def test_freq_range(self):
# Test that freqresp() finds a reasonable frequency range.
# 1st order low-pass filter: H(s) = 1 / (s + 1)
# Expected range is from 0.01 to 10.
system = lti([1], [1, 1])
n = 10
expected_w = np.logspace(-2, 1, n)
w, H = freqresp(system, n=n)
assert_almost_equal(w, expected_w)
def test_freq_range(self):
# Test that freqresp() finds a reasonable frequency range.
# 1st order low-pass filter: H(s) = 1 / (s + 1)
# Expected range is from 0.01 to 10.
system = lti([1], [1, 1])
n = 10
expected_w = np.logspace(-2, 1, n)
w, H = freqresp(system, n=n)
assert_almost_equal(w, expected_w)
def test_imag_part(self):
# Test freqresp() imaginary part calculation.
# 1st order low-pass filter: H(s) = 1 / (s + 1)
system = lti([1], [1, 1])
w = [0.1, 1, 10, 100]
w, H = freqresp(system, w=w)
jw = w * 1j
y = np.polyval(system.num, jw) / np.polyval(system.den, jw)
expected_im = y.imag
assert_almost_equal(H.imag, expected_im)
def test_imag_part(self):
# Test freqresp() imaginary part calculation.
# 1st order low-pass filter: H(s) = 1 / (s + 1)
system = lti([1], [1, 1])
w = [0.1, 1, 10, 100]
w, H = freqresp(system, w=w)
jw = w * 1j
y = np.polyval(system.num, jw) / np.polyval(system.den, jw)
expected_im = y.imag
assert_almost_equal(H.imag, expected_im)
def test_imag_part_manual(self):
# Test freqresp() imaginary part calculation (manual sanity check).
# 1st order low-pass filter: H(s) = 1 / (s + 1),
# im(H(s=0.1)) ~= -0.099
# im(H(s=1)) ~= -0.5
# im(H(s=10)) ~= -0.099
system = lti([1], [1, 1])
w = [0.1, 1, 10]
w, H = freqresp(system, w=w)
expected_im = [-0.099, -0.5, -0.099]
assert_almost_equal(H.imag, expected_im, decimal=1)
def test_real_part_manual(self):
# Test freqresp() real part calculation (manual sanity check).
# 1st order low-pass filter: H(s) = 1 / (s + 1),
# re(H(s=0.1)) ~= 0.99
# re(H(s=1)) ~= 0.5
# re(H(s=10)) ~= 0.0099
system = lti([1], [1, 1])
w = [0.1, 1, 10]
w, H = freqresp(system, w=w)
expected_re = [0.99, 0.5, 0.0099]
assert_almost_equal(H.real, expected_re, decimal=1)
def test_imag_part_manual(self):
# Test freqresp() imaginary part calculation (manual sanity check).
# 1st order low-pass filter: H(s) = 1 / (s + 1),
# im(H(s=0.1)) ~= -0.099
# im(H(s=1)) ~= -0.5
# im(H(s=10)) ~= -0.099
system = lti([1], [1, 1])
w = [0.1, 1, 10]
w, H = freqresp(system, w=w)
expected_im = [-0.099, -0.5, -0.099]
assert_almost_equal(H.imag, expected_im, decimal=1)
def test_real_part_manual(self):
# Test freqresp() real part calculation (manual sanity check).
# 1st order low-pass filter: H(s) = 1 / (s + 1),
# re(H(s=0.1)) ~= 0.99
# re(H(s=1)) ~= 0.5
# re(H(s=10)) ~= 0.0099
system = lti([1], [1, 1])
w = [0.1, 1, 10]
w, H = freqresp(system, w=w)
expected_re = [0.99, 0.5, 0.0099]
assert_almost_equal(H.real, expected_re, decimal=1)
def test_freq_range(self):
# Test that freqresp() finds a reasonable frequency range.
# 1st order low-pass filter: H(s) = 1 / (s + 1)
# Expected range is from 0.01 to 10.
system = lti([1], [1, 1])
vals = linalg.eigvals(system.A)
minpole = min(abs(np.real(vals)))
maxpole = max(abs(np.real(vals)))
n = 10
expected_w = np.logspace(-2, 1, n)
w, H = freqresp(system, n=n)
assert_almost_equal(w, expected_w)
def test_freq_range(self):
# Test that freqresp() finds a reasonable frequency range.
# 1st order low-pass filter: H(s) = 1 / (s + 1)
# Expected range is from 0.01 to 10.
system = lti([1], [1, 1])
vals = linalg.eigvals(system.A)
minpole = min(abs(np.real(vals)))
maxpole = max(abs(np.real(vals)))
n = 10
expected_w = np.logspace(-2, 1, n)
w, H = freqresp(system, n=n)
assert_almost_equal(w, expected_w)
def test_from_state_space(self):
# Ensure that freqresp works with a system that was created from the
# state space representation matrices A, B, C, D. In this case,
# system.num will be a 2-D array with shape (1, n+1), where (n,n) is
# the shape of A.
# A Butterworth lowpass filter is used, so we know the exact
# frequency response.
a = np.array([1.0, 2.0, 2.0, 1.0])
A = linalg.companion(a).T
B = np.array([[0.0], [0.0], [1.0]])
C = np.array([[1.0, 0.0, 0.0]])
D = np.array([[0.0]])
with warnings.catch_warnings():
warnings.simplefilter("ignore", BadCoefficients)
system = lti(A, B, C, D)
w, H = freqresp(system, n=100)
expected_magnitude = np.sqrt(1.0 / (1.0 + w**6))
assert_almost_equal(np.abs(H), expected_magnitude)
def test_from_state_space(self):
# Ensure that freqresp works with a system that was created from the
# state space representation matrices A, B, C, D. In this case,
# system.num will be a 2-D array with shape (1, n+1), where (n,n) is
# the shape of A.
# A Butterworth lowpass filter is used, so we know the exact
# frequency response.
a = np.array([1.0, 2.0, 2.0, 1.0])
A = linalg.companion(a).T
B = np.array([[0.0],[0.0],[1.0]])
C = np.array([[1.0, 0.0, 0.0]])
D = np.array([[0.0]])
with warnings.catch_warnings():
warnings.simplefilter("ignore", BadCoefficients)
system = lti(A, B, C, D)
w, H = freqresp(system, n=100)
expected_magnitude = np.sqrt(1.0 / (1.0 + w**6))
assert_almost_equal(np.abs(H), expected_magnitude)
def test_pole_zero(self):
# Test that freqresp() doesn't fail on a system with a pole at 0.
# integrator, pole at zero: H(s) = 1 / s
system = lti([1], [1, 0])
w, H = freqresp(system, n=2)
assert_equal(w[0], 0.01) # a fail would give not-a-number
def test_pole_zero(self):
# Test that freqresp() doesn't fail on a system with a pole at 0.
# integrator, pole at zero: H(s) = 1 / s
system = lti([1], [1, 0])
w, H = freqresp(system, n=2)
assert_equal(w[0], 0.01) # a fail would give not-a-number
