def test_FIRuncFilter_corr():
# get an instance of noise, the covariance and the covariance-matrix with the specified color
color = "white"
noise = power_law_noise(N=nTime, color_value=color, std=sigma_noise)
Ux = power_law_acf(nTime, color_value=color, std=sigma_noise)
# input signal
x = rect(time,100*Ts,250*Ts,1.0,noise=noise)
# apply uncertain FIR filter (GUM formula)
for blow in [None, b2]:
y, Uy = FIRuncFilter(x, Ux, b1, Ub, blow=blow, kind="corr")
assert len(y) == len(x)
assert len(Uy) == len(x)
def test_power_law_acf():
# check function output for even/uneven N and different alphas
for color_value in possible_inputs:
# definitions
N = np.random.choice(possible_lengths)
std = 0.5
# calculate theoretic covariance
Rxx = pn.power_law_acf(N, color_value=color_value, std=std)
assert Rxx.shape == (N, )
if color_value == 0.0:
assert Rxx[0] == pytest.approx(std**2)
assert np.mean(Rxx[1:]) == pytest.approx(0)
y, Uy = FIRuncFilter(
x, sigma_noise, b1, Ub, blow=blow,
kind=kind) # apply uncertain FIR filter (GUM formula)
yMC, UyMC = MC(
x, sigma_noise, b1, [1.0], Ub, runs=runs,
blow=blow) # apply uncertain FIR filter (Monte Carlo)
elif kind == "corr":
# get an instance of noise, the covariance and the covariance-matrix with the specified color
color = "red"
noise = power_law_noise(N=nTime,
color_value=color,
std=sigma_noise)
Ux = power_law_acf(nTime, color_value=color, std=sigma_noise)
# input signal
x = rect(time, 100 * Ts, 250 * Ts, 1.0, noise=noise)
# build Ux_matrix from autocorrelation Ux
Ux_matrix = toeplitz(trimOrPad(Ux, nTime))
# run methods
y, Uy = FIRuncFilter(
x, Ux, b1, Ub, blow=blow,
kind=kind) # apply uncertain FIR filter (GUM formula)
yMC, UyMC = MC(
x, Ux_matrix, b1, [1.0], Ub, runs=runs,
blow=blow) # apply uncertain FIR filter (Monte Carlo)
def conduct_validation_of_FIRuncFilter():
# parameters of simulated measurement
Fs = 100e3 # sampling frequency (in Hz)
Ts = 1 / Fs # sampling interval length (in s)
# nominal system parameters
fcut = 20e3 # low-pass filter cut-off frequency (6 dB)
L = 100 # filter order
b1 = kaiser_lowpass(L, fcut, Fs)[0]
b2 = kaiser_lowpass(L - 20, fcut, Fs)[0]
# uncertain knowledge: cutoff between 19.5kHz and 20.5kHz
runs = 1000
FC = fcut + (2 * np.random.rand(runs) - 1) * 0.5e3
B = np.zeros((runs, L + 1))
for k in range(
runs): # Monte Carlo for filter coefficients of low-pass filter
B[k, :] = kaiser_lowpass(L, FC[k], Fs)[0]
Ub = make_semiposdef(np.cov(
B, rowvar=False)) # covariance matrix of MC result
# simulate input and output signals
nTime = 500
time = np.arange(nTime) * Ts # time values
# different cases
sigma_noise = 1e-2 # 1e-5
for kind in ["float", "corr", "diag"]:
for blow in [None, b2]:
print(kind, type(blow))
if kind == "float":
# input signal + run methods
x = rect(time, 100 * Ts, 250 * Ts, 1.0, noise=sigma_noise)
Uy, UyMC, y, yMC = _conduct_FIRuncFilter_and_MonteCarlo(
Ub, b1, blow, kind, runs, sigma_noise, x)
elif kind == "corr":
# get an instance of noise, the covariance and the covariance-matrix
# with
# the specified color
color = "red"
noise = power_law_noise(N=nTime,
color_value=color,
std=sigma_noise)
Ux = power_law_acf(nTime, color_value=color, std=sigma_noise)
# input signal
x = rect(time, 100 * Ts, 250 * Ts, 1.0, noise=noise)
# build Ux_matrix from autocorrelation Ux
Ux_matrix = toeplitz(trimOrPad(Ux, nTime))
# run methods
y, Uy = FIRuncFilter(
x, Ux, b1, Ub, blow=blow,
kind=kind) # apply uncertain FIR filter (GUM formula)
yMC, UyMC = MC(
x, Ux_matrix, b1, np.ones(1), Ub, runs=runs,
blow=blow) # apply uncertain FIR filter (Monte Carlo)
elif kind == "diag":
sigma_diag = sigma_noise * (
1 +
np.heaviside(np.arange(len(time)) - len(time) // 2.5, 0)
) # std doubles after half of the time
noise = sigma_diag * white_gaussian(len(time))
# input signal + run methods
x = rect(time, 100 * Ts, 250 * Ts, 1.0, noise=noise)
Uy, UyMC, y, yMC = _conduct_FIRuncFilter_and_MonteCarlo(
Ub, b1, blow, kind, runs, sigma_diag, x)
# compare FIR and MC results
plt.figure(1)
plt.cla()
plt.plot(time, x, label="input")
plt.plot(time, y, label="output FIR direct")
plt.plot(time, yMC, label="output FIR MC")
plt.xlabel("time [s]")
plt.ylabel("signal amplitude [1]")
plt.legend()
plt.figure(2)
plt.cla()
plt.plot(time, Uy, label="FIR formula")
plt.plot(time, np.sqrt(np.diag(UyMC)), label="Monte Carlo")
plt.xlabel("time [s]")
plt.ylabel("signal uncertainty [1]")
plt.legend()
plt.show()