"""Functions and utilities for transforming power spectra."""
import numpy as np
from fooof.sim.params import update_sim_ap_params
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[docs]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
[docs]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
[docs]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
[docs]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
[docs]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
[docs]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))