got frequency, need plot sinus wave

Question

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.

real data and sinus

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 plot a sine with constant amplitude (5). Thus, you cannot expect it to match your data which has an amplitude, which seems to more or less linearly increase until it reaches 60. But without the form of your data and any information about what it represent, one cannot really decide how to fit your data. Best one can do is plot something that qualitatively looks similar... — jotasi, Sep 02 '16 at 07:49
What I need now is to match data olny with their frequency. Amplitude can I do as a next step. Thats why I multiplied with constant number. — Robin Popelka, Sep 02 '16 at 08:13
You can plot a sine with those frequencies, but the problem is, they do not match your real data, as you can simply check by comparing them with 1/(Dt) with Dt being time between maximums or minimums in you real data... — jotasi, Sep 02 '16 at 09:22
You can do a better estimation of the frequencies. But actually, I do not really understand what exactly you want to achieve. As far as I understand, you want to have a sine-like curve that looks "similar" to your data. What you can do is interpolate the discrete frequencies at every step. But that will give you a rather complicated argument for the sine meaning that you don't really have a sine anymore. Can you tell us, why you want to do this? What is the usecase? — jotasi, Sep 02 '16 at 11:14

score 0 · Accepted Answer · answered Sep 02 '16 at 14:43

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):

got frequency, need plot sinus wave

1 Answers1