Module libquantum.atoms_inverse
This module performs the inverse Gabor transform
Expand source code
"""
This module performs the inverse Gabor transform
"""
import numpy as np
from libquantum import scales
from typing import Tuple
"""
Atom Reconstruction - inverse CWT for Dictionary 0. Not for chirps, yet.
"""
def morlet2_reconstruct(band_order_Nth: float,
scale_frequency_center_hz: float,
frequency_sample_rate_hz: float) -> Tuple[float, float]:
"""
Reconstruction coefficients from Garces (2020)
:param band_order_Nth: Nth order of constant Q bands
:param scale_frequency_center_hz: center frequency fc in Hz
:param frequency_sample_rate_hz: sample rate of frequency in Hz
:return: atom scale, reconstruction coefficients
"""
cycles_M, quality_factor_Q = scales.wavelet_MQ_from_N(band_order_Nth)
morlet2_scale = cycles_M*frequency_sample_rate_hz/scale_frequency_center_hz/(2. * np.pi)
reconstruct = np.pi**0.25/2/np.sqrt(morlet2_scale)
return morlet2_scale, reconstruct
def inv_morlet2_prep(band_order_Nth: float,
time_s: np.ndarray,
offset_time_s: float,
scale_frequency_center_hz: float,
frequency_sample_rate_hz: float) -> Tuple[float, float, float, float]:
"""
Pre-conditioning before inversion
:param band_order_Nth: Nth order of constant Q bands
:param time_s: time in seconds
:param offset_time_s: offset time in seconds, should be between min and max of time_s
:param scale_frequency_center_hz: center frequency fc in Hz
:param frequency_sample_rate_hz: sample rate of frequency in Hz
:return: scaled shifted time, atom scale, number of cycles M, reconstruction coefficients
"""
cycles_M, quality_factor_Q = scales.wavelet_MQ_from_N(band_order_Nth)
morlet2_scale, reconstruct = morlet2_reconstruct(band_order_Nth, scale_frequency_center_hz, frequency_sample_rate_hz)
xtime_shifted = frequency_sample_rate_hz*(time_s-offset_time_s)
return xtime_shifted, morlet2_scale, cycles_M, reconstruct
def inv_morlet2_real(band_order_Nth: float,
time_s: np.ndarray,
offset_time_s: float,
scale_frequency_center_hz: float,
cwt_amp_real: float,
frequency_sample_rate_hz: float) -> np.ndarray:
"""
Real part of the inverse Morlet
:param band_order_Nth: Nth order of constant Q bands
:param time_s: time in seconds
:param offset_time_s: offset time in seconds, should be between min and max of time_s
:param scale_frequency_center_hz: center frequency fc in Hz
:param cwt_amp_real: real amplitude coefficient
:param frequency_sample_rate_hz: sample rate of frequency in Hz
:return: real inverse
"""
xtime_shifted, xscale, cycles_M, rescale = \
inv_morlet2_prep(band_order_Nth, time_s, offset_time_s, scale_frequency_center_hz, frequency_sample_rate_hz)
wavelet_gauss = np.exp(-0.5 * (xtime_shifted / xscale) ** 2)
wavelet_gabor_real = wavelet_gauss * np.cos(cycles_M*(xtime_shifted / xscale))
# Rescale to Morlet wavelet and take the conjugate for imag
morlet2_inv_real = cwt_amp_real*wavelet_gabor_real
morlet2_inv_real *= rescale
return morlet2_inv_real
def inv_morlet2_imag(band_order_Nth: float,
time_s: np.ndarray,
offset_time_s: float,
scale_frequency_center_hz: float,
cwt_amp_imag: float,
frequency_sample_rate_hz: float) -> np.ndarray:
"""
Inverse part of the inverse Morlet
:param band_order_Nth: Nth order of constant Q bands
:param time_s: time in seconds
:param offset_time_s: offset time in seconds, should be between min and max of time_s
:param scale_frequency_center_hz: center frequency fc in Hz
:param cwt_amp_imag: imaginary amplitude coefficient
:param frequency_sample_rate_hz: sample rate of frequency in Hz
:return: imaginary inverse
"""
xtime_shifted, xscale, cycles_M, rescale = \
inv_morlet2_prep(band_order_Nth, time_s, offset_time_s, scale_frequency_center_hz, frequency_sample_rate_hz)
wavelet_gauss = np.exp(-0.5 * (xtime_shifted / xscale) ** 2)
wavelet_gabor_imag = wavelet_gauss * np.sin(cycles_M*(xtime_shifted / xscale))
# Rescale to Morlet wavelet and take the conjugate for imag
morlet2_inv_imag = -cwt_amp_imag*wavelet_gabor_imag
morlet2_inv_imag *= rescale
return morlet2_inv_imagFunctions
def inv_morlet2_imag(band_order_Nth: float, time_s: numpy.ndarray, offset_time_s: float, scale_frequency_center_hz: float, cwt_amp_imag: float, frequency_sample_rate_hz: float) ‑> numpy.ndarray-
Inverse part of the inverse Morlet
:param band_order_Nth: Nth order of constant Q bands :param time_s: time in seconds :param offset_time_s: offset time in seconds, should be between min and max of time_s :param scale_frequency_center_hz: center frequency fc in Hz :param cwt_amp_imag: imaginary amplitude coefficient :param frequency_sample_rate_hz: sample rate of frequency in Hz :return: imaginary inverse
Expand source code
def inv_morlet2_imag(band_order_Nth: float, time_s: np.ndarray, offset_time_s: float, scale_frequency_center_hz: float, cwt_amp_imag: float, frequency_sample_rate_hz: float) -> np.ndarray: """ Inverse part of the inverse Morlet :param band_order_Nth: Nth order of constant Q bands :param time_s: time in seconds :param offset_time_s: offset time in seconds, should be between min and max of time_s :param scale_frequency_center_hz: center frequency fc in Hz :param cwt_amp_imag: imaginary amplitude coefficient :param frequency_sample_rate_hz: sample rate of frequency in Hz :return: imaginary inverse """ xtime_shifted, xscale, cycles_M, rescale = \ inv_morlet2_prep(band_order_Nth, time_s, offset_time_s, scale_frequency_center_hz, frequency_sample_rate_hz) wavelet_gauss = np.exp(-0.5 * (xtime_shifted / xscale) ** 2) wavelet_gabor_imag = wavelet_gauss * np.sin(cycles_M*(xtime_shifted / xscale)) # Rescale to Morlet wavelet and take the conjugate for imag morlet2_inv_imag = -cwt_amp_imag*wavelet_gabor_imag morlet2_inv_imag *= rescale return morlet2_inv_imag def inv_morlet2_prep(band_order_Nth: float, time_s: numpy.ndarray, offset_time_s: float, scale_frequency_center_hz: float, frequency_sample_rate_hz: float) ‑> Tuple[float, float, float, float]-
Pre-conditioning before inversion
:param band_order_Nth: Nth order of constant Q bands :param time_s: time in seconds :param offset_time_s: offset time in seconds, should be between min and max of time_s :param scale_frequency_center_hz: center frequency fc in Hz :param frequency_sample_rate_hz: sample rate of frequency in Hz :return: scaled shifted time, atom scale, number of cycles M, reconstruction coefficients
Expand source code
def inv_morlet2_prep(band_order_Nth: float, time_s: np.ndarray, offset_time_s: float, scale_frequency_center_hz: float, frequency_sample_rate_hz: float) -> Tuple[float, float, float, float]: """ Pre-conditioning before inversion :param band_order_Nth: Nth order of constant Q bands :param time_s: time in seconds :param offset_time_s: offset time in seconds, should be between min and max of time_s :param scale_frequency_center_hz: center frequency fc in Hz :param frequency_sample_rate_hz: sample rate of frequency in Hz :return: scaled shifted time, atom scale, number of cycles M, reconstruction coefficients """ cycles_M, quality_factor_Q = scales.wavelet_MQ_from_N(band_order_Nth) morlet2_scale, reconstruct = morlet2_reconstruct(band_order_Nth, scale_frequency_center_hz, frequency_sample_rate_hz) xtime_shifted = frequency_sample_rate_hz*(time_s-offset_time_s) return xtime_shifted, morlet2_scale, cycles_M, reconstruct def inv_morlet2_real(band_order_Nth: float, time_s: numpy.ndarray, offset_time_s: float, scale_frequency_center_hz: float, cwt_amp_real: float, frequency_sample_rate_hz: float) ‑> numpy.ndarray-
Real part of the inverse Morlet
:param band_order_Nth: Nth order of constant Q bands :param time_s: time in seconds :param offset_time_s: offset time in seconds, should be between min and max of time_s :param scale_frequency_center_hz: center frequency fc in Hz :param cwt_amp_real: real amplitude coefficient :param frequency_sample_rate_hz: sample rate of frequency in Hz :return: real inverse
Expand source code
def inv_morlet2_real(band_order_Nth: float, time_s: np.ndarray, offset_time_s: float, scale_frequency_center_hz: float, cwt_amp_real: float, frequency_sample_rate_hz: float) -> np.ndarray: """ Real part of the inverse Morlet :param band_order_Nth: Nth order of constant Q bands :param time_s: time in seconds :param offset_time_s: offset time in seconds, should be between min and max of time_s :param scale_frequency_center_hz: center frequency fc in Hz :param cwt_amp_real: real amplitude coefficient :param frequency_sample_rate_hz: sample rate of frequency in Hz :return: real inverse """ xtime_shifted, xscale, cycles_M, rescale = \ inv_morlet2_prep(band_order_Nth, time_s, offset_time_s, scale_frequency_center_hz, frequency_sample_rate_hz) wavelet_gauss = np.exp(-0.5 * (xtime_shifted / xscale) ** 2) wavelet_gabor_real = wavelet_gauss * np.cos(cycles_M*(xtime_shifted / xscale)) # Rescale to Morlet wavelet and take the conjugate for imag morlet2_inv_real = cwt_amp_real*wavelet_gabor_real morlet2_inv_real *= rescale return morlet2_inv_real def morlet2_reconstruct(band_order_Nth: float, scale_frequency_center_hz: float, frequency_sample_rate_hz: float) ‑> Tuple[float, float]-
Reconstruction coefficients from Garces (2020)
:param band_order_Nth: Nth order of constant Q bands :param scale_frequency_center_hz: center frequency fc in Hz :param frequency_sample_rate_hz: sample rate of frequency in Hz :return: atom scale, reconstruction coefficients
Expand source code
def morlet2_reconstruct(band_order_Nth: float, scale_frequency_center_hz: float, frequency_sample_rate_hz: float) -> Tuple[float, float]: """ Reconstruction coefficients from Garces (2020) :param band_order_Nth: Nth order of constant Q bands :param scale_frequency_center_hz: center frequency fc in Hz :param frequency_sample_rate_hz: sample rate of frequency in Hz :return: atom scale, reconstruction coefficients """ cycles_M, quality_factor_Q = scales.wavelet_MQ_from_N(band_order_Nth) morlet2_scale = cycles_M*frequency_sample_rate_hz/scale_frequency_center_hz/(2. * np.pi) reconstruct = np.pi**0.25/2/np.sqrt(morlet2_scale) return morlet2_scale, reconstruct