i fighting modulation of sinus wave. have got frequency (from messured data - changing in time) , need plot sinus wave coresponding frequency.
the blue line plotted points of real data , green did till now, not corespond real data @ all.
the code plot sin wave bottom:
def plotmodulsin(): n = 530 f1, f2 = 16, 50 # frequency t = linspace(6.94,8.2,530) dt = t[1] - t[0] # needed integration print t[1] print t[0] f_inst = logspace(log10(f1), log10(f2), n) phi = 2 * pi * cumsum(f_inst) * dt # integrate phase pylab.plot(t, 5*sin(phi)) amplitude vector:
[2.64, -2.64, 6.14, -6.14, 9.56, -9.56, 12.57, -12.57, 15.55, -15.55, 18.04, -18.04, 21.17, -21.17, 23.34, -23.34, 25.86, -25.86, 28.03, -28.03, 30.49, -30.49, 33.28, -33.28, 35.36, -35.36, 36.47, -36.47, 38.86, -38.86, 41.49, -41.49, 42.91, -42.91, 44.41, -44.41, 45.98, -45.98, 47.63, -47.63, 47.63, -47.63, 51.23, -51.23, 51.23, -51.23, 53.18, -53.18, 55.24, -55.24, 55.24, -55.24, 55.24, -55.24, 57.43, -57.43, 57.43, -57.43, 59.75, -59.75, 59.75, -59.75, 59.75, -59.75, 59.75, -59.75, 62.22, -62.22, 59.75, -59.75, 62.22, -62.22, 59.75, -59.75, 62.22, -62.22, 62.22, -62.22, 59.75, -59.75, 62.22, -62.22, 62.22, -62.22, 59.75, -59.75, 62.22, -62.22, 62.22, -62.22, 62.22, -62.22, 59.75, -59.75, 62.22, -62.22, 59.75, -59.75, 62.22, -62.22, 59.75, -59.75, 59.75]
time vector real data:
[6.954, 6.985, 7.016, 7.041, 7.066, 7.088, 7.11, 7.13, 7.149, 7.167, 7.186, 7.202, 7.219, 7.235, 7.251, 7.266, 7.282, 7.296, 7.311, 7.325, 7.339, 7.352, 7.366, 7.379, 7.392, 7.404, 7.417, 7.43, 7.442, 7.454, 7.466, 7.478, 7.49, 7.501, 7.513, 7.524, 7.536, 7.547, 7.558, 7.569, 7.58, 7.591, 7.602, 7.613, 7.624, 7.634, 7.645, 7.655, 7.666, 7.676, 7.686, 7.697, 7.707, 7.717, 7.728, 7.738, 7.748, 7.758, 7.768, 7.778, 7.788, 7.798, 7.808, 7.818, 7.828, 7.838, 7.848, 7.858, 7.868, 7.877, 7.887, 7.897, 7.907, 7.917, 7.927, 7.937, 7.946, 7.956, 7.966, 7.976, 7.986, 7.996, 8.006, 8.016, 8.026, 8.035, 8.045, 8.055, 8.065, 8.075, 8.084, 8.094, 8.104, 8.114, 8.124, 8.134, 8.144, 8.154, 8.164, 8.174, 8.184, 8.194, 8.20]
so need generate sinus constant amplitude , following frequency:
[10.5, 16.03, 20.0, 22.94, 25.51, 27.47, 29.76, 31.25, 32.89, 34.25, 35.71, 37.31, 38.46, 39.06, 40.32, 41.67, 42.37, 43.1, 43.86, 44.64, 44.64, 46.3, 46.3, 47.17, 48.08, 48.08, 48.08, 49.02, 49.02, 50.0, 50.0, 50.0, 50.0]
you can try match function sine- or cosine-like, extracting estimates frequency , amplitude data. if understood correctly, data maximums , minimums , want have trigonometric function resembles that. if data saved in 2 arrays time , value, amplitude estimates given np.abs(value). frequencies given inverse of 2 times time difference between maximum , minimum. freq = 0.5/(time[1:]-time[:-1]) gives frequency estimates mid points of each time interval. corresponding times given freqtimes = (time[1:]+time[:-1])/2..
to smoother curve, can interpolate amplitude , frequency values estimates values in between. simple way use of np.interp, simple linear interpolation. have specify @ points in time interpolate. construct array , interpolate by:
n = 10000 timestointerpolate = np.linspace(time[0], time[-1], n, endpoint=true) freqinterpolated = np.interp(timestointerpolate, freqtimes, freq) amplinterpolated = np.interp(timestointerpolate, time, np.abs(value)) now can integration, had in example doing:
phi = (2*np.pi*np.cumsum(freqinterpolated) *(timestointerpolate[1]-timestointerpolate[0])) and can plot. putting gives you:
import numpy np import matplotlib.pyplot plt time = np.array([6.954, 6.985, 7.016, 7.041, 7.066, 7.088, 7.11, 7.13]) #... value = np.array([2.64, -2.64, 6.14, -6.14, 9.56, -9.56, 12.57, -12.57]) #... freq = 0.5/(time[1:]-time[:-1]) freqtimes = (time[1:]+time[:-1])/2. n = 10000 timestointerpolate = np.linspace(time[0], time[-1], n, endpoint=true) freqinterpolated = np.interp(timestointerpolate, freqtimes, freq) amplinterpolated = np.interp(timestointerpolate, time, np.abs(value)) phi = (2*np.pi*np.cumsum(freqinterpolated) *(timestointerpolate[1]-timestointerpolate[0])) plt.plot(time, value) plt.plot(timestointerpolate, amplinterpolated*np.cos(phi)) #or np.sin(phi+np.pi/2) plt.show() the result looks (if include full arrays):
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