text: """Functions and utilities for transforming power spectra."""
  
  import numpy as np
  
  from fooof.sim.params import update_sim_ap_params
  
  ###################################################################################################
  ###################################################################################################
  
  def rotate_spectrum(freqs, power_spectrum, delta_exponent, f_rotation):
      """Rotate a power spectrum about a frequency point, changing the aperiodic exponent.
  
      Parameters
      ----------
      freqs : 1d array
          Frequency axis of input power spectrum, in Hz.
      power_spectrum : 1d array
          Power values of the spectrum.
      delta_exponent : float
          Change in aperiodic exponent to be applied, where:
  
          - positive is clockwise rotation (steepen)
          - negative is counterclockwise rotation (flatten)
      f_rotation : float
          Frequency value, in Hz, about which rotation is applied, at which power is unchanged.
  
      Returns
      -------
      rotated_spectrum : 1d array
          Rotated power spectrum.
  
      Raises
      ------
      ValueError
          If the rotation frequency is invalid.
  
      Notes
      -----
      Rotating in log-log spacing is equivalent to multiplying with a 1/f shaped mask that is:
  
      - unity at the rotation frequency
      - has an exponent of the desired delta exponent
  
      This mask, when applied to a spectrum as 'spectrum * mask', should result in:
  
      - rotated_spectrum = 1/f^(original_exponent + delta_exponent), where
      - spectrum[rotation_frequency] == rotated spectrum[rotation_frequency]
  
      This mask is defined as:
  
      - mask = (freqs / rotation_frequency) ** -delta_exponent
  
      Note that this approach / function should only be applied to spectra without a knee:
  
      - If using simulated data, this is spectra created in 'fixed' mode.
      - This is because the rotation applied is inconsistent with the formulation of spectra
        with a knee. This transformation will change them in an unspecified way, not just
        limited to doing the rotation.
  
      Examples
      --------
      Rotate a simulated spectrum, changing the exponent around a rotation point of 25 Hz:
  
      >>> from fooof.sim.gen import gen_power_spectrum
      >>> freqs, powers = gen_power_spectrum([1, 50], [1, 1], [10, 0.5, 1])
      >>> rotated_powers = rotate_spectrum(freqs, powers, 0.5, 25)
      """
  
      # Rotations are undefined for frequency value of exactly zero
      #   We also do not support (in this implementation) negative frequencies
      if f_rotation <= 0.:
          raise ValueError("The rotation frequency cannot be less than or equal to zero.")
  
      mask = (np.abs(freqs) / f_rotation)**-delta_exponent
      rotated_spectrum = mask * power_spectrum
  
      return rotated_spectrum
  
  
  def translate_spectrum(power_spectrum, delta_offset):
      """Translate a spectrum, changing the offset value.
  
      Parameters
      ----------
      power_spectrum : 1d array
          Power values of the spectrum.
      delta_offset : float
          Amount to change the offset by, where:
  
          - positive values are an upwards translation
          - negative are are a downwards translation
  
      Returns
      -------
      translated_spectrum : 1d array
          Translated power spectrum.
  
      Examples
      --------
      Translate a simulated spectrum, moving the offset up:
  
      >>> from fooof.sim.gen import gen_power_spectrum
      >>> freqs, powers = gen_power_spectrum([1, 50], [1, 1], [10, 0.5, 1])
      >>> translated_powers = translate_spectrum(powers, 0.5)
      """
  
      translated_spectrum = np.power(10, delta_offset, dtype='float') * power_spectrum
  
      return translated_spectrum
  
  
  def rotate_sim_spectrum(freqs, power_spectrum, delta_exponent, f_rotation, sim_params):
      """Rotate a simulated power spectrum, updating a SimParams object.
  
      Parameters
      ----------
      freqs : 1d array
          Frequency axis of input power spectrum, in Hz.
      power_spectrum : 1d array
          Power values of the spectrum.
      delta_exponent : float
          Change in aperiodic exponent to be applied, where:
  
          - positive is clockwise rotation (steepen)
          - negative is counterclockwise rotation (flatten)
      f_rotation : float
          Frequency value, in Hz, about which rotation is applied, at which power is unchanged.
      sim_params : SimParams
          Object storing the current parameter definitions.
  
      Returns
      -------
      rotated_spectrum : 1d array
          Rotated power spectrum.
      new_sim_params : SimParams
          New parameter definitions.
  
      Notes
      -----
      Warning: This function should only be applied to spectra without a knee.
      If using simulated data, this is spectra created in 'fixed' mode.
      This is because the rotation applied is inconsistent with
      the formulation of knee spectra, and will change them in an
      unspecified way, not just limited to doing the rotation.
  
      Examples
      --------
      Rotate a simulated spectrum, changing the exponent around a rotation point of 25 Hz:
  
      >>> from fooof.sim.gen import gen_power_spectrum
      >>> freqs, powers, sp = gen_power_spectrum([1, 50], [1, 1], [10, 0.5, 1], return_params=True)
      >>> rotated_powers, new_sp = rotate_sim_spectrum(freqs, powers, 0.5, 25, sp)
      """
  
      rotated_spectrum = rotate_spectrum(freqs, power_spectrum, delta_exponent, f_rotation)
      delta_offset = compute_rotation_offset(delta_exponent, f_rotation)
  
      new_sim_params = update_sim_ap_params(sim_params, [delta_offset, delta_exponent])
  
      return rotated_spectrum, new_sim_params
  
  
  def translate_sim_spectrum(power_spectrum, delta_offset, sim_params):
      """Translate a simulated spectrum, updating a SimParams object.
  
      Parameters
      ----------
      power_spectrum : 1d array
          Power values of the spectrum.
      delta_offset : float
          Amount to change the offset by, where:
  
          - positive values are an upwards translation
          - negative are are a downwards translation
      sim_params : SimParams
          Object storing the current parameter definitions.
  
      Returns
      -------
      translated_spectrum : 1d array
          Translated power spectrum.
      new_sim_params : SimParams
          New parameter definitions.
  
      Examples
      --------
      Translate a simulated spectrum, moving the offset up:
  
      >>> from fooof.sim.gen import gen_power_spectrum
      >>> freqs, powers, sp = gen_power_spectrum([1, 50], [1, 1], [10, 0.5, 1], return_params=True)
      >>> translated_powers, new_sp = translate_sim_spectrum(powers, 0.5, sp)
      """
  
      translated_spectrum = translate_spectrum(power_spectrum, delta_offset)
      new_sim_params = update_sim_ap_params(sim_params, delta_offset, 'offset')
  
      return translated_spectrum, new_sim_params
  
  
  def compute_rotation_offset(delta_exponent, f_rotation):
      """Calculate the change in offset from a given rotation.
  
      Parameters
      ----------
      delta_exponent : float
          The change in aperiodic exponent value.
      f_rotation : float
          The frequency value, in Hz, where rotation is applied.
  
      Returns
      -------
      float
          The amount the offset will change for the specified exponent change.
  
      Examples
      --------
      Calculate the induced change in offset of a change in exponent of 0.5 at 25 Hz:
  
      >>> delta_offset = compute_rotation_offset(0.5, 25)
      """
  
      return -np.log10(f_rotation) * -delta_exponent
  
  
  def compute_rotation_frequency(delta_exponent_b, f_rotation_b, delta_exponent_c, f_rotation_c):
      """Calculate the rotation frequency between two rotated power spectra.
  
      Parameters
      ----------
      delta_exponent_b : float
          The applied change in exponent value for power spectrum 'B'.
      f_rotation_b : float
          The rotation frequency applied to power spectrum 'B'.
      delta_exponent_c : float
          The applied change in exponent value for power spectrum 'C'.
      f_rotation_c : float
          The rotation frequency applied to power spectrum 'C'.
  
      Returns
      -------
      float
          The frequency rotation point between spectra 'B' & 'C'.
  
      Notes
      -----
      **Code Notes**
  
      This computes the rotation frequency for two power spectra 'B' & 'C',
      under the assumption that they are both rotated versions of a the
      same original power spectrum 'A'.
  
      **Derivation**
  
      Given an original power spectrum A, then:
  
      - B = A*(f_rotation_b/freqs)^delta_exponent_b
      - C = A*(f_rotation_c/freqs)^delta_exponent_c
  
      Therefore, what you want is f_rotation_bc, which is the frequency where B==C.
  
      To find this, we can plug everything back into the equation, to find where
      B[freqs] == C[freqs], which is how we arrive at the solution below.
  
      Examples
      --------
      Calculate the rotation frequency between two transformed power spectra:
  
      >>> f_rotation = compute_rotation_frequency(0.5, 25, -0.25, 10)
      """
  
      return (((f_rotation_c**delta_exponent_c) / (f_rotation_b**delta_exponent_b))) ** \
          (1/(delta_exponent_c-delta_exponent_b))
  