


from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter


def      a	(							SCREAMING_SNAKE_CASE_      :		Optional[Any]							,			SCREAMING_SNAKE_CASE_      :		Dict							,			SCREAMING_SNAKE_CASE_      :		List[Any] = 1 / sqrt(2       )       ):






							"""simple docstring"""





							UpperCamelCase    :	Dict   	=		tau * frequency / samplerate
							UpperCamelCase    :	Optional[Any]   	=		sin(__snake_case       )
							UpperCamelCase    :	Tuple   	=		cos(__snake_case       )
							UpperCamelCase    :	Union[str, Any]   	=		_sin / (2 * q_factor)

							UpperCamelCase    :	Union[str, Any]   	=		(1 - _cos) / 2
							UpperCamelCase    :	Tuple   	=		1 - _cos

							UpperCamelCase    :	List[str]   	=		1 + alpha
							UpperCamelCase    :	List[str]   	=		-2 * _cos
							UpperCamelCase    :	Tuple   	=		1 - alpha

							UpperCamelCase    :	List[str]   	=		IIRFilter(2       )
							filt.set_coefficients([aa, aa, aa]							,			[ba, ba, ba]       )
							return filt


def      a	(							SCREAMING_SNAKE_CASE_      :		List[Any]							,			SCREAMING_SNAKE_CASE_      :		List[Any]							,			SCREAMING_SNAKE_CASE_      :		Optional[int] = 1 / sqrt(2       )       ):






							"""simple docstring"""





							UpperCamelCase    :	Tuple   	=		tau * frequency / samplerate
							UpperCamelCase    :	Tuple   	=		sin(__snake_case       )
							UpperCamelCase    :	int   	=		cos(__snake_case       )
							UpperCamelCase    :	List[Any]   	=		_sin / (2 * q_factor)

							UpperCamelCase    :	Dict   	=		(1 + _cos) / 2
							UpperCamelCase    :	Optional[Any]   	=		-1 - _cos

							UpperCamelCase    :	Optional[Any]   	=		1 + alpha
							UpperCamelCase    :	Optional[int]   	=		-2 * _cos
							UpperCamelCase    :	List[Any]   	=		1 - alpha

							UpperCamelCase    :	List[str]   	=		IIRFilter(2       )
							filt.set_coefficients([aa, aa, aa]							,			[ba, ba, ba]       )
							return filt


def      a	(							SCREAMING_SNAKE_CASE_      :		Any							,			SCREAMING_SNAKE_CASE_      :		List[str]							,			SCREAMING_SNAKE_CASE_      :		int = 1 / sqrt(2       )       ):






							"""simple docstring"""





							UpperCamelCase    :	Optional[Any]   	=		tau * frequency / samplerate
							UpperCamelCase    :	Optional[int]   	=		sin(__snake_case       )
							UpperCamelCase    :	Optional[int]   	=		cos(__snake_case       )
							UpperCamelCase    :	Optional[Any]   	=		_sin / (2 * q_factor)

							UpperCamelCase    :	Dict   	=		_sin / 2
							UpperCamelCase    :	Optional[int]   	=		0
							UpperCamelCase    :	Optional[int]   	=		-ba

							UpperCamelCase    :	List[Any]   	=		1 + alpha
							UpperCamelCase    :	str   	=		-2 * _cos
							UpperCamelCase    :	int   	=		1 - alpha

							UpperCamelCase    :	Tuple   	=		IIRFilter(2       )
							filt.set_coefficients([aa, aa, aa]							,			[ba, ba, ba]       )
							return filt


def      a	(							SCREAMING_SNAKE_CASE_      :		Tuple							,			SCREAMING_SNAKE_CASE_      :		str							,			SCREAMING_SNAKE_CASE_      :		Any = 1 / sqrt(2       )       ):






							"""simple docstring"""





							UpperCamelCase    :	Any   	=		tau * frequency / samplerate
							UpperCamelCase    :	int   	=		sin(__snake_case       )
							UpperCamelCase    :	List[Any]   	=		cos(__snake_case       )
							UpperCamelCase    :	Dict   	=		_sin / (2 * q_factor)

							UpperCamelCase    :	Any   	=		1 - alpha
							UpperCamelCase    :	Union[str, Any]   	=		-2 * _cos
							UpperCamelCase    :	Any   	=		1 + alpha

							UpperCamelCase    :	str   	=		IIRFilter(2       )
							filt.set_coefficients([ba, ba, ba]							,			[ba, ba, ba]       )
							return filt


def      a	(							SCREAMING_SNAKE_CASE_      :		Union[str, Any]							,			SCREAMING_SNAKE_CASE_      :		int							,			SCREAMING_SNAKE_CASE_      :		Optional[Any]							,			SCREAMING_SNAKE_CASE_      :		int = 1 / sqrt(2       )							,			):






							"""simple docstring"""





							UpperCamelCase    :	int   	=		tau * frequency / samplerate
							UpperCamelCase    :	Tuple   	=		sin(__snake_case       )
							UpperCamelCase    :	Any   	=		cos(__snake_case       )
							UpperCamelCase    :	List[str]   	=		_sin / (2 * q_factor)
							UpperCamelCase    :	List[str]   	=		1_0 ** (gain_db / 4_0)

							UpperCamelCase    :	Optional[int]   	=		1 + alpha * big_a
							UpperCamelCase    :	List[str]   	=		-2 * _cos
							UpperCamelCase    :	List[Any]   	=		1 - alpha * big_a
							UpperCamelCase    :	Union[str, Any]   	=		1 + alpha / big_a
							UpperCamelCase    :	str   	=		-2 * _cos
							UpperCamelCase    :	Optional[Any]   	=		1 - alpha / big_a

							UpperCamelCase    :	int   	=		IIRFilter(2       )
							filt.set_coefficients([aa, aa, aa]							,			[ba, ba, ba]       )
							return filt


def      a	(							SCREAMING_SNAKE_CASE_      :		Dict							,			SCREAMING_SNAKE_CASE_      :		Union[str, Any]							,			SCREAMING_SNAKE_CASE_      :		str							,			SCREAMING_SNAKE_CASE_      :		int = 1 / sqrt(2       )							,			):






							"""simple docstring"""





							UpperCamelCase    :	str   	=		tau * frequency / samplerate
							UpperCamelCase    :	Optional[int]   	=		sin(__snake_case       )
							UpperCamelCase    :	Dict   	=		cos(__snake_case       )
							UpperCamelCase    :	Optional[int]   	=		_sin / (2 * q_factor)
							UpperCamelCase    :	Optional[Any]   	=		1_0 ** (gain_db / 4_0)
							UpperCamelCase    :	int   	=		(big_a + 1) - (big_a - 1) * _cos
							UpperCamelCase    :	Tuple   	=		(big_a + 1) + (big_a - 1) * _cos
							UpperCamelCase    :	Optional[int]   	=		(big_a - 1) - (big_a + 1) * _cos
							UpperCamelCase    :	str   	=		(big_a - 1) + (big_a + 1) * _cos
							UpperCamelCase    :	int   	=		2 * sqrt(__snake_case       ) * alpha

							UpperCamelCase    :	List[Any]   	=		big_a * (pmc + aaa)
							UpperCamelCase    :	Optional[Any]   	=		2 * big_a * mpc
							UpperCamelCase    :	Dict   	=		big_a * (pmc - aaa)
							UpperCamelCase    :	Tuple   	=		ppmc + aaa
							UpperCamelCase    :	Optional[int]   	=		-2 * pmpc
							UpperCamelCase    :	Optional[int]   	=		ppmc - aaa

							UpperCamelCase    :	Optional[Any]   	=		IIRFilter(2       )
							filt.set_coefficients([aa, aa, aa]							,			[ba, ba, ba]       )
							return filt


def      a	(							SCREAMING_SNAKE_CASE_      :		Dict							,			SCREAMING_SNAKE_CASE_      :		int							,			SCREAMING_SNAKE_CASE_      :		Tuple							,			SCREAMING_SNAKE_CASE_      :		Any = 1 / sqrt(2       )							,			):






							"""simple docstring"""





							UpperCamelCase    :	Optional[int]   	=		tau * frequency / samplerate
							UpperCamelCase    :	Union[str, Any]   	=		sin(__snake_case       )
							UpperCamelCase    :	Optional[int]   	=		cos(__snake_case       )
							UpperCamelCase    :	Dict   	=		_sin / (2 * q_factor)
							UpperCamelCase    :	List[Any]   	=		1_0 ** (gain_db / 4_0)
							UpperCamelCase    :	List[Any]   	=		(big_a + 1) - (big_a - 1) * _cos
							UpperCamelCase    :	List[Any]   	=		(big_a + 1) + (big_a - 1) * _cos
							UpperCamelCase    :	Dict   	=		(big_a - 1) - (big_a + 1) * _cos
							UpperCamelCase    :	Optional[int]   	=		(big_a - 1) + (big_a + 1) * _cos
							UpperCamelCase    :	str   	=		2 * sqrt(__snake_case       ) * alpha

							UpperCamelCase    :	Optional[Any]   	=		big_a * (ppmc + aaa)
							UpperCamelCase    :	Union[str, Any]   	=		-2 * big_a * pmpc
							UpperCamelCase    :	Any   	=		big_a * (ppmc - aaa)
							UpperCamelCase    :	Dict   	=		pmc + aaa
							UpperCamelCase    :	List[str]   	=		2 * mpc
							UpperCamelCase    :	Dict   	=		pmc - aaa

							UpperCamelCase    :	Optional[Any]   	=		IIRFilter(2       )
							filt.set_coefficients([aa, aa, aa]							,			[ba, ba, ba]       )
							return filt





from itertools import product

from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey
from numpy import dot, exp, mgrid, pi, ravel, square, uinta, zeros


def      a	(							SCREAMING_SNAKE_CASE_      :		List[Any]							,			SCREAMING_SNAKE_CASE_      :		List[str]       ):






       """simple docstring"""





       UpperCamelCase    :	List[str]   	=		k_size // 2
       UpperCamelCase	, UpperCamelCase    :	Optional[int]   	=		mgrid[0 - center : k_size - center, 0 - center : k_size - center]
       UpperCamelCase    :	Dict   	=		1 / (2 * pi * sigma) * exp(-(square(SCREAMING_SNAKE_CASE_       ) + square(SCREAMING_SNAKE_CASE_       )) / (2 * square(SCREAMING_SNAKE_CASE_       ))       )
       return g


def      a	(							SCREAMING_SNAKE_CASE_      :		Dict							,			SCREAMING_SNAKE_CASE_      :		Optional[int]							,			SCREAMING_SNAKE_CASE_      :		int       ):






       """simple docstring"""





       UpperCamelCase	, UpperCamelCase    :	Tuple   	=		image.shape[0], image.shape[1]
       # dst image height and width
       UpperCamelCase    :	str   	=		height - k_size + 1
       UpperCamelCase    :	Optional[int]   	=		width - k_size + 1

       # im2col, turn the k_size*k_size pixels into a row and np.vstack all rows
       UpperCamelCase    :	List[Any]   	=		zeros((dst_height * dst_width, k_size * k_size)       )
       UpperCamelCase    :	Tuple   	=		0
       for i, j in product(range(SCREAMING_SNAKE_CASE_       )							,			range(SCREAMING_SNAKE_CASE_       )       ):
              UpperCamelCase    :	Dict   	=		ravel(image[i : i + k_size, j : j + k_size]       )
              UpperCamelCase    :	Dict   	=		window
              row += 1

       #  turn the kernel into shape(k*k, 1)
       UpperCamelCase    :	Optional[int]   	=		gen_gaussian_kernel(SCREAMING_SNAKE_CASE_							,			SCREAMING_SNAKE_CASE_       )
       UpperCamelCase    :	List[Any]   	=		ravel(SCREAMING_SNAKE_CASE_       )

       # reshape and get the dst image
       UpperCamelCase    :	Optional[int]   	=		dot(SCREAMING_SNAKE_CASE_							,			SCREAMING_SNAKE_CASE_       ).reshape(SCREAMING_SNAKE_CASE_							,			SCREAMING_SNAKE_CASE_       ).astype(SCREAMING_SNAKE_CASE_       )

       return dst


if __name__ == "__main__":
  # read original image
  __UpperCAmelCase : Union[str, Any] 			=				imread(r"../image_data/lena.jpg")
  # turn image in gray scale value
  __UpperCAmelCase : Optional[Any] 			=				cvtColor(img, COLOR_BGR2GRAY)

  # get values with two different mask size
  __UpperCAmelCase : Optional[int] 			=				gaussian_filter(gray, 3, sigma=1)
  __UpperCAmelCase : List[Any] 			=				gaussian_filter(gray, 5, sigma=0.8)

  # show result images
  imshow("gaussian filter with 3x3 mask", gaussianaxa)
  imshow("gaussian filter with 5x5 mask", gaussianaxa)
  waitKey()

