print("** Fourier Spectrum")
freq, amp = ppk.FourierSpectrum(t, a, fmax=20)
# freq, amp = ppk.Fourier_fft(t, a) # use fast algorithm
frequency = freq[np.where(amp == max(amp))]
print(" --> Frequenz mit max. Amplitude: ", frequency)
# calculate autocorrelation function
print("** Autocorrelation Function")
ac_a = ppk.autocorrelate(a)
ac_t = t - t[0]
# run peak finder
width = 80
# use convoluted template filter
pidx = ppk.convolutionPeakfinder(ac_a, width, th=0.4)
if len(pidx) > 3:
print(" --> %i auto-correlation peaks found" % (len(pidx)))
pidx[0] = 0 # first peak is at 0 by construction
tp, ap = np.array(ac_t[pidx]), np.array(ac_a[pidx])
else:
print("*!!* not enough peaks found - tune peakfinder parameters!")
sys.exit(1)
# Filter peaks and dips: keep only largest ones
# !!! need inspection by eye to ensure correct peaks are identified
tpm = []
apm = []
for i, ti in enumerate(tp):
if ap[i] > 0.137:
tpm.append(tp[i])
print("** numerical derivative")
dt = t[1] - t[0]
omega = np.gradient(phi, dt)
# calculate fourier spectrum
print("** Fourier Spectrum")
freq, amp = ppk.FourierSpectrum(t, phi, fmax=1.)
# freq, amp = ppk.Fourier_fft(t, phi) # fast algorithm
frequency = freq[np.where(amp == max(amp))]
print(" --> Frequenz: ", frequency)
# run a peak finder
# first, determine width of typical peaks and dips
width = 0.5 * len(t) / (t[-1] - t[0]) / frequency
# use convoluted template filter
peakind = ppk.convolutionPeakfinder(phi, width, th=0.53)
dipind = ppk.convolutionPeakfinder(-phi, width, th=0.53)
if len(peakind) > 5:
print(" --> %i peaks and %i dips found" % (len(peakind), len(dipind)))
tp, phip = np.array(t[peakind]), np.array(phi[peakind])
td, phid = np.array(t[dipind]), np.array(phi[dipind])
else:
print("*!!* not enough peaks found for envelope fit")
print(" tune peakfinder parameters!")
sys.exit(1)
# cubic spline interpolation with scipy.interpolate
print("** spline interpolation")
cs_phi = interpolate.UnivariateSpline(t, phi, s=0)
cs_omega = cs_phi.derivative()
#Bestimmung von T ___________________________________________________________________________
hlines, data = ppk.readCSV('HandyPendel.csv')
t = data[0]
a = data[2]
#Glätten der Funktion
a_smooth = ppk.meanFilter(a, 7)
# calculate autocorrelation function
ac_a = ppk.autocorrelate(a_smooth)
ac_t = t
# find maxima and minima using convolution peak finder
width = 3
pidxac = ppk.convolutionPeakfinder(ac_a, width, th=0.66)
didxac = ppk.convolutionPeakfinder(-ac_a, width, th=0.66)
if len(pidxac) > 1:
print(" --> %i auto-correlation peaks found" % (len(pidxac)))
pidxac[0] = 0 # first peak is at 0 by construction
ac_tp, ac_ap = np.array(ac_t[pidxac]), np.array(ac_a[pidxac])
ac_td, ac_ad = np.array(ac_t[didxac]), np.array(ac_a[didxac])
else:
print("*!!* not enough correlation peaks found")
#Plot erstellen
fig = plt.figure(1, figsize=(7.5, 10))
fig.subplots_adjust(left=0.14,
bottom=0.1,
right=0.97,
top=0.93,
