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 zplane(self,
b=None,
a=1,
z=None,
p=None,
k=1,
pn_eps=1e-3,
analog=False,
plt_ax=None,
plt_poles=True,
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()
plt_poles : Boolean (default : True)
Plot poles. This can be used to suppress poles for FIR systems
where all poles are at the origin.
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 color of 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]) # overridden by next option
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)
# and print their multiplicity
for i in range(len(z)):
logger.debug('z: {0} | {1} | {2}'.format(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='top',
color=mzc)
if plt_poles:
# Plot the poles
ax.scatter(p.real,
p.imag,
s=mps * mps,
zorder=2,
marker='x',
color=mpc,
lw=lw,
label=plabel)
# and print their multiplicity
for i in range(len(p)):
logger.debug('p:{0} | {1} | {2}'.format(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',
color=mpc)
# =============================================================================
# # 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))
return z, p, k
#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.process_time()
for i in range(Navg):
roots, mult = dsp.unique_roots(vals, rtype=rtype, rdist='manhattan')
t2 = time.process_time()
T_dsp = (t2 - t1) / Navg
print(mult)
print('============ signal.unique_roots() =============================')
t1 = time.process_time()
for i in range(Navg):
roots, mult = sig.unique_roots(vals, rtype=rtype)
t2 = time.process_time()
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)