def reddening_spectrum(self,
wave,
flux,
reddening_curve,
cHbeta=None,
E_BV=None,
R_v=None):
# cHbeta format
if isinstance(cHbeta, float):
cHbeta_mag = cHbeta
elif isinstance(cHbeta, UFloat):
cHbeta_mag = cHbeta
# If it is negative we set it to zero
if cHbeta_mag < 0.0:
cHbeta_mag = 0.0
# By default we perform the calculation using the colour excess
E_BV = E_BV if E_BV != None else self.Ebv_from_cHbeta(
cHbeta, reddening_curve, R_v)
# Perform dereddening
wavelength_range_Xx = self.reddening_Xx(wave, reddening_curve, R_v)
flux_range_red = flux * np_power(10, -0.4 * wavelength_range_Xx * E_BV)
return flux_range_red
def X_x_Cardelli1989(self):
x_true = 1.0 / (self.wavelength_rc / 10000.0)
y = x_true - 1.82
y_coeffs = array([
ones(len(y)), y,
np_power(y, 2),
np_power(y, 3),
np_power(y, 4),
np_power(y, 5),
np_power(y, 6),
np_power(y, 7)
])
a_coeffs = array([
1, 0.17699, -0.50447, -0.02427, 0.72085, 0.01979, -0.77530, 0.32999
])
b_coeffs = array([
0, 1.41338, 2.28305, 1.07233, -5.38434, -0.62251, 5.30260, -2.09002
])
a_x = dot(a_coeffs, y_coeffs)
b_x = dot(b_coeffs, y_coeffs)
X_x = a_x + b_x / self.R_v
return X_x
def inner(start_time, end_time):
data = pitcache_getter(lnmkvdata_name,
10).get_tsdata(start_time, end_time)
data = np_power(data, exponent)
return data
def gaussian(x, mu, sig):
return np_exp(-np_power(x - mu, 2.) / (2 * np_power(sig, 2.)))
def gammatone(freq, k=5, fs=48000, is_plot=False):
"""
ECMA-418-2 Gammatone filter design
This function computes the coefficients of a gammatone digital filter according to ECMA-418-2 section 5.1.3.
Parameters
----------
freq: float
Center frequency of the filter ['Hz'].
k: int, optional
The order of the filter. Default is "5" according to ECMA-418.2.
fs: float, optional
The sampling frequency of the signal. Default is 48000 Hz.
Returns
-------
bm_prim, am_prim: ndarray, ndarray
Numerator (b) and denominator (a) polynomials of the filter.
"""
# ECMA-418-2 constants
af_f0 = 81.9289
c = 0.1618
# Bandwidth (ECMA 418-2 equation 7)
delta_f = sqrt((af_f0 ** 2) + ((c * freq) ** 2))
# Time constant, delay (ECMA 418-2 equation 5)
binom = comb(2 * k - 2, k - 1, exact=True)
tau = (1 / (2 ** (2 * k - 1))) * binom * (1.0 / delta_f)
# "d" coefficient
d = exp(-1 / (fs * tau))
# coeff am (ECMA 418-2 equation 11)
m = arange(5) + 1
am = np_power((-d), m) * comb(5, m)
am = np_insert(am, 0, 1)
# coeff bm (ECMA 418-2 equation 12)
em = np_array([0, 1, 11, 11, 1])
i = arange(4) + 1
denom = np_sum(em[i] * d ** i)
m = arange(5)
bm = ((1 - d) ** k) / denom * (d ** m) * em[m]
# band pass filter coefficients (ECMA 418-2 equation 13 & 14)
# [by modifying the filter ceofficients with a negative exponential,
# the filter is a low-pass filter instead of the expected bandpass
# filter]
m = arange(6)
exponential = exp(-1j * 2 * pi * freq * m / fs)
am_prim_ecma = am * exponential
bm_prim_ecma = bm * exponential[:-1]
# band pass filter coefficients (ECMA 418-2 from equation 13 & 14)
# [corrected to get a bandpass filter, to be validated]
m = arange(6)
exponential = exp(1j * 2 * pi * freq * m / fs)
am_prim = am * exponential
bm_prim = bm * exponential[:-1]
if is_plot:
w, h = freqz(bm, am, worN=round(fs / 2), fs=fs)
h_db = 20.0 * log10(np_abs(h))
plt.semilogx(w, h_db, label="am, bm from eq. 11 and 12")
w, h = freqz(bm_prim_ecma, am_prim_ecma, worN=round(fs / 2), fs=fs)
h_db = 20.0 * log10(np_abs(h))
plt.semilogx(w, h_db, label="am', bm' from eq. 13 and 14")
w, h = freqz(bm_prim, am_prim, worN=round(fs / 2), fs=fs)
h_db = 20.0 * log10(np_abs(h))
plt.semilogx(w, h_db, label="am', bm' with positive exp")
plt.xlabel("Frequency [Hz]")
plt.ylabel("Amplitude [dB]")
plt.grid(which="both", axis="both")
plt.legend()
return bm_prim, am_prim
si = (dl-Data_Dict['dg'][ilo]) / (Data_Dict['dg'][ilo+1]-Data_Dict['dg'][ilo])
tj = (tl-Data_Dict['Tg'][jlo]) / (Data_Dict['Tg'][jlo+1]-Data_Dict['Tg'][jlo])
uk = (op-Data_Dict['taug'][klo]) / (Data_Dict['taug'][klo+1]-Data_Dict['taug'][klo])
Data_Dict['ilo'] = ilo
Data_Dict['jlo'] = jlo
Data_Dict['klo'] = klo
Data_Dict['si'] = si
Data_Dict['tj'] = tj
Data_Dict['uk'] = uk
#Check the coordinates calculation
manage_warnings('Check coordinates', Data_Dict)
#Need to include density multiplications since precomputed level populations do not have density divided out...
dd1 = np_power(10, Data_Dict['dg'][ilo])
dd1 = dd1 * dd1 * Data_Dict['AHe']
dd2 = np_power(10, Data_Dict['dg'][ilo + 1])
dd2 = dd2 * dd2 * Data_Dict['AHe']
#Trilinear interpolation (8 vertices)
v1 = (1-si) * (1-tj) * (1-uk) * Data_Dict['pg'][ku2, ilo, jlo, klo]
v2 = si * (1-tj) * (1-uk) * Data_Dict['pg'][ku2, ilo+1, jlo, klo]
v3 = (1-si) * tj * (1-uk) * Data_Dict['pg'][ku2, ilo, jlo+1, klo]
v4 = si * tj * (1-uk) * Data_Dict['pg'][ku2, ilo+1, jlo+1, klo]
v5 = (1-si) * (1-tj) * uk * Data_Dict['pg'][ku2, ilo, jlo , klo+1]
v6 = si * (1-tj) * uk * Data_Dict['pg'][ku2,ilo+1,jlo ,klo+1]
v7 = (1-si) * tj * uk * Data_Dict['pg'][ku2,ilo ,ilo+1,klo+1]
v8 = si * tj * uk * Data_Dict['pg'][ku2,ilo+1,jlo+1,klo+1]
uppop = (1e10/dd1) * (v1+v3+v5+v7) + (1e10/dd2) * (v2+v4+v6+v8)
uppop = uppop * (den * Data_Dict['denHe']/1e10)