def sequence_to_HdW(sequence,
return_magnitude=True,
return_w=True,
plot_magnitude=False):
"""
Purpose: To find the values of the DTFT on the unit circle
for a given sequence
"""
if type(sequence) == pu.Polynomial1D or type(sequence) == pu.Polynomial:
P1 = sequence
else:
P1 = pu.Polynomial1D(sequence)
w = np.linspace(-pi, pi, 10000)
unit_circle_values = np.array([exp(1j * wi) for wi in w])
#plt.scatter(np.real(unit_circle_values),np.imag(unit_circle_values))
Hd_w_values = np.array([P1.evaluate(zi) for zi in unit_circle_values])
if return_magnitude:
Hd_w_values = Hdw_to_magnitude(Hd_w_values)
if plot_magnitude:
plot_Hdw_magnitude(Hd_w_values, w=w)
if return_w:
return Hd_w_values, w
else:
return Hd_w_values
def sequence_to_Hdw_at_specific_ws(sequence,
ws,
return_magnitude=True,
verbose=False):
"""
To turn a radians/sample frequency
into the DTFT value on the unit circle
"""
if not nu.is_array_like(ws):
ws = [ws]
singular_flag = True
else:
singular_flag = False
P1 = pu.Polynomial1D(sequence)
hdw = [P1.evaluate(exp(1j * w)) for w in ws]
if return_magnitude:
hdw = np.abs(hdw)
if verbose:
for hd, w in zip(hdw, ws):
print(f"For {w}: Hd(ejw) = {hd}")
if singular_flag:
return hdw[0]
else:
return hdw
def sequence_to_plot_roots(sequence,
plot_unit_circle=False,
set_zoom_to_unit_circle=False):
"""
Purpose: Will plot the roots of a sequence
"""
sequence = pu.Polynomial1D(sequence)
mu.plot_real_imaginary(sequence.roots, show_at_end=False)
ax = plt.gca()
if plot_unit_circle:
unit_circle_values = np.array(
[exp(1j * k) for k in np.linspace(0, 2 * pi, 1000)])
circle_real = np.real(unit_circle_values)
circle_imag = np.imag(unit_circle_values)
ax.plot(circle_real, circle_imag)
if set_zoom_to_unit_circle:
delta = 0.2
ax.set_xlim([-1 - delta, 1 + delta])
ax.set_ylim([-1 - delta, 1 + delta])
plt.show()