def seq_filters(self):
"""
:return:
"""
# Linear delay filter. Builtin filter.
delay = DelayFilter()
# The incoming signal is unchanged.
original = delay(0)
# The norm of the signal. Builtin filter.
norm = NormFilter()
# Abstract sliding window. Builtin filter.
sw = BaseSWFilter(min_size=2)
sw_mean = sw | numeric.mean
# or sw_mean = MeanSWFilter()
return [
FilterDescription(
name='$F_{L_1} = |F_{t}|_{L_1}$',
plot_options=PlotOptions(
style='-',
color='lightgray',
width=3.0,
),
formula=original | norm(l=1),
),
FilterDescription(name='$M_{50} = |\hat{\mu}_{50}(F_{L_1})|$',
plot_options=PlotOptions(
style='-',
color='orange',
width=2.0,
),
formula=norm(l=1) | sw_mean(s=50)),
FilterDescription(name='$M_{100} = |\hat{\mu}_{100}(F_{L_1})|$',
plot_options=PlotOptions(
style='-',
color='red',
width=2.0,
),
formula=norm(l=1) | sw_mean(s=100)),
FilterDescription(name='$M_{200} = |\hat{\mu}_{200}(F_{L_1})|$',
plot_options=PlotOptions(
style='-',
color='blue',
width=2.0,
),
formula=norm(l=1) | sw_mean(s=200)),
]
def seq_filters(self):
"""
:return:
"""
# Linear delay filter. Builtin filter.
delay = DelayFilter()
# The incoming signal is unchanged.
original = delay(0)
# Shift signal to one frame. Builtin filter.
shift = ShiftSWFilter()
# The difference between neighboring frames.
diff = original - shift
# The norm of the signal. Builtin filter.
norm = NormFilter()
# Abstract sliding window. Builtin filter.
sw = BaseSWFilter(min_size=2)
sw_mean = sw | numeric.mean
# or sw_mean = MeanSWFilter()
sw_median = MedianSWFilter(size=10)
# sw_max = sw | max
sign_change = SignChangeFilter()
atan = (diff
| original * 256.0
| numeric.math.atan
| original * 2.0
| original / numeric.math.pi)
# or atan = AtanFilter()
def sw_mean_diff(g, l):
"""
:param g:
:param l:
:return:
"""
return (norm(l=1)
| sw_median(s=10)
| (sw_mean(s=g) - sw_mean(s=l))
| (sign_change * atan))
# Sequence of voters.
voters = range(self.VOTER_COUNT)
# Sequence of sliding window sizes.
sizes = list(self.VOTER_SIZE * (i + 1) for i in voters)
# Sequence of votes of different range normalizations.
sw_mean_diff_seq = tuple(
sw_mean_diff(g=g_size, l=l_size) for g_size in sizes
for l_size in sizes if g_size > l_size)
# fork = ForkFilter()
#
# bulk = BulkFilter()
# Average vote of different range normalizations.
sw_mean_diff_norm = (original
| sum(sw_mean_diff_seq)
| original / len(sw_mean_diff_seq))
#
# print('sw_mean_diff(25,12) = ', sw_mean_diff_norm)
return [
FilterDescription(
name='$F_{L_1} = |F_{t}|_{L_1}$',
plot_options=PlotOptions(
style='-',
color='lightgray',
width=3.0,
),
formula=norm(l=1),
),
#
#
# FilterDescription(
# name='$M_{50} = |\hat{\mu}_{50}(F_{L_1})|$',
# plot_options=PlotOptions(
# style='-',
# color='orange',
# width=2.0,
# ),
# formula=norm(l=1) | sw_mean(s=50)
# ),
#
# FilterDescription(
# name='$M_{100} = |\hat{\mu}_{100}(F_{L_1})|$',
# plot_options=PlotOptions(
# style='-',
# color='red',
# width=2.0,
# ),
# formula=norm(l=1) | sw_mean(s=100)
# ),
#
# FilterDescription(
# name='$M_{200} = |\hat{\mu}_{200}(F_{L_1})|$',
# plot_options=PlotOptions(
# style='-',
# color='blue',
# width=2.0,
# ),
# formula=norm(l=1) | sw_mean(s=200)
# ),
#
#
# FilterDescription(
# name='$|M_{200} - M_{50}| \\to_{\pm} 0$',
# plot_options=PlotOptions(
# style='--',
# color='blue',
# width=1.2,
# ),
# formula=(
# norm(l=1)
# | (sw_mean(s=200) - sw_mean(s=50))
# # | sign_changes
# # | abs
# # | original * 0.9
# )
# ),
#
#
# FilterDescription(
# name='$M_{50} = |\hat{\mu}_{50}(F_{L_1})|$',
# plot_options=PlotOptions(
# style='-',
# color='orange',
# width=2.0,
# ),
# formula=norm(l=1) | sw_mean(s=50)
# ),
#
#
#
# FilterDescription(
# name='$M_{50} = |\hat{\mu}_{50}(F_{L_1})|$',
# plot_options=PlotOptions(
# style='-',
# color='orange',
# width=2.0,
# ),
# formula=norm(l=1) | sw_mean(s=50)
# ),
FilterDescription(name='25',
plot_options=PlotOptions(
style='-',
color='orange',
width=2.0,
),
formula=norm(l=1) | sw_mean(s=25)),
FilterDescription(name='50',
plot_options=PlotOptions(
style='-',
color='red',
width=2.0,
),
formula=norm(l=1) | sw_mean(s=50)),
FilterDescription(name='75',
plot_options=PlotOptions(
style='-',
color='green',
width=2.0,
),
formula=norm(l=1) | sw_mean(s=75)),
FilterDescription(name='100',
plot_options=PlotOptions(
style='-',
color='purple',
width=2.0,
),
formula=norm(l=1) | sw_mean(s=100)),
FilterDescription(name='$A|M_{200} - M_{100}| \\to_{\pm} 0$',
plot_options=PlotOptions(
style='--',
color='blue',
width=1.0,
),
formula=norm(l=1) | sw_mean_diff_norm
# sw_mean_diff(25,12)
),
]
def seq_filters(self):
"""
:return:
"""
delay = DelayFilter()
norm = NormFilter()
modulus = ModulusFilter()
shift = ShiftSWFilter()
diff = delay(0) - shift
mean = MeanSWFilter()
std = StdSWFilter()
dtr = DecisionTreeRegressorSWFilter(regressor_depth=2)
def bill(c=3.0, s=1):
"""
:param c:
:param s:
:return:
"""
# noinspection PyTypeChecker
return (delay(0) > (mean(s=s) + c * std(s=s))) | int
return [
FilterDescription(
name='$F_{L_1} = |F_{t}|_{L_1}$',
plot_options=PlotOptions(
style='-',
color='lightgray',
width=3.0,
),
formula=norm(l=1),
),
FilterDescription(name='$DTR_{300,2}$',
plot_options=PlotOptions(
style='-',
color='red',
width=2.0,
),
formula=norm(l=1) | dtr(s=300, d=2)),
FilterDescription(name='$S = '
'1/k\sum_{i=1}^{k+1} DTR_{i \cdot 25, 2} $',
plot_options=PlotOptions(
style='-',
color='green',
width=2.0,
),
formula=norm(l=1)
| sum(dtr(s=25 * i + 1)
for i in range(1, 9)) / 8),
FilterDescription(name="$B_{50}/n = "
"(|S'| > |(\hat{\mu}_{50} "
"+ A \hat{\sigma}_{50})(S')|)"
"/n$",
plot_options=PlotOptions(
style='-',
color='magenta',
width=2.0,
),
formula=norm(l=1)
| sum(dtr(s=25 * i + 1) for i in range(1, 9)) / 8
| diff | modulus | bill(s=50) / 8),
FilterDescription(name='$V(t) = '
'1/n\sum_{j=1}^{n+1} B_{j \cdot 25} $',
plot_options=PlotOptions(
style=':',
color='blue',
width=2.0,
),
formula=norm(l=1)
| sum(dtr(s=25 * i + 1)
for i in range(1, 9)) / 8 | diff | modulus
| sum(bill(s=25 * j) for j in range(1, 9)) / 8),
]
dht = DHTFilter()
log = LogFilter()
exp = ExpFilter()
colour = ColourFilter()
extrema = ExtremaSWFilter(
strict_windows=True,
overlap_size=0,
cs=False,
)
delay = DelayFilter()
original = delay(0)
savgol = SavitzkyGolaySWFilter(
window_size=50,
strict_windows=True,
overlap_size=0,
# cs=False
)
wiener = WienerSWFilter(
window_size=50,
strict_windows=True,
overlap_size=0,
)
def seq_filters(self):
"""
Returns filter chart options.
What we do:
1. Declare «builtin» filters.
2. Build custom filters.
3. Build target filter.
4. Plot them with `FilterDescription`
:returns: filter descriptions for rescaling normalization.
:rtype: list of FilterDescription
"""
# Linear delay filter. Builtin filter.
delay = DelayFilter()
# The incoming signal is unchanged.
original = delay(0)
# Shift signal to one frame. Builtin filter.
shift = ShiftSWFilter()
# The difference between neighboring frames.
diff = original - shift
# The norm of the signal. Builtin filter.
norm = NormFilter()
# Threshold filter.
threshold = original > self.THRESHOLD
# Abstract sliding window. Builtin filter.
sw = BaseSWFilter(size=self.SLIDING_WINDOW_SIZE, min_size=2)
# Sliding window that returns maximum.
sw_max = sw | max
# Sliding window that returns minimum.
sw_min = sw | min
# Sum of absolute difference filter.
sad_filter = diff | abs | norm(l=1)
# Range normalization.
sw_norm = (original - sw_min) / (sw_max - sw_min)
# Frame difference rescaling normalization by span.
rescaling_filter = sad_filter | sw_norm
return [
FilterDescription(
# Original signal.
name='$F_{L_1} = ||F_{t}||_{L_1}$',
plot_options=PlotOptions(
style='-',
color='gray',
width=3.0,
),
formula=norm(l=1),
),
FilterDescription(
# Rescaling Normalization by Span.
name=('$D_{{\,{size},t}} '
'= sw\_norm_{{\,{size} }} D_{{t}}$'.format(
size=self.SLIDING_WINDOW_SIZE)),
plot_options=PlotOptions(
style='-',
color='green',
width=1.0,
),
formula=rescaling_filter),
FilterDescription(
# Sum of absolute difference filter.
name='$D_{t} = ||F_{t} - F_{t-1}||_{L_1}$',
plot_options=PlotOptions(
style='-',
color='blue',
width=2.0,
),
formula=sad_filter | norm(l=1)),
FilterDescription(
# rescaling filter > threshold.
name=('$D_{{\,{size},t}} > T_{{const}} $'.format(
size=self.SLIDING_WINDOW_SIZE)),
plot_options=PlotOptions(
style=':',
color='teal',
width=2.0,
),
formula=rescaling_filter | threshold),
FilterDescription(
# The threshold value.
name=('$T_{{const}} = {} \in (0; 1)$'.format(self.THRESHOLD)),
plot_options=PlotOptions(
style='-',
color='black',
width=2.0,
),
formula=norm(l=1) | self.THRESHOLD,
),
]
def seq_filters(self):
"""
Returns filter chart options.
What we do:
1. Declare «builtin» filters.
2. Build custom filters.
3. Build target filter.
4. Plot them with `FilterDescription`
:returns: filter descriptions for average normalization.
:rtype: list of FilterDescription
"""
# Linear delay filter. Builtin filter.
delay = DelayFilter()
# The incoming signal is unchanged.
original = delay(0)
# Shift signal to one frame. Builtin filter.
shift = ShiftSWFilter()
# The difference between neighboring frames.
diff = original - shift
# The norm of the signal. Builtin filter.
norm = NormFilter()
# Threshold filter.
# noinspection PyUnusedLocal
threshold = original > self.THRESHOLD
# Sum of absolute difference filter.
sad_filter = diff | abs | norm(l=1)
# Abstract sliding window. Builtin filter.
sw = BaseSWFilter(size=self.SLIDING_WINDOW_SIZE, min_size=2)
# Sliding window that returns maximum.
sw_max = sw | max
# Sliding window that returns minimum.
sw_min = sw | min
# Range normalization.
sw_norm = (original - sw_min) / (sw_max - sw_min)
# Sequence of voters.
voters = range(self.VOTER_COUNT)
# Sequence of sliding window sizes.
sizes = (self.VOTER_SIZE * (i + 1) for i in voters)
# Sequence of votes of different range normalizations.
sw_norm_votes_seq = (sw_norm(size=size) for size in sizes)
# Average vote of different range normalizations.
sw_vote_norm = Filter.sum(sw_norm_votes_seq) / self.VOTER_COUNT
return (
FilterDescription(
# Original signal.
name='$F_{L_1} = ||F_{t}||_{L_1}$',
plot_options=PlotOptions(
style='-',
color='gray',
width=3.0,
),
formula=norm(l=1),
),
FilterDescription(
# Sum of absolute difference filter.
name='$D_{t} = ||F_{t} - F_{t-1}||_{L_1}$',
plot_options=PlotOptions(
style=':',
color='gray',
width=1.0,
),
formula=sad_filter),
FilterDescription(
# Rescaling normalization with neighborhood size = 100.
name=('$D_{{\,{size},t}}'
'= sw\_norm_{{\,{size} }} D_{{t}}$'.format(size=100)),
plot_options=PlotOptions(
style='--',
color='purple',
width=1.0,
),
formula=sad_filter | sw_norm(size=100)),
FilterDescription(
# Rescaling normalization with neighborhood size = 200.
name=('$D_{{\,{size},t}} '
'= sw\_norm_{{\,{size} }} D_{{t}}$'.format(size=200)),
plot_options=PlotOptions(
style='-',
color='orange',
width=1.0,
),
formula=sad_filter | sw_norm(s=200)),
FilterDescription(
# Rescaling normalization with neighborhood size = 300.
name=('$D_{{\,{size},t}} '
'= sw\_norm_{{\,{size} }} D_{{t}}$'.format(size=300)),
plot_options=PlotOptions(
style='-',
color='violet',
width=1.0,
),
formula=sad_filter | sw_norm(s=300)),
FilterDescription(
# Rescaling normalization with neighborhood size = 400.
name=('$D_{{\,{size},t}} '
'= sw\_norm_{{\,{size} }} D_{{t}}$'.format(size=400)),
plot_options=PlotOptions(
style='-',
color='red',
width=1.0,
),
formula=sad_filter | sw_norm(s=400)),
FilterDescription(
# Average vote of different range normalizations.
name=('$V_{{\,{size},v,t}} = '
'\sum^{{i=v+1}}_{{i=1}} '
'\\frac{{ D_{{\,{size} i,t}} }}{{v}};'
' v = {voter_count}$'.format(
size=self.VOTER_SIZE, voter_count=self.VOTER_COUNT)),
plot_options=PlotOptions(
style='-',
color='green',
width=2.0,
),
formula=sad_filter | sw_vote_norm),
FilterDescription(
# The threshold value.
name=('$T_{{const}} = {} \in (0; 1)$'.format(self.THRESHOLD)),
plot_options=PlotOptions(
style='-',
color='black',
width=2.0,
),
formula=norm(l=1) | self.THRESHOLD,
),
)
def seq_filters(self):
"""
:return:
"""
delay = DelayFilter()
norm = NormFilter()
shift = ShiftSWFilter()
original = delay(0)
diff = original - shift
# noinspection PyPep8Naming
T_CONST = 0.8
# noinspection PyPep8Naming,PyUnusedLocal
S_CONST = 100
# noinspection PyUnusedLocal
threshold = original > T_CONST
# noinspection PyUnusedLocal
mean = MedianSWFilter(
size=200
)
# noinspection PyUnusedLocal
median = MedianSWFilter(
size=200
)
sad_filter = norm(l=1) | diff | abs
def pow_2(x):
"""
:param x:
:return:
"""
return x * x
d_chi = (
(diff | pow_2)
/ (Filter.to_tuple(original, shift) | max)
)
return (
FilterDescription(
# Original signal.
name='$F_{L_1} = |F_{t}|_{L_1}$',
plot_options=PlotOptions(
style='-',
color='gray',
width=3.0,
),
formula=norm(l=1),
),
# FilterDescription(
# name='$D_{{\,{size},t}} '
# '= swnorm_{{\,{size} }} D_{{t}}$'.format(
# size=S_CONST
# ),
# plot_options=dict(
# linestyle='-',
# color='green',
# linewidth=1.0,
# ),
# filter=sad_filter | norm(l=1) | swnorm
# ),
FilterDescription(
name='$D_{t} = |F_{t} - F_{t-1}|_{L_1}$',
plot_options=PlotOptions(
style='-',
color='blue',
width=2.0,
),
formula=sad_filter | norm(l=1)
),
FilterDescription(
# Original signal.
name='$F_{L_1} d_{chi} = |F_{t}|_{L_1}$',
plot_options=PlotOptions(
style='-',
color='red',
width=3.0,
),
formula=norm(l=1) | d_chi,
),
# FilterDescription(
# # The threshold value.
# name='$T_{{const}} = {} \in (0; 1)$'.format(T_CONST),
# plot_options=dict(
# linestyle='-',
# color='black',
# linewidth=2.0,
# ),
# filter=norm(l=1) | T_CONST,
# ),
)
def seq_filters(self):
"""
:return:
"""
sgn_changes = SignAngleDiff1DFilter()
delay = DelayFilter()
norm = NormFilter()
modulus = ModulusFilter()
shift = ShiftSWFilter()
diff = delay(0) - shift
mean = MeanSWFilter()
std = StdSWFilter()
# noinspection PyUnusedLocal
dtr = DecisionTreeRegressorSWFilter(regressor_depth=2)
def bill(c=3.0, s=1):
"""
:param c:
:param s:
:return:
"""
# noinspection PyTypeChecker
return (delay(0) > (mean(s=s) + c * std(s=s))) | int
def mdiff_bill(s=1):
"""
:param s:
:return:
"""
return (mean(s=s * 2) - mean(s=s)) | sgn_changes
return [
FilterDescription(
name='$F_{L_1} = |F_{t}|_{L_1}$',
plot_options=PlotOptions(
style='-',
color='lightgray',
width=3.0,
),
formula=norm(l=1),
),
FilterDescription(name='$V(t) = '
'1/n\sum_{j=1}^{n+1} B_{j \cdot 25} $',
plot_options=PlotOptions(
style=':',
color='blue',
width=2.0,
),
formula=norm(l=1)
| sum(mdiff_bill(s=i * 25)
for i in range(1, 9)) / 8),
FilterDescription(name='$V(t) = '
'1/n\sum_{j=1}^{n+1} B_{j \cdot 25} $',
plot_options=PlotOptions(
style=':',
color='blue',
width=2.0,
),
formula=norm(l=1)
| sum(mdiff_bill(s=i * 25)
for i in range(1, 9)) / 8 | diff | modulus
| sum(bill(s=25 * j) for j in range(1, 9)) / 8),
]
def seq_filters(self):
"""
:return:
"""
# Linear delay filter. Builtin filter.
delay = DelayFilter()
# The incoming signal is unchanged.
original = delay(0)
# Shift signal to one frame. Builtin filter.
shift = ShiftSWFilter()
# The difference between neighboring frames.
diff = original - shift
# The norm of the signal. Builtin filter.
norm = NormFilter()
# Abstract sliding window. Builtin filter.
sw = BaseSWFilter(min_size=2)
# Sum of absolute difference filter.
sad_filter = original | diff | abs | norm(l=1)
sw_mean = sw | numeric.mean
# or sw_mean = MeanSWFilter()
sw_std = sw | numeric.std
# or sw_std = StdSWFilter()
def z_score(size=1):
"""
:param size:
:return:
"""
return (((original - sw_mean(s=size)) / sw_std(s=size)) /
numeric.sqrt(size)
| abs)
def z_test(size=1):
"""
...
"""
estimation = z_score(size)
return estimation
# Sequence of voters.
voters = range(self.VOTER_COUNT)
# Sequence of sliding window sizes.
sizes = (self.VOTER_SIZE * (i + 1) for i in voters)
# Sequence of votes of different sizes.
z_vote_seq = (z_test(size=size) for size in sizes)
# Average vote of different sizes.
z_vote = sum(z_vote_seq) / self.VOTER_COUNT
return [
FilterDescription(
name='$F_{L_1} = ||F_{t}||_{L_1}$',
plot_options=PlotOptions(
style='-',
color='gray',
width=3.0,
),
formula=norm(l=1),
),
FilterDescription(
# Sum of absolute difference filter.
name='$D_{t} = ||F_{t} - F_{t-1}||_{L_1}$',
plot_options=PlotOptions(
style='-',
color='blue',
width=2.0,
),
formula=sad_filter),
FilterDescription(
name=('$D_{{t}} > E_{{ {size} }}\ (D_{{t}})$'.format(
size=100)),
plot_options=PlotOptions(
style='--',
color='green',
width=1.0,
),
formula=(diff | norm(l=1)
| z_test(size=50))),
FilterDescription(
name=('$D_{{t}} > E_{{ {size} }}\ (D_{{t}})$'.format(
size=200)),
plot_options=PlotOptions(
style='--',
color='red',
width=1.0,
),
formula=(diff | norm(l=1)
| z_test(size=200))),
FilterDescription(name=('VOTE'),
plot_options=PlotOptions(
style='-',
color='red',
width=2.0,
),
formula=(diff | norm(l=1)
| z_vote)),
]
def seq_filters(self):
"""
:return:
"""
# Linear delay filter. Builtin filter.
delay = DelayFilter()
# The incoming signal is unchanged.
original = delay(0)
# Shift signal to one frame. Builtin filter.
shift = ShiftSWFilter()
# The difference between neighboring frames.
diff = original - shift
# The norm of the signal. Builtin filter.
norm = NormFilter()
# Abstract sliding window. Builtin filter.
sw = BaseSWFilter(min_size=2)
# Sum of absolute difference filter.
sad_filter = diff | abs | norm(l=1)
sw_mean = sw | numeric.mean
# or sw_mean = MeanSWFilter()
sw_std = sw | numeric.std
# or sw_std = StdSWFilter()
def sigma_estimation(sigma=3.0, size=1):
"""
:param float sigma:
:param int size:
:return:
"""
return sw_mean(s=size) + sigma * sw_std(s=size)
def sigma_check(**kwargs):
"""
...
"""
return original > sigma_estimation(**kwargs)
return [
FilterDescription(
name='$F_{L_1} = ||F_{t}||_{L_1}$',
plot_options=PlotOptions(
style='-',
color='gray',
width=3.0,
),
formula=norm(l=1),
),
FilterDescription(
# Sum of absolute difference filter.
name='$D_{t} = ||F_{t} - F_{t-1}||_{L_1}$',
plot_options=PlotOptions(
style='-',
color='blue',
width=2.0,
),
formula=sad_filter),
FilterDescription(
# Estimation for sum of absolute difference
name=('$E_{{ {size} }}\ (D_{{t}}) = '
'\hat{{\mu}}_{{ {size} }}[D_{{t}}] + A \cdot '
'\hat{{\sigma}}_{{ {size} }}[D_{{t}}]$'.format(
size=100)),
plot_options=PlotOptions(
style='-',
color='orange',
width=2.0,
),
formula=(sad_filter
| sigma_estimation(size=100))),
FilterDescription(
# Estimation for sum of absolute difference
name=('$E_{{ {size} }}\ (D_{{t}}) = '
'\hat{{\mu}}_{{ {size} }}[D_{{t}}] + A \cdot '
'\hat{{\sigma}}_{{ {size} }}[D_{{t}}]$'.format(
size=200)),
plot_options=PlotOptions(
style='-',
color='red',
width=2.0,
),
formula=(sad_filter
| sigma_estimation(size=200))),
FilterDescription(
name=('$D_{{t}} > E_{{ {size} }}\ (D_{{t}})$'.format(
size=100)),
plot_options=PlotOptions(
style='--',
color='green',
width=1.0,
),
formula=(sad_filter
| sigma_check(size=100))),
FilterDescription(
name=('$D_{{t}} > E_{{ {size} }}\ (D_{{t}})$'.format(
size=200)),
plot_options=PlotOptions(style='--',
color='red',
width=1.5,
marker='x'),
formula=(sad_filter
| sigma_check(size=200) * 0.8)),
]
def seq_filters():
"""
:return:
"""
delay = DelayFilter()
original = delay(0)
norm = NormFilter()
shift = ShiftSWFilter(
window_size=2,
strict_windows=False,
cs=False,
)
mean = MeanSWFilter(
window_size=25,
# strict_windows=True,
cs=False)
std = StdSWFilter(
window_size=25,
strict_windows=True,
)
dtr = DecisionTreeRegressorSWFilter(
window_size=100,
strict_windows=True,
overlap_size=0,
cs=False,
)
sad = original - shift
def sigma3(c=3.0, **kwargs):
"""
:param c:
:param kwargs:
:return:
"""
# noinspection PyTypeChecker
return (original > (mean(**kwargs) + c * std(**kwargs))) | int
return [
SmartDict(
name='$F_{L_1} = |F_{t}|_{L_1}$',
plot_options=SmartDict(
linestyle='-',
color='lightgray',
linewidth=3.0,
),
filter=norm(l=1),
),
SmartDict(name='$DTR_{300,2}$',
plot_options=SmartDict(
linestyle='-',
color='red',
linewidth=2.0,
),
filter=norm(l=1) | dtr(s=300, d=2)),
SmartDict(name='$S_{DTR} = '
'\\frac{1}{k}\sum_{i=1}^{k} DTR_{i \cdot 25, 2} $',
plot_options=SmartDict(
linestyle='-',
color='green',
linewidth=2.0,
),
filter=norm(l=1)
| sum([dtr(s=25 * i + 1) for i in range(1, 9)]) / 8),
SmartDict(name='$B_{DTR} = \\frac{1}{k}\sum_{i=1}^{k} '
'DTR_{i \cdot 25, 2} $',
plot_options=SmartDict(
linestyle='-',
color='magenta',
linewidth=2.0,
),
filter=norm(l=1)
| sum([dtr(s=25 * i + 1) for i in range(1, 9)]) / 8 |
(sad | abs) | sum(sigma3(s=25 * j)
for j in range(1, 2)) / 8),
SmartDict(name="$V(t)$",
plot_options=SmartDict(
linestyle=':',
color='blue',
linewidth=2.0,
),
filter=norm(l=1)
| sum(dtr(s=25 * i + 1) for i in range(1, 9)) / 8 |
(sad | abs) | sum(sigma3(s=25 * j)
for j in range(1, 9)) / 8),
]
def seq_filters(self):
"""
Returns chart option sequence for SAD filter illustration.
What we do:
1. Declare «builtin» filters.
2. Build custom filters.
3. Build target filter.
4. Plot them with `FilterDescription`
:returns: filter descriptions for SAD filter.
:rtype: list of FilterDescription
"""
# Linear delay filter. Builtin filter.
delay = DelayFilter()
# The incoming signal is unchanged.
original = delay(0)
# Shift signal to one frame. Builtin filter.
shift = ShiftSWFilter()
# The difference between neighboring frames.
diff = original - shift
# The norm of the signal. Builtin filter.
norm = NormFilter()
# Threshold filter.
threshold = original > self.THRESHOLD
# Sum of absolute difference filter.
sad_filter = diff | abs | norm(l=1)
return (
FilterDescription(
# Original signal.
name='$F_{L_1} = ||F_{t}||_{L_1}$',
plot_options=PlotOptions(
style='-',
color='gray',
width=3.0,
),
formula=norm(l=1),
),
FilterDescription(
# Sum of absolute difference filter.
name='$D_{t} = ||F_{t} - F_{t-1}||_{L_1}$',
plot_options=PlotOptions(
style='-',
color='blue',
width=2.0,
),
formula=sad_filter),
FilterDescription(
# Sum of absolute difference filter > threshold.
name='$D_{t} > T_{const} $',
plot_options=PlotOptions(
style=':',
color='green',
width=2.0,
),
formula=sad_filter | threshold),
FilterDescription(
# The threshold value.
name='$T_{{const}} = {threshold} \in (0; 1)$'.format(
threshold=self.THRESHOLD),
plot_options=PlotOptions(
style='-',
color='black',
width=2.0,
),
formula=norm(l=1) | self.THRESHOLD,
),
)
def seq_filters(self):
"""
:return:
"""
# Linear delay filter. Builtin filter.
delay = DelayFilter()
# The incoming signal is unchanged.
original = delay(0)
# The norm of the signal. Builtin filter.
norm = NormFilter()
# Abstract sliding window. Builtin filter.
sw = BaseSWFilter(min_size=2)
sw_mean = sw | numeric.mean
# or sw_mean = MeanSWFilter()
sign_change = SignChangeFilter()
return [
FilterDescription(
name='$F_{L_1} = |F_{t}|_{L_1}$',
plot_options=PlotOptions(
style='-',
color='lightgray',
width=3.0,
),
formula=norm(l=1),
),
FilterDescription(name='$M_{50} = |\hat{\mu}_{50}(F_{L_1})|$',
plot_options=PlotOptions(
style='-',
color='orange',
width=2.0,
),
formula=norm(l=1) | sw_mean(s=50)),
FilterDescription(name='$M_{100} = |\hat{\mu}_{100}(F_{L_1})|$',
plot_options=PlotOptions(
style='-',
color='red',
width=2.0,
),
formula=norm(l=1) | sw_mean(s=100)),
FilterDescription(name='$M_{200} = |\hat{\mu}_{200}(F_{L_1})|$',
plot_options=PlotOptions(
style='-',
color='blue',
width=2.0,
),
formula=norm(l=1) | sw_mean(s=200)),
FilterDescription(name='$|M_{100} - M_{50}| \\to_{\pm} 0$',
plot_options=PlotOptions(
style=':',
color='purple',
width=1.1,
),
formula=(norm(l=1)
| (sw_mean(s=100) - sw_mean(s=50))
| sign_change
| abs
| original * 1)),
FilterDescription(name='$|M_{200} - M_{50}| \\to_{\pm} 0$',
plot_options=PlotOptions(
style='--',
color='blue',
width=1.2,
),
formula=(norm(l=1)
| (sw_mean(s=200) - sw_mean(s=50))
| sign_change
| abs
| original * 0.9)),
FilterDescription(name='$|M_{200} - M_{100}| \\to_{\pm} 0$',
plot_options=PlotOptions(
style='-',
marker='x',
color='green',
width=1.3,
),
formula=(norm(l=1)
| (sw_mean(s=200) - sw_mean(s=100))
| sign_change
| abs
| original * 0.8))
]
def seq_filters(self):
"""
:return:
"""
# Linear delay filter. Builtin filter.
delay = DelayFilter()
# The incoming signal is unchanged.
original = delay(0)
# Shift signal to one frame. Builtin filter.
shift = ShiftSWFilter()
# The difference between neighboring frames.
diff = original - shift
# The norm of the signal. Builtin filter.
norm = NormFilter()
# Abstract sliding window. Builtin filter.
sw = BaseSWFilter(min_size=2)
# Sum of absolute difference filter.
sad_filter = diff | abs | norm(l=1)
sw_mean = sw | numeric.mean
# or sw_mean = MeanSWFilter()
sw_std = sw | numeric.std
# or sw_std = StdSWFilter()
def sigma_estimation(sigma=3.0, size=1):
"""
:param float sigma:
:param int size:
:return:
"""
return sw_mean(s=size) + sigma * sw_std(s=size)
def sigma_check(**kwargs):
"""
...
"""
return original > sigma_estimation(**kwargs)
# Sequence of voters.
voters = range(self.VOTER_COUNT)
# Sequence of sliding window sizes.
sizes = (self.VOTER_SIZE * (i + 1) for i in voters)
# Sequence of votes of different sizes.
sigma_vote_seq = (sigma_check(size=size) for size in sizes)
# Average vote of different sizes.
sigma_vote = sum(sigma_vote_seq) / self.VOTER_COUNT
return [
FilterDescription(
name='$F_{L_1} = ||F_{t}||_{L_1}$',
plot_options=PlotOptions(
style='-',
color='gray',
width=3.0,
),
formula=norm(l=1),
),
FilterDescription(
# Sum of absolute difference filter.
name='$D_{t} = ||F_{t} - F_{t-1}||_{L_1}$',
plot_options=PlotOptions(
style='-',
color='blue',
width=2.0,
),
formula=sad_filter),
FilterDescription(
name=('$D_{{t}} > E_{{ {size} }}\ (D_{{t}})$'.format(
size=100)),
plot_options=PlotOptions(
style='--',
color='green',
width=1.0,
),
formula=(sad_filter
| sigma_check(size=100))),
FilterDescription(
name=('$D_{{t}} > E_{{ {size} }}\ (D_{{t}})$'.format(
size=200)),
plot_options=PlotOptions(style='--',
color='red',
width=1.5,
marker='x'),
formula=(sad_filter
| sigma_check(size=200) * 0.8)),
FilterDescription(name=('VOTE'),
plot_options=PlotOptions(
style='-',
color='green',
width=1.5,
),
formula=(sad_filter
| sigma_vote)),
FilterDescription(
# The threshold value.
name=('$T_{{const}} = {} \in (0; 1)$'.format(self.THRESHOLD)),
plot_options=PlotOptions(
style='-',
color='black',
width=2.0,
),
formula=norm(l=1) | self.THRESHOLD,
),
]
def seq_filters(self):
"""
Returns chart options for FFMpeg-like filter.
What we do:
1. Declare «builtin» filters.
2. Build custom filters.
3. Build target filter.
4. Plot them with `FilterDescription`
:returns: filter descriptions for FFMpeg-like filter.
:rtype: list of FilterDescription
"""
# Linear delay filter. Builtin filter.
delay = DelayFilter()
# The incoming signal is unchanged.
original = delay(0)
# Shift signal to one frame. Builtin filter.
shift = ShiftSWFilter()
# The difference between neighboring frames.
diff = original - shift
# The norm of the signal. Builtin filter.
norm = NormFilter()
# Threshold filter.
threshold = (original > self.THRESHOLD) * 1.1
# Sum of absolute difference filter.
sad_filter = diff | abs | norm(l=1)
# The absolute difference of two consecutive differences.
sad_diff_filter = sad_filter | diff | abs
# The minimum between the difference
# and the difference in the difference.
ffmpeg_like = Filter.to_tuple(sad_filter, sad_diff_filter) | min
# Faster implementation of FFMpeg-like filter.
# ffmpeg_like_fast = FFMpegLikeThresholdSWFilter()
return (
FilterDescription(
# Original signal.
name='$F_{L_1} = ||F_{t}||_{L_1}$',
plot_options=PlotOptions(
style='-',
color='gray',
width=3.0,
),
formula=norm(l=1),
),
FilterDescription(
# FFMpeg-like filter.
name='$D^{ffmpeg}_{t} = \min(D_t, |D_t-D_{t-1}|)$',
plot_options=PlotOptions(
style='-',
color='red',
width=2.0,
),
formula=ffmpeg_like),
FilterDescription(
# FFMpeg-like filter > threshold.
name='$D^{ffmpeg}_{t} > T_{const} $',
plot_options=PlotOptions(
style=':',
color='orange',
width=2.0,
),
formula=ffmpeg_like | threshold),
FilterDescription(
# The threshold value.
name='$T_{{const}} = {threshold} \in (0; 1)$'.format(
threshold=self.THRESHOLD),
plot_options=PlotOptions(
style='-',
color='black',
width=2.0,
),
formula=norm(l=1) | self.THRESHOLD,
),
)
def seq_filters(self):
"""
:return:
"""
# Linear delay filter. Builtin filter.
delay = DelayFilter()
# The incoming signal is unchanged.
original = delay(0)
# Shift signal to one frame. Builtin filter.
shift = ShiftSWFilter()
# The difference between neighboring frames.
diff = original - shift
# The norm of the signal. Builtin filter.
norm = NormFilter()
# Abstract sliding window. Builtin filter.
sw = BaseSWFilter(min_size=2)
sw_mean = sw | numeric.mean
# or sw_mean = MeanSWFilter()
sign_change = SignChangeFilter()
atan = (diff
| original * 256.0
| numeric.math.atan
| 2 * original
| original / numeric.math.pi)
# or atan = AtanFilter()
def sw_mean_diff(g, l):
"""
:param g:
:param l:
:return:
"""
return (norm(l=1)
| (sw_mean(s=g) - sw_mean(s=l))
| (sign_change * atan))
return [
FilterDescription(
name='$F_{L_1} = |F_{t}|_{L_1}$',
plot_options=PlotOptions(
style='-',
color='lightgray',
width=3.0,
),
formula=norm(l=1),
),
FilterDescription(name='$M_{50} = |\hat{\mu}_{50}(F_{L_1})|$',
plot_options=PlotOptions(
style='-',
color='orange',
width=2.0,
),
formula=norm(l=1) | sw_mean(s=50)),
FilterDescription(name='$M_{100} = |\hat{\mu}_{100}(F_{L_1})|$',
plot_options=PlotOptions(
style='-',
color='red',
width=2.0,
),
formula=norm(l=1) | sw_mean(s=100)),
FilterDescription(name='$M_{200} = |\hat{\mu}_{200}(F_{L_1})|$',
plot_options=PlotOptions(
style='-',
color='blue',
width=2.0,
),
formula=norm(l=1) | sw_mean(s=200)),
FilterDescription(
name='$|M_{200} - M_{50}| \\to_{\pm} 0$',
plot_options=PlotOptions(
style='--',
color='blue',
width=1.2,
),
formula=(
norm(l=1)
| (sw_mean(s=200) - sw_mean(s=50))
# | sign_changes
# | abs
# | original * 0.9
)),
FilterDescription(name='$A|M_{200} - M_{50}| \\to_{\pm} 0$',
plot_options=PlotOptions(
style='-',
marker='x',
color='green',
width=1.3,
),
formula=sw_mean_diff(200, 50)),
FilterDescription(
# The threshold value.
name='0',
plot_options=PlotOptions(
style='-',
color='black',
width=2.0,
),
formula=norm(l=1) | 0),
]