# -*- coding: utf-8 -*-
from numpy import clip, sqrt, mean, array, linspace, sum, log10
# Project Imports
from mosqito.sq_metrics.loudness.loudness_ecma._band_pass_signals import (
_band_pass_signals,
)
from mosqito.sq_metrics.loudness.loudness_ecma._ecma_time_segmentation import (
_ecma_time_segmentation,
)
from mosqito.sq_metrics.loudness.loudness_ecma._nonlinearity import _nonlinearity
from mosqito.sq_metrics.loudness.loudness_ecma._preprocessing import (
_preprocessing,
)
# Data import
# Threshold in quiet
from mosqito.sq_metrics.loudness.loudness_ecma._loudness_ecma_data import ltq_z
[docs]
def loudness_ecma(signal, fs, sb=2048, sh=1024):
"""Calculation of the specific and total loudness according to ECMA-418-2
(2nd Ed, 2022), Section 5.
This function computes the acoustic loudness according to ECMA-418-2 section 5 method for
stationary signals.
Parameters
----------
signal: numpy.array
Signal time values [Pa]. The sampling frequency of the signal must be 48000 Hz.
sb: int or list of int
Block size.
sh: int or list of int
Hop size.
Returns
-------
N : float
Overall loudness representative value [sone_HMS].
N_time : numpy.ndarray
Loudness over time [sone_HMS], size (Ntime,).
N_specific : numpy.ndarray
Specific loudness [sone_HMS/bark], size (Nbark, Ntime).
Each of the 53 elements of the list corresponds to the time-dependant specific loudness for a given bark band. Can be a ragged array if a different sb/sh are used for each band.
bark_axis : numpy.ndarray
Corresponding bark axis, size (Nbark,).
time_array : numpy.ndarray
Time axis, size (Nbark, Ntime).
Warning
-------
The sampling frequency of the signal must be 48 kHz.
See Also
--------
.loudness_zwst : Zwicker and Fastl loudness computation for a stationary time signal
.loudness_zwtv : Zwicker and Fastl loudness computation for a non-stationary time signal
References
----------
:cite:empty:`L_ecma-ECMA-418-2`
.. bibliography::
:keyprefix: L_ecma-
Examples
--------
.. plot::
:include-source:
>>> from mosqito.sq_metrics import loudness_ecma
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> f=1000
>>> fs=48000
>>> d=0.2
>>> dB=60
>>> time = np.arange(0, d, 1/fs)
>>> stimulus = 0.5 * (1 + np.sin(2 * np.pi * f * time))
>>> rms = np.sqrt(np.mean(np.power(stimulus, 2)))
>>> ampl = 0.00002 * np.power(10, dB / 20) / rms
>>> stimulus = stimulus * ampl
>>> N, N_time, N_spec, bark_axis, time_array = loudness_ecma(stimulus, fs)
>>> plt.plot(time_array[0], N_time)
>>> plt.xlabel("Time [s]")
>>> plt.ylabel("Loudness [Sone]")
"""
if fs != 48000:
print(
"[Warning] Signal resampled to 48 kHz fulfill the standard requirements and allow calculation."
)
from scipy.signal import resample
signal = resample(signal, int(48000 * len(signal) / fs))
fs = 48000
# Windowing and zero-padding (5.1.2)
signal, n_new = _preprocessing(signal, sb, sh)
# Computaton of band-pass signals (5.1.3 to 5.1.4)
bandpass_signals = _band_pass_signals(signal, sb, sh)
# 5.1.5 Segmentation into blocks
block_array, time_array = _ecma_time_segmentation(bandpass_signals, sb, sh, n_new)
# Segmentation into blocks (5.1.5)
#block_array, time_array = _ecma_time_segmentation(bandpass_signals, sb, sh, n_new)
# Rectification (5.1.6)
block_array_rect = clip(block_array, a_min=0.00, a_max=None)
# Calculation of specific loudness (5.1.7 to 5.1.9)
N_spec = []
for band_number in range(53):
# root mean square values (eq. 22)
rms_block_value = sqrt(
2 * mean(array(block_array_rect[band_number]) ** 2, axis=1)
)
# non-linear transformation of sound pressure to specific loudness
a_prime = _nonlinearity(rms_block_value)
# specific loudness considering the lower threshold of hearing.
a_prime[a_prime < ltq_z[band_number]] = ltq_z[band_number]
N_prime = a_prime - ltq_z[band_number]
N_spec.append(N_prime)
# Time dependent values (eq. 116)
delta_z = 0.5
N_time = sum(N_spec, axis=0) * delta_z
# Single-value loudness (eq. 117)
e = 1 / log10(2)
N = (mean(N_time**e)) ** (1 / e)
bark_axis = linspace(0.5, 26.5, num=53, endpoint=True)
return N, N_time, N_spec, bark_axis, time_array
