got frequency, need plot sinus wave

I am just fighting with modulation of sinus wave. I have got a frequency (from messured data - changing in time) and now I need to plot sinus wave with coresponding frequency.

The blue line are just plotted points of real data and the green is what I did till now, but it does not corespond with real data at all.

The code to plot sin wave is bottom:

def plotmodulsin():
    n = 530
    f1, f2 = 16, 50 # frequency

    t = linspace(6.94,8.2,530)
    dt = t[1] - t[0] # needed for integration
    print t[1]
    print t[0]
    f_inst = logspace(log10(f1), log10(f2), n)
    phi = 2 * pi * cumsum(f_inst) * dt # integrate to get 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 for 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 I need generate sinus with constant amplitude and 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 to match you function with something sine- or actually cosine-like, by extracting estimates for the frequency and the amplitude from your data. If I understood you correctly, your data are maximums and minimums and you want to have a trigonometric function that resembles that. If your data is saved in two arrays time and value, amplitude estimates are simply given by np.abs(value). Frequencies are given as the inverse of two times the time difference between a maximum and a minimum. freq = 0.5/(time[1:]-time[:-1]) gives you frequency estimates for the mid points of each time interval. The corresponding times are thus given as freqTimes = (time[1:]+time[:-1])/2..

To get a smoother curve, you can now interpolate those amplitude and frequency values to get estimates for the values in between. A very simple way to do this is by use of np.interp, which will do a simple linear interpolation. You will have to specify at which points in time to interpolate. We will construct an array for that and then 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 you can do the integration, that you already had in your example by doing:

phi = (2*np.pi*np.cumsum(freqInterpolated)
       *(timesToInterpolate[1]-timesToInterpolate[0]))

And now you can plot. So putting it all together gives you:

import numpy as np
import matplotlib.pyplot as 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 like this (if you include the full arrays):