old_contents: # -*- coding: utf-8 -*-
  
  # Standard library imports
  import numpy as np
  
  
  def _filter_bandwidth(fc, n=3, N=3):
      """Define nth octave filter bandwidth
  
      The filter bandwidth is designed according to the Order-N
      specification of the ANSI S1.1-1986 standard. Default
      value for N is 3.
  
      References:
          ANSI S1.1-1986 (ASA 65-1986): Specifications for
          Octave-Band and Fractional-Octave-Band Analog and
          Digital Filters.
  
      Parameters
      ----------
      fc : ndarray
          Filters exact center frequencies
      n : int, optional
          Number of bands pr octave. Default to 3
      N : int, optional
          Filter order. Default to 3
  
      Outputs
      -------
      alpha : numpy.ndarray
          Ratio of the upper and lower band-edge frequencies to the mid-band
          frequency
      """
  
      """
      TODO: Check compliancy with the following standards
          - IEC 61260 – 1 (2014), 1/1-octave Bands and 1/3-octave Bands, Class 1
          - IEC 61260 (1995 – 07) plus Amendment 1 (2001 – 09), 1/1-octave Bands and 1/3-octave Bands, Class 0
          - ANSI S1.11 – 1986, 1/1-octave Bands and 1/3-octave Bands, Order 3, Type 0 – C
          - ANSI S1.11 – 2004, 1/1-octave Bands and 1/3-octave Bands, Class 0
          - ANSI/ASA S1.11 – 2014 Part 1, 1/1-octave Bands and 1/3-octave Bands, Class 1
      """
  
      # Design for Butterworth 2Nth-order nth-octave filter
      # Note: BUTTER is based on a bilinear transformation, as suggested in
      # ANSI S1.1-1986.
      b = 1 / n
      f1 = fc / (2 ** (b / 2))  # ANSI eq5
      f2 = fc * (2 ** (b / 2))  # ANSI eq6
      # Reference bandwidth quotient
      qr = fc / (f2 - f1)  # ANSI eq7 & 8
      # Design bandwidth quotient
      qd = (np.pi / 2 / N) / (np.sin(np.pi / 2 / N)) * qr  # ANSI eq9
      # Ratio of the upper and lower band-edge frequencies to the mid-band frequency
      alpha = (1 + np.sqrt(1 + 4 * qd ** 2)) / 2 / qd
  
      return alpha
  
  
  if __name__ == "__main__":
      pass
  
new_contents: # -*- coding: utf-8 -*-
  
  # Standard library imports
  import numpy as np
  
  
  def _filter_bandwidth(fc, n=3, N=3):
      """Define nth octave filter bandwidth
  
      The filter bandwidth is designed according to the Order-N
      specification of the ANSI S1.1-1986 standard. Default
      value for N is 3.
  
      References:
          ANSI S1.1-1986 (ASA 65-1986): Specifications for
          Octave-Band and Fractional-Octave-Band Analog and
          Digital Filters.
  
      Parameters
      ----------
      fc : ndarray
          Filters exact center frequencies
      n : int, optional
          Number of bands pr octave. Default to 3
      N : int, optional
          Filter order. Default to 3
  
      Outputs
      -------
      alpha : numpy.ndarray
          Ratio of the upper and lower band-edge frequencies to the mid-band
          frequency
      """
  
      """
      TODO: Check compliancy with the following standards
          - IEC 61260 – 1 (2014), 1/1-octave Bands and 1/3-octave Bands, Class 1
          - IEC 61260 (1995 – 07) plus Amendment 1 (2001 – 09), 1/1-octave Bands and 1/3-octave Bands, Class 0
          - ANSI S1.11 – 1986, 1/1-octave Bands and 1/3-octave Bands, Order 3, Type 0 – C
          - ANSI S1.11 – 2004, 1/1-octave Bands and 1/3-octave Bands, Class 0
          - ANSI/ASA S1.11 – 2014 Part 1, 1/1-octave Bands and 1/3-octave Bands, Class 1
      """
  
      # Design for Butterworth 2Nth-order nth-octave filter
      # Note: BUTTER is based on a bilinear transformation, as suggested in
      # ANSI S1.1-1986.
      b = 1 / n
      f1 = fc / (2 ** (b / 2))  # ANSI eq5
      f2 = fc * (2 ** (b / 2))  # ANSI eq6
      # Reference bandwidth quotient
      qr = fc / (f2 - f1)  # ANSI eq7 & 8
      # Design bandwidth quotient
      qd = (np.pi / 2 / N) / (np.sin(np.pi / 2 / N)) * qr  # ANSI eq9
      # Ratio of the upper and lower band-edge frequencies to the mid-band frequency
      alpha = (1 + np.sqrt(1 + 4 * qd ** 2)) / 2 / qd
  
      return alpha, f1, f2
  
  
  if __name__ == "__main__":
      pass
  
subject: return low and high frequency of each band on top of the center frequency