.6000, 0.8000, 1.0000, 0.8000, 0.6000, 0.4000, 0.2000]) c Cs|dkrt}td||||dkr:tjd||||dS|dkrVtjd||||dSd}d|sd|n|d}tj|||d||||||d }dt|S) Nr rr.r/r0rDrBr2)r$r5r&r6rEr7r9r@rrrr s$-z Computes the general cosine window. The general cosine window is defined as follows: .. math:: w_n = \sum^{M-1}_{i=0} (-1)^i a_i \cos{ \left( \frac{2 \pi i n}{M - 1}\right)} a {normalization} Arguments: {M} Keyword args: a (Iterable): the coefficients associated to each of the cosine functions. {sym} {dtype} {layout} {device} {requires_grad} Examples:: >>> # Generates a symmetric general cosine window with 3 coefficients. >>> torch.signal.windows.general_cosine(10, a=[0.46, 0.23, 0.31], sym=True) tensor([0.5400, 0.3376, 0.1288, 0.4200, 0.9136, 0.9136, 0.4200, 0.1288, 0.3376, 0.5400]) >>> # Generates a periodic general cosine window wit 2 coefficients. >>> torch.signal.windows.general_cosine(10, a=[0.5, 1 - 0.5], sym=False) tensor([0.0000, 0.0955, 0.3455, 0.6545, 0.9045, 1.0000, 0.9045, 0.6545, 0.3455, 0.0955]) )rMr*r r!r+r,r"c Cs|dkrt}td||||dkr:tjd||||dS|dkrVtjd||||dSt|tshtd|sttdd tj |s|n|d}tj d|d||||||d }tj d d t |D|||d } tj | jd| j| j| jd} | dt| d|dS)Nrrr.r/r0rDz!Coefficients must be a list/tuplezCoefficients cannot be emptyrBr2cSsg|]\}}d||qS)rNr).0iwrrr sz"general_cosine..)r+r r,)r r+r,rN)r$r5r&r6rE isinstancer TypeErrorr#r>r7rG enumerateZarangeshaper r+r,Z unsqueezecossum) rrMr*r r!r+r,r:r;Za_irPrrrr^s.,   z 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?rJ)rKr*r r!r+r,r"c Cst||d|g|||||dS)Nr'rLr)rrKr*r r!r+r,rrrrs- u 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``. u {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|ddddg|||||dS)NgzD?g;%N?g1|?gC˅?rLrYrIrrrrs7 )#typingrrr$mathrrZtorch._torch_docsrrr__all__Zwindow_common_argsrstrintr r!r&formatr%floatboolr+r r r rrrr r rrrrrrrs   1) ()$ *&(  '& ( '''"1