def test_shocklikeGaussian():
m0 = 1 + np.random.rand() * 0.2
sigma = 50 * Ts
# zero noise
x = shocklikeGaussian(time, t0, m0, sigma, noise=0.0)
assert x.max() == approx(m0)
assert np.std(x[:N // 10]) < 1e-10
# noisy signal
nstd = 1e-2
x = shocklikeGaussian(time, t0, m0, sigma, noise=nstd)
assert np.round(np.std(x[:N // 10]) * 100) / 100 == approx(nstd)
def test_shocklikeGaussian():
m0 = 1 + np.random.rand() * 0.2
sigma = 50 * Ts
# zero noise
x = shocklikeGaussian(time, t0, m0, sigma, noise=0.0)
assert_almost_equal(np.max(x), m0)
assert np.std(x[: N // 10]) < 1e-10
# noisy signal
nstd = 1e-2
x = shocklikeGaussian(time, t0, m0, sigma, noise=nstd)
assert_almost_equal(np.round(np.std(x[: N // 10]) * 100) / 100, nstd)
# sensor/measurement system
f0 = 36e3
uf0 = 0.01 * f0 # resonance frequency
S0 = 0.124
uS0 = 0.001 * S0 # static gain
delta = 0.0055
udelta = 0.1 * delta # damping
# transform continuous system to digital filter
bc, ac = sos_phys2filter(S0, delta,
f0) # calculate analogue filter coefficients
b, a = dsp.bilinear(bc, ac, Fs) # transform to digital filter coefficients
# simulate input and output signals
time = np.arange(0, 4e-3 - Ts, Ts) # time values
x = shocklikeGaussian(time, t0=2e-3, sigma=1e-5, m0=0.8) # input signal
y = dsp.lfilter(b, a, x) # output signal
noise = 1e-3 # noise std
yn = y + rst.randn(np.size(y)) * noise # add white noise
# Monte Carlo for calculation of unc. assoc. with [real(H),imag(H)]
runs = 10000
MCf0 = f0 + rst.randn(runs) * uf0 # MC draws of resonance frequency
MCS0 = S0 + rst.randn(runs) * uS0 # MC draws of static gain
MCd = delta + rst.randn(runs) * udelta # MC draws of damping
f = np.linspace(0, 120e3,
200) # frequencies at which to calculate frequency response
HMC = np.zeros((runs, len(f)),
dtype=complex) # initialise frequency response with zeros
for k in range(runs): # actual Monte Carlo
bc_, ac_ = sos_phys2filter(
# parameters of simulated measurement
Fs = 500e3 # sampling frequency (in Hz)
Ts = 1 / Fs # sampling intervall length (in s)
# sensor/measurement system
f0 = 36e3; uf0 = 0.01*f0 # resonance frequency
S0 = 0.124; uS0= 0.001*S0 # static gain
delta = 0.0055; udelta = 0.1*delta # damping
# transform continuous system to digital filter
bc, ac = sos_phys2filter(S0,delta,f0) # calculate analogue filter coefficients
b, a = dsp.bilinear(bc, ac, Fs) # transform to digital filter coefficients
# simulate input and output signals
time = np.arange(0, 4e-3 - Ts, Ts) # time values
x = shocklikeGaussian(time, t0 = 2e-3, sigma = 1e-5, m0=0.8) # input signal
y = dsp.lfilter(b, a, x) # output signal
noise = 1e-3 # noise std
yn = y + rst.randn(np.size(y)) * noise # add white noise
# Monte Carlo for calculation of unc. assoc. with [real(H),imag(H)]
runs = 10000
MCf0 = f0 + rst.randn(runs)*uf0 # MC draws of resonance frequency
MCS0 = S0 + rst.randn(runs)*uS0 # MC draws of static gain
MCd = delta+ rst.randn(runs)*udelta # MC draws of damping
f = np.linspace(0, 120e3, 200) # frequencies at which to calculate frequency response
HMC = np.zeros((runs, len(f)),dtype=complex) # initialise frequency response with zeros
for k in range(runs): # actual Monte Carlo
bc_,ac_ = sos_phys2filter(MCS0[k], MCd[k], MCf0[k]) # calculate analogue filter coefficients
b_,a_ = dsp.bilinear(bc_,ac_,Fs) # transform to digital filter coefficients
HMC[k,:] = dsp.freqz(b_,a_,2*np.pi*f/Fs)[1] # calculate DFT frequency response