def hsll(wnd, res=20, neighbors=2):
"""
Highest Side Lobe Level (dB).
Parameters
----------
res :
Zero-padding factor. 1 for no zero-padding, 2 for twice the length, etc..
neighbors :
Number of neighbors needed by ``get_peaks`` to define a peak.
"""
spectrum = dB20(rfft(wnd, res * len(wnd)))
first_peak = next(get_peaks(spectrum, neighbors=neighbors))
return max(spectrum[first_peak:]) - spectrum[0]
def hsll(wnd, res=20, neighbors=2):
"""
Highest Side Lobe Level (dB).
Parameters
----------
res :
Zero-padding factor. 1 for no zero-padding, 2 for twice the length, etc..
neighbors :
Number of neighbors needed by ``get_peaks`` to define a peak.
"""
spectrum = dB20(rfft(wnd, res * len(wnd)))
first_peak = next(get_peaks(spectrum, neighbors=neighbors))
return max(spectrum[first_peak:]) - spectrum[0]
def find_xdb_bin(wnd, power=.5, res=1500):
"""
A not so fast way to find the x-dB cutoff frequency "bin" index.
Parameters
----------
wnd:
The window itself as an iterable.
power:
The power value (squared amplitude) where the x-dB value should lie,
using ``x = dB10(power)``.
res :
Zero-padding factor. 1 for no zero-padding, 2 for twice the length, etc..
"""
spectrum = dB20(rfft(wnd, res * len(wnd)))
root_at_xdb = spectrum - spectrum[0] - dB10(power)
return next(i for i, el in enumerate(zcross(root_at_xdb)) if el) / res
def find_xdb_bin(wnd, power=.5, res=1500):
"""
A not so fast way to find the x-dB cutoff frequency "bin" index.
Parameters
----------
wnd:
The window itself as an iterable.
power:
The power value (squared amplitude) where the x-dB value should lie,
using ``x = dB10(power)``.
res :
Zero-padding factor. 1 for no zero-padding, 2 for twice the length, etc..
"""
spectrum = dB20(rfft(wnd, res * len(wnd)))
root_at_xdb = spectrum - spectrum[0] - dB10(power)
return next(i for i, el in enumerate(zcross(root_at_xdb)) if el) / res
plt.xlabel("Frequency (Hz)")
plt.ylabel("Gain (dB)")
plt.figure(2)
plt.subplot(2, ceil(len(plot_freq_time) / 2), idx)
plt.title("Impulse response - {0} Hz".format(fc))
plt.xlabel("Time (ms)")
plt.ylabel("Amplitude")
# Plots each filter frequency and impulse response
for gt, config in zip(gammatone, ["b-", "g--", "r-.", "k:"]):
filt = gt(fc * Hz, bw)
plt.figure(1)
plt.plot(freq,
dB20(filt.freq_response(freq * Hz)),
config,
label=gt.__name__)
plt.figure(2)
plt.plot(time_scale,
filt(impulse()).take(num_samples),
config,
label=gt.__name__)
# Finish
for graph in fig1.axes + fig2.axes:
graph.grid()
graph.legend(loc="best")
fig1.tight_layout()
def scalloping_loss(wnd):
""" Positive number with the scalloping loss in dB. """
return -dB20(abs(sum(wnd * cexp(line(len(wnd), 0, -1j * pi)))) / sum(wnd))
def slfo(wnd, res=50, neighbors=2, max_miss=.7, start_delta=1e-4):
"""
Side Lobe Fall Off (dB/oct).
Finds the side lobe peak fall off numerically in dB/octave by using the
``scipy.optimize.fmin`` function.
Hint
----
Originally, Harris rounded the results he found to a multiple of -6, you can
use the AudioLazy ``rint`` function for that: ``rint(falloff, 6)``.
Parameters
----------
res :
Zero-padding factor. 1 for no zero-padding, 2 for twice the length, etc..
neighbors :
Number of neighbors needed by ``get_peaks`` to define a peak.
max_miss :
Maximum percent of peaks that might be missed when approximating them
by a line.
start_delta :
Minimum acceptable value for an orthogonal deviation from the
approximation line to include a peak.
"""
# Finds all side lobe peaks, to find the "best" line for it afterwards
spectrum = dB20(rfft(wnd, res * len(wnd)))
peak_indices = list(get_peaks(spectrum, neighbors=neighbors))
log2_peak_indices = np.log2(
peak_indices) # Base 2 ensures result in dB/oct
peaks = spectrum[peak_indices]
npeaks = len(peak_indices)
# This length (actually, twice the length) is the "weight" of each peak
lengths = np.array([0] + (1 - z**-2)(log2_peak_indices).skip(2).take(inf) +
[0]) # Extreme values weights to zero
max_length = sum(lengths)
# First guess for the polynomial "a*x + b" is at the center
idx = np.searchsorted(log2_peak_indices,
.5 * (log2_peak_indices[-1] + log2_peak_indices[0]))
a = ((peaks[idx + 1] - peaks[idx]) /
(log2_peak_indices[idx + 1] - log2_peak_indices[idx]))
b = peaks[idx] - a * log2_peak_indices[idx]
# Scoring for the optimization function
def score(vect, show=False):
a, b = vect
h = start_delta * (1 + a**2)**.5 # Vertical deviation
while True:
pdelta = peaks - (a * log2_peak_indices + b)
peaks_idx_included = np.nonzero((pdelta < h) & (pdelta > -h))
missing = npeaks - len(peaks_idx_included[0])
if missing < npeaks * max_miss:
break
h *= 2
pdelta_included = pdelta[peaks_idx_included]
real_delta = max(pdelta_included) - min(pdelta_included)
total_length = sum(lengths[peaks_idx_included])
if show: # For debug
print(real_delta, len(peaks_idx_included[0]))
return -total_length / max_length + 4 * real_delta**.5
a, b = so.fmin(score, [a, b], xtol=1e-12, ftol=1e-12, disp=False)
# # For Debug only
# score([a, b], show=True)
# plt.figure()
# plt.plot(log2_peak_indices, peaks, "x-")
# plt.plot(log2_peak_indices, a * log2_peak_indices + b)
# plt.show()
return a
("scallop", "Scallop loss (dB)"), #
("wcpl", "Worst case process loss (dB)"), #
("bw6", "25% power bandwidth (bins)"), #
("ol75", "75% overlap correlation (percent)"), #
("ol50", "50% overlap correlation (percent)"), #
])
size = 50 # Must be even!
full_size = 20 * size
table = []
for name, wnd_func in iteritems(table_wnds):
if name in has_separator_before:
table.append([".."] + [""] * (len(schema) - 1))
wnd = wnd_func(size)
spectrum = dB20(rfft(wnd, full_size))
wnd_full = wnd_func(full_size)
wnd_data = {
"name": name,
"hsll": hsll(wnd_full),
"slfo": slfo(wnd_full),
"cg": coherent_gain(wnd_full),
"enbw": enbw(wnd_full),
"bw3": 2 * find_xdb_bin(wnd, .5),
"scallop": scalloping_loss(wnd_full),
"wcpl": worst_case_processing_loss(wnd_full),
"bw6": 2 * find_xdb_bin(wnd, .25),
"ol75": overlap_correlation(wnd_full, .25 * full_size) * 100,
"ol50": overlap_correlation(wnd_full, .5 * full_size) * 100,
}
def find_xdb_bin(wnd, power=.5, res=1500): """ A not so fast way to find the x-dB cutoff frequency "bin" index """ spectrum = dB20(rfft(wnd, res * len(wnd))) root_at_xdb = spectrum - spectrum[0] - dB10(power) return next(i for i, el in enumerate(zcross(root_at_xdb)) if el) / res
from matplotlib import pyplot as plt
import numpy as np
from audiolazy import lazy_lpc as lpc
from audiolazy import dB20
from audiolazy.lazy_synth import line
from math import pi
data = eval(file("inputbufferdata.txt").read())
#plt.plot(data)
# see http://stackoverflow.com/questions/22328920/extract-numerical-values-from-zfilter-object-in-python-in-audiolazy-library
gain = 1e-2 # Gain just for alignment with DFT
samples = 1024
min_freq = 0
max_freq = pi
new_data = gain / lpc.lpc(data, order=20)
freqs = list(line(samples, min_freq, max_freq, finish=True))
data = new_data.freq_response(freqs)
print dB20(data)
plt.plot(dB20(data))
plt.show()
def scalloping_loss(wnd): """ Positive number with the scalloping loss in dB. """ return -dB20(abs(sum(wnd * cexp(line(len(wnd), 0, -1j * pi)))) / sum(wnd))
def slfo(wnd, res=50, neighbors=2, max_miss=.7, start_delta=1e-4):
"""
Side Lobe Fall Off (dB/oct).
Finds the side lobe peak fall off numerically in dB/octave by using the
``scipy.optimize.fmin`` function.
Hint
----
Originally, Harris rounded the results he found to a multiple of -6, you can
use the AudioLazy ``rint`` function for that: ``rint(falloff, 6)``.
Parameters
----------
res :
Zero-padding factor. 1 for no zero-padding, 2 for twice the length, etc..
neighbors :
Number of neighbors needed by ``get_peaks`` to define a peak.
max_miss :
Maximum percent of peaks that might be missed when approximating them
by a line.
start_delta :
Minimum acceptable value for an orthogonal deviation from the
approximation line to include a peak.
"""
# Finds all side lobe peaks, to find the "best" line for it afterwards
spectrum = dB20(rfft(wnd, res * len(wnd)))
peak_indices = list(get_peaks(spectrum, neighbors=neighbors))
log2_peak_indices = np.log2(peak_indices) # Base 2 ensures result in dB/oct
peaks = spectrum[peak_indices]
npeaks = len(peak_indices)
# This length (actually, twice the length) is the "weight" of each peak
lengths = np.array([0] + (1 - z **-2)(log2_peak_indices).skip(2).take(inf) +
[0]) # Extreme values weights to zero
max_length = sum(lengths)
# First guess for the polynomial "a*x + b" is at the center
idx = np.searchsorted(log2_peak_indices,
.5 * (log2_peak_indices[-1] + log2_peak_indices[0]))
a = ((peaks[idx+1] - peaks[idx]) /
(log2_peak_indices[idx+1] - log2_peak_indices[idx]))
b = peaks[idx] - a * log2_peak_indices[idx]
# Scoring for the optimization function
def score(vect, show=False):
a, b = vect
h = start_delta * (1 + a ** 2) ** .5 # Vertical deviation
while True:
pdelta = peaks - (a * log2_peak_indices + b)
peaks_idx_included = np.nonzero((pdelta < h) & (pdelta > -h))
missing = npeaks - len(peaks_idx_included[0])
if missing < npeaks * max_miss:
break
h *= 2
pdelta_included = pdelta[peaks_idx_included]
real_delta = max(pdelta_included) - min(pdelta_included)
total_length = sum(lengths[peaks_idx_included])
if show: # For debug
print(real_delta, len(peaks_idx_included[0]))
return -total_length / max_length + 4 * real_delta ** .5
a, b = so.fmin(score, [a, b], xtol=1e-12, ftol=1e-12, disp=False)
# # For Debug only
# score([a, b], show=True)
# plt.figure()
# plt.plot(log2_peak_indices, peaks, "x-")
# plt.plot(log2_peak_indices, a * log2_peak_indices + b)
# plt.show()
return a
("scallop", "Scallop loss (dB)"), #
("wcpl", "Worst case process loss (dB)"), #
("bw6", "25% power bandwidth (bins)"), #
("ol75", "75% overlap correlation (percent)"), #
("ol50", "50% overlap correlation (percent)"), #
])
size = 50 # Must be even!
full_size = 20 * size
table = []
for name, wnd_func in iteritems(table_wnds):
if name in has_separator_before:
table.append([".."] + [""] * (len(schema) - 1))
wnd = wnd_func(size)
spectrum = dB20(rfft(wnd, full_size))
wnd_full = wnd_func(full_size)
wnd_data = {
"name": name,
"hsll": hsll(wnd_full),
"slfo": slfo(wnd_full),
"cg": coherent_gain(wnd_full),
"enbw": enbw(wnd_full),
"bw3": 2 * find_xdb_bin(wnd, .5),
"scallop": scalloping_loss(wnd_full),
"wcpl": worst_case_processing_loss(wnd_full),
"bw6": 2 * find_xdb_bin(wnd, .25),
"ol75": overlap_correlation(wnd_full, .25 * full_size) * 100,
"ol50": overlap_correlation(wnd_full, .5 * full_size) * 100,
}
plt.title("Frequency response - {0} Hz".format(fc))
plt.xlabel("Frequency (Hz)")
plt.ylabel("Gain (dB)")
plt.figure(2)
plt.subplot(2, ceil(len(plot_freq_time) / 2), idx)
plt.title("Impulse response - {0} Hz".format(fc))
plt.xlabel("Time (ms)")
plt.ylabel("Amplitude")
# Plots each filter frequency and impulse response
for gt, config in zip(gammatone, ["b-", "g--", "r-.", "k:"]):
filt = gt(fc * Hz, bw)
plt.figure(1)
plt.plot(freq, dB20(filt.freq_response(freq * Hz)), config,
label=gt.__name__)
plt.figure(2)
plt.plot(time_scale, filt(impulse()).take(num_samples), config,
label=gt.__name__)
# Finish
for graph in fig1.axes + fig2.axes:
graph.grid()
graph.legend(loc="best")
fig1.tight_layout()
fig2.tight_layout()
plt.show()
plt.title("Frequency response - {0} Hz".format(fc))
plt.xlabel("Frequency (Hz)")
plt.ylabel("Gain (dB)")
plt.figure(2)
plt.subplot(2, ceil(len(plot_freq_time) / 2), idx)
plt.title("Impulse response - {0} Hz".format(fc))
plt.xlabel("Time (ms)")
plt.ylabel("Amplitude")
# Plots each filter frequency and impulse response
for gt, config in zip(gammatone, ["b-", "g--", "r-.", "k:"]):
filt = gt(fc * Hz, bw)
plt.figure(1)
plt.plot(freq, dB20(filt.freq_response(freq * Hz)), config,
label=gt.__name__)
plt.figure(2)
plt.plot(time_scale, filt(impulse()).take(num_samples), config,
label=gt.__name__)
# Finish
for graph in fig1.axes + fig2.axes:
graph.grid()
graph.legend(loc="best")
fig1.tight_layout()
fig2.tight_layout()
plt.show()
plt.title("Frequency response - {0} Hz".format(fc))
plt.xlabel("Frequency (Hz)")
plt.ylabel("Gain (dB)")
plt.figure(2)
plt.subplot(2, ceil(len(plot_freq_time) / 2), idx)
plt.title("Impulse response - {0} Hz".format(fc))
plt.xlabel("Time (ms)")
plt.ylabel("Amplitude")
# Plots each filter frequency and impulse response
for gt, config in zip(gammatone, ["b-", "g--", "r-.", "k:"]):
filt = gt(fc * Hz, bw)
plt.figure(1)
plt.plot(freq, dB20(filt.freq_response(freq * Hz)), config, label=gt.__name__)
plt.figure(2)
plt.plot(time_scale, filt(impulse()).take(num_samples), config, label=gt.__name__)
# Finish
for graph in fig1.axes + fig2.axes:
graph.grid()
graph.legend(loc="best")
fig1.tight_layout()
fig2.tight_layout()
plt.ioff()
plt.show()
from matplotlib import pyplot as plt
import numpy as np
from audiolazy import lazy_lpc as lpc
from audiolazy import dB20
from audiolazy.lazy_synth import line
from math import pi
data = eval(file("inputbufferdata.txt").read())
#plt.plot(data)
# see http://stackoverflow.com/questions/22328920/extract-numerical-values-from-zfilter-object-in-python-in-audiolazy-library
gain = 1e-2 # Gain just for alignment with DFT
samples = 1024
min_freq = 0
max_freq = pi
new_data = gain/lpc.lpc(data, order=20)
freqs = list(line(samples, min_freq, max_freq, finish=True))
data = new_data.freq_response(freqs)
print dB20(data)
plt.plot(dB20(data))
plt.show()