def FuT(roots_in, *kwargs):
"""Select Function-Under-Test (FuT)"""
return unique_roots(roots_in,
tol=1e-3,
magsort=magsort,
rtype=rtype,
rdist=rdist)
def sort_dict_freqs(self):
"""
- Sort visible filter dict frequency spec entries with ascending frequency if
the sort button is activated
- Update the visible QLineEdit frequency widgets
The method is called when:
- update_UI has been called after changing the filter design algorithm # that the response type has been changed
eg. from LP -> HP, requiring a different order of frequency entries
- a frequency spec field has been edited
- the sort button has been clicked (from filter_specs.py)
"""
f_specs = [
fb.fil[0][str(self.qlineedit[i].objectName())]
for i in range(self.n_cur_labels)
]
if fb.fil[0]['freq_specs_sort']:
f_specs.sort()
# Make sure normalized freqs are in the range ]0, 0.5[ and are different
# by at least MIN_FREQ_STEP
for i in range(self.n_cur_labels):
if f_specs[i] <= MIN_FREQ:
logger.warning("Frequencies must be > 0, changed {0} from {1:.4g} to {2:.4g}."\
.format(str(self.qlineedit[i].objectName()),f_specs[i]*fb.fil[0]['f_S'],
(MIN_FREQ + MIN_FREQ_STEP)*fb.fil[0]['f_S']))
f_specs[i] = MIN_FREQ + MIN_FREQ_STEP
if f_specs[i] >= MAX_FREQ:
logger.warning("Frequencies must be < f_S /2, changed {0} from {1:.4g} to {2:.4g}."\
.format(str(self.qlineedit[i].objectName()),f_specs[i]*fb.fil[0]['f_S'],
(MAX_FREQ - MIN_FREQ_STEP)*fb.fil[0]['f_S']))
f_specs[i] = MAX_FREQ - MIN_FREQ_STEP
fb.fil[0][str(self.qlineedit[i].objectName())] = f_specs[i]
# check for (nearly) identical elements:
_, mult = unique_roots(f_specs, tol=MIN_FREQ_STEP)
ident = [x for x in mult if x > 1]
if ident:
logger.warning("Frequencies must differ by at least {0:.4g}"\
.format(MIN_FREQ_STEP * fb.fil[0]['f_S']))
self.load_dict()
def sort_dict_freqs(self):
"""
- Sort visible filter dict frequency spec entries with ascending frequency if
the sort button is activated
- Update the visible QLineEdit frequency widgets
The method is called when:
- update_UI has been called after changing the filter design algorithm # that the response type has been changed
eg. from LP -> HP, requiring a different order of frequency entries
- a frequency spec field has been edited
- the sort button has been clicked (from filter_specs.py)
"""
f_specs = [fb.fil[0][str(self.qlineedit[i].objectName())]
for i in range(self.n_cur_labels)]
if fb.fil[0]['freq_specs_sort']:
f_specs.sort()
# Make sure normalized freqs are in the range ]0, 0.5[ and are different
# by at least MIN_FREQ_STEP
for i in range(self.n_cur_labels):
if f_specs[i] <= MIN_FREQ:
logger.warning("Frequencies must be > 0, changed {0} from {1:.4g} to {2:.4g}."\
.format(str(self.qlineedit[i].objectName()),f_specs[i]*fb.fil[0]['f_S'],
(MIN_FREQ + MIN_FREQ_STEP)*fb.fil[0]['f_S']))
f_specs[i] = MIN_FREQ + MIN_FREQ_STEP
if f_specs[i] >= MAX_FREQ:
logger.warning("Frequencies must be < f_S /2, changed {0} from {1:.4g} to {2:.4g}."\
.format(str(self.qlineedit[i].objectName()),f_specs[i]*fb.fil[0]['f_S'],
(MAX_FREQ - MIN_FREQ_STEP)*fb.fil[0]['f_S']))
f_specs[i] = MAX_FREQ - MIN_FREQ_STEP
fb.fil[0][str(self.qlineedit[i].objectName())] = f_specs[i]
# check for (nearly) identical elements:
_, mult = unique_roots(f_specs, tol = MIN_FREQ_STEP)
ident = [x for x in mult if x > 1]
if ident:
logger.warning("Frequencies must differ by at least {0:.4g}"\
.format(MIN_FREQ_STEP * fb.fil[0]['f_S']))
self.load_dict()
def FuT(roots_in, *kwargs):
"""Select Function-Under-Test (FuT)"""
return unique_roots(roots_in, tol=1e-3, magsort = magsort, rtype = rtype, rdist = rdist)
def zplane(self, b=None, a=1, z=None, p=None, k =1, pn_eps=1e-3, analog=False, plt_ax = None,
verbose=False, style='square', anaCircleRad=0, lw=2,
mps = 10, mzs = 10, mpc = 'r', mzc = 'b', plabel = '', zlabel = ''):
"""
Plot the poles and zeros in the complex z-plane either from the
coefficients (`b,`a) of a discrete transfer function `H`(`z`) (zpk = False)
or directly from the zeros and poles (z,p) (zpk = True).
When only b is given, an FIR filter with all poles at the origin is assumed.
Parameters
----------
b : array_like
Numerator coefficients (transversal part of filter)
When b is not None, poles and zeros are determined from the coefficients
b and a
a : array_like (optional, default = 1 for FIR-filter)
Denominator coefficients (recursive part of filter)
z : array_like, default = None
Zeros
When b is None, poles and zeros are taken directly from z and p
p : array_like, default = None
Poles
analog : boolean (default: False)
When True, create a P/Z plot suitable for the s-plane, i.e. suppress
the unit circle (unless anaCircleRad > 0) and scale the plot for
a good display of all poles and zeros.
pn_eps : float (default : 1e-2)
Tolerance for separating close poles or zeros
plt_ax : handle to axes for plotting (default: None)
When no axes is specified, the current axes is determined via plt.gca()
pltLib : string (default: 'matplotlib')
Library for plotting the P/Z plane. Currently, only matplotlib is
implemented. When pltLib = 'none' or when matplotlib is not
available, only pass the poles / zeros and their multiplicity
verbose : boolean (default: False)
When verbose == True, print poles / zeros and their multiplicity.
style : string (default: 'square')
Style of the plot, for style == 'square' make scale of x- and y-
axis equal.
mps : integer (default: 10)
Size for pole marker
mzs : integer (default: 10)
Size for zero marker
mpc : char (default: 'r')
Pole marker colour
mzc : char (default: 'b')
Zero marker colour
lw : integer (default: 2)
Linewidth for unit circle
plabel, zlabel : string (default: '')
This string is passed to the plot command for poles and zeros and
can be displayed by legend()
Returns
-------
z, p, k : ndarray
Notes
-----
"""
# TODO:
# - polar option
# - add keywords for size, color etc. of markers and circle -> **kwargs
# - add option for multi-dimensional arrays and zpk data
# make sure that all inputs are arrays
b = np.atleast_1d(b)
a = np.atleast_1d(a)
z = np.atleast_1d(z) # make sure that p, z are arrays
p = np.atleast_1d(p)
if b.any(): # coefficients were specified
if len(b) < 2 and len(a) < 2:
logger.error('No proper filter coefficients: both b and a are scalars!')
return z, p, k
# The coefficients are less than 1, normalize the coefficients
if np.max(b) > 1:
kn = np.max(b)
b = b / float(kn)
else:
kn = 1.
if np.max(a) > 1:
kd = np.max(a)
a = a / abs(kd)
else:
kd = 1.
# Calculate the poles, zeros and scaling factor
p = np.roots(a)
z = np.roots(b)
k = kn/kd
elif not (len(p) or len(z)): # P/Z were specified
logger.error('Either b,a or z,p must be specified!')
return z, p, k
# find multiple poles and zeros and their multiplicities
if len(p) < 2: # single pole, [None] or [0]
if not p or p == 0: # only zeros, create equal number of poles at origin
p = np.array(0,ndmin=1) #
num_p = np.atleast_1d(len(z))
else:
num_p = [1.] # single pole != 0
else:
#p, num_p = sig.signaltools.unique_roots(p, tol = pn_eps, rtype='avg')
p, num_p = unique_roots(p, tol = pn_eps, rtype='avg')
# p = np.array(p); num_p = np.ones(len(p))
if len(z) > 0:
z, num_z = unique_roots(z, tol = pn_eps, rtype='avg')
# z = np.array(z); num_z = np.ones(len(z))
#z, num_z = sig.signaltools.unique_roots(z, tol = pn_eps, rtype='avg')
else:
num_z = []
ax = plt_ax#.subplot(111)
if analog == False:
# create the unit circle for the z-plane
uc = patches.Circle((0,0), radius=1, fill=False,
color='grey', ls='solid', zorder=1)
ax.add_patch(uc)
if style == 'square':
r = 1.1
ax.axis([-r, r, -r, r], 'equal')
ax.axis('equal')
# ax.spines['left'].set_position('center')
# ax.spines['bottom'].set_position('center')
# ax.spines['right'].set_visible(True)
# ax.spines['top'].set_visible(True)
else: # s-plane
if anaCircleRad > 0:
# plot a circle with radius = anaCircleRad
uc = patches.Circle((0,0), radius=anaCircleRad, fill=False,
color='grey', ls='solid', zorder=1)
ax.add_patch(uc)
# plot real and imaginary axis
ax.axhline(lw=2, color = 'k', zorder=1)
ax.axvline(lw=2, color = 'k', zorder=1)
# Plot the zeros
ax.scatter(z.real, z.imag, s=mzs*mzs, zorder=2, marker = 'o',
facecolor = 'none', edgecolor = mzc, lw = lw, label=zlabel)
# t1 = plt.plot(z.real, z.imag, 'go', ms=10, label=label)
# plt.setp( t1, markersize=mzs, markeredgewidth=2.0,
# markeredgecolor=mzc, markerfacecolor='none')
# Plot the poles
ax.scatter(p.real, p.imag, s=mps*mps, zorder=2, marker='x',
color=mpc, lw=lw, label=plabel)
# Print multiplicity of poles / zeros
for i in range(len(z)):
if verbose == True: print('z', i, z[i], num_z[i])
if num_z[i] > 1:
ax.text(np.real(z[i]), np.imag(z[i]),' (' + str(num_z[i]) +')',va = 'bottom')
for i in range(len(p)):
if verbose == True: print('p', i, p[i], num_p[i])
if num_p[i] > 1:
ax.text(np.real(p[i]), np.imag(p[i]), ' (' + str(num_p[i]) +')',va = 'bottom')
# increase distance between ticks and labels
# to give some room for poles and zeros
for tick in ax.get_xaxis().get_major_ticks():
tick.set_pad(12.)
tick.label1 = tick._get_text1()
for tick in ax.get_yaxis().get_major_ticks():
tick.set_pad(12.)
tick.label1 = tick._get_text1()
xl = ax.get_xlim(); Dx = max(abs(xl[1]-xl[0]), 0.05)
yl = ax.get_ylim(); Dy = max(abs(yl[1]-yl[0]), 0.05)
ax.set_xlim((xl[0]-Dx*0.05, max(xl[1]+Dx*0.05,0)))
ax.set_ylim((yl[0]-Dy*0.05, yl[1] + Dy*0.05))
# print(ax.get_xlim(),ax.get_ylim())
return z, p, k
#vals = np.roots(np.convolve(ones(500),ones(100))) # 100 double and 400 single complex roots,
#vals = np.roots(np.convolve(ones(500),ones(500))) # 500 double complex roots
#vals = np.roots(np.convolve(ones(5),ones(7))) # 4 double complex roots
## tests with nans
#vals = list(ones(5) * 1j); vals.append(np.nan); vals.append(np.nan)
#vals = []
#print(vals)
Navg = 1000
rtype = 'min'
print('============ dsp.unique_roots() ================================')
t1 = time.clock()
for i in range(Navg):
roots, mult = dsp.unique_roots(vals, rtype = rtype, rdist='manhattan')
t2 = time.clock()
T_dsp = (t2 - t1)/Navg
print (mult)
print('============ signal.unique_roots() =============================')
t1 = time.clock()
for i in range(Navg):
roots, mult = sig.unique_roots(vals, rtype = rtype)
t2 = time.clock()
T_sig = (t2 - t1)/Navg
print (mult)
print("T_dsp = ",T_dsp, " s")
print("T_sig = ",T_sig, " s")
print("T_dsp / T_sig = ", T_dsp / T_sig)
def zplane(self, b=None, a=1, z=None, p=None, k =1, pn_eps=1e-3, analog=False, plt_ax = None,
verbose=False, style='square', anaCircleRad=0, lw=2,
mps = 10, mzs = 10, mpc = 'r', mzc = 'b', plabel = '', zlabel = ''):
"""
Plot the poles and zeros in the complex z-plane either from the
coefficients (`b,`a) of a discrete transfer function `H`(`z`) (zpk = False)
or directly from the zeros and poles (z,p) (zpk = True).
When only b is given, an FIR filter with all poles at the origin is assumed.
Parameters
----------
b : array_like
Numerator coefficients (transversal part of filter)
When b is not None, poles and zeros are determined from the coefficients
b and a
a : array_like (optional, default = 1 for FIR-filter)
Denominator coefficients (recursive part of filter)
z : array_like, default = None
Zeros
When b is None, poles and zeros are taken directly from z and p
p : array_like, default = None
Poles
analog : boolean (default: False)
When True, create a P/Z plot suitable for the s-plane, i.e. suppress
the unit circle (unless anaCircleRad > 0) and scale the plot for
a good display of all poles and zeros.
pn_eps : float (default : 1e-2)
Tolerance for separating close poles or zeros
plt_ax : handle to axes for plotting (default: None)
When no axes is specified, the current axes is determined via plt.gca()
pltLib : string (default: 'matplotlib')
Library for plotting the P/Z plane. Currently, only matplotlib is
implemented. When pltLib = 'none' or when matplotlib is not
available, only pass the poles / zeros and their multiplicity
verbose : boolean (default: False)
When verbose == True, print poles / zeros and their multiplicity.
style : string (default: 'square')
Style of the plot, for style == 'square' make scale of x- and y-
axis equal.
mps : integer (default: 10)
Size for pole marker
mzs : integer (default: 10)
Size for zero marker
mpc : char (default: 'r')
Pole marker colour
mzc : char (default: 'b')
Zero marker colour
lw : integer (default: 2)
Linewidth for unit circle
plabel, zlabel : string (default: '')
This string is passed to the plot command for poles and zeros and
can be displayed by legend()
Returns
-------
z, p, k : ndarray
Notes
-----
"""
# TODO:
# - polar option
# - add keywords for size, color etc. of markers and circle -> **kwargs
# - add option for multi-dimensional arrays and zpk data
# make sure that all inputs are arrays
b = np.atleast_1d(b)
a = np.atleast_1d(a)
z = np.atleast_1d(z) # make sure that p, z are arrays
p = np.atleast_1d(p)
if b.any(): # coefficients were specified
if len(b) < 2 and len(a) < 2:
logger.error('No proper filter coefficients: both b and a are scalars!')
return z, p, k
# The coefficients are less than 1, normalize the coefficients
if np.max(b) > 1:
kn = np.max(b)
b = b / float(kn)
else:
kn = 1.
if np.max(a) > 1:
kd = np.max(a)
a = a / abs(kd)
else:
kd = 1.
# Calculate the poles, zeros and scaling factor
p = np.roots(a)
z = np.roots(b)
k = kn/kd
elif not (len(p) or len(z)): # P/Z were specified
logger.error('Either b,a or z,p must be specified!')
return z, p, k
# find multiple poles and zeros and their multiplicities
if len(p) < 2: # single pole, [None] or [0]
if not p or p == 0: # only zeros, create equal number of poles at origin
p = np.array(0,ndmin=1) #
num_p = np.atleast_1d(len(z))
else:
num_p = [1.] # single pole != 0
else:
#p, num_p = sig.signaltools.unique_roots(p, tol = pn_eps, rtype='avg')
p, num_p = unique_roots(p, tol = pn_eps, rtype='avg')
# p = np.array(p); num_p = np.ones(len(p))
if len(z) > 0:
z, num_z = unique_roots(z, tol = pn_eps, rtype='avg')
# z = np.array(z); num_z = np.ones(len(z))
#z, num_z = sig.signaltools.unique_roots(z, tol = pn_eps, rtype='avg')
else:
num_z = []
ax = plt_ax#.subplot(111)
if analog == False:
# create the unit circle for the z-plane
uc = patches.Circle((0,0), radius=1, fill=False,
color='grey', ls='solid', zorder=1)
ax.add_patch(uc)
if style == 'square':
r = 1.1
ax.axis([-r, r, -r, r], 'equal')
ax.axis('equal')
# ax.spines['left'].set_position('center')
# ax.spines['bottom'].set_position('center')
# ax.spines['right'].set_visible(True)
# ax.spines['top'].set_visible(True)
else: # s-plane
if anaCircleRad > 0:
# plot a circle with radius = anaCircleRad
uc = patches.Circle((0,0), radius=anaCircleRad, fill=False,
color='grey', ls='solid', zorder=1)
ax.add_patch(uc)
# plot real and imaginary axis
ax.axhline(lw=2, color = 'k', zorder=1)
ax.axvline(lw=2, color = 'k', zorder=1)
# Plot the zeros
ax.scatter(z.real, z.imag, s=mzs*mzs, zorder=2, marker = 'o',
facecolor = 'none', edgecolor = mzc, lw = lw, label=zlabel)
# t1 = plt.plot(z.real, z.imag, 'go', ms=10, label=label)
# plt.setp( t1, markersize=mzs, markeredgewidth=2.0,
# markeredgecolor=mzc, markerfacecolor='none')
# Plot the poles
ax.scatter(p.real, p.imag, s=mps*mps, zorder=2, marker='x',
color=mpc, lw=lw, label=plabel)
# Print multiplicity of poles / zeros
for i in range(len(z)):
if verbose == True: print('z', i, z[i], num_z[i])
if num_z[i] > 1:
ax.text(np.real(z[i]), np.imag(z[i]),' (' + str(num_z[i]) +')',va = 'bottom')
for i in range(len(p)):
if verbose == True: print('p', i, p[i], num_p[i])
if num_p[i] > 1:
ax.text(np.real(p[i]), np.imag(p[i]), ' (' + str(num_p[i]) +')',va = 'bottom')
# increase distance between ticks and labels
# to give some room for poles and zeros
for tick in ax.get_xaxis().get_major_ticks():
tick.set_pad(12.)
tick.label1 = tick._get_text1()
for tick in ax.get_yaxis().get_major_ticks():
tick.set_pad(12.)
tick.label1 = tick._get_text1()
xl = ax.get_xlim(); Dx = max(abs(xl[1]-xl[0]), 0.05)
yl = ax.get_ylim(); Dy = max(abs(yl[1]-yl[0]), 0.05)
ax.set_xlim((xl[0]-Dx*0.05, max(xl[1]+Dx*0.05,0)))
ax.set_ylim((yl[0]-Dy*0.05, yl[1] + Dy*0.05))
# print(ax.get_xlim(),ax.get_ylim())
return z, p, k