# between the actual data and our "guessed" parameters # Define the function to optimize, in this case, we want to minimize the difference This might already be good enough for youĭata_first_guess = guess_std*np.sin(t+guess_phase) + guess_mean # we'll use this to plot our first estimate. This leads to the following code: import numpy as npį = 1.15247 # Optional!! Advised not to useĭata = 3.0*np.sin(f*t+0.001) + 0.5 + np.random.randn(N) # create artificial data with noise Thus, use at your discretion, my advise would be to not use frequency fitting unless frequency error is smaller than a few percent. This does not work very well (can lead to extremely poor fits). Note: as a later edit, frequency fitting has also been added. In case of fitting a sin function, the 3 parameters to fit are the offset ('a'), amplitude ('b') and the phase ('c').Īs long as you provide a reasonable first guess of the parameters, the optimization should converge well.Fortunately for a sine function, first estimates of 2 of these are easy: the offset can be estimated by taking the mean of the data and the amplitude via the RMS (3*standard deviation/sqrt(2)). You can use the least-square optimization function in scipy to fit any arbitrary function to another. Plt.plot(tt, yynoise, "ok", label="y with noise") Print( "Amplitude=%(amp)s, Angular freq.=%(omega)s, phase=%(phase)s, offset=%(offset)s, Max. Yy = amp*numpy.sin(omega*tt + phase) + offset #N, amp, omega, phase, offset, noise = 50, 1. N, amp, omega, phase, offset, noise = 500, 1., 2. The fitting result is almost perfect assuming there is only one dominant frequency (other than the zero frequency peak). The initial frequency guess is given by the peak frequency in the frequency domain using FFT. Popt, pcov = _fit(sinfunc, tt, yy, p0=guess)įitfunc = lambda t: A * numpy.sin(w*t + p) + c Guess = numpy.array()ĭef sinfunc(t, A, w, p, c): return A * numpy.sin(w*t + p) + c Guess_freq = abs(ff)+1]) # excluding the zero frequency "peak", which is related to offset '''Fit sin to the input time sequence, and return fitting parameters "amp", "omega", "phase", "offset", "freq", "period" and "fitfunc"'''įf = (len(tt), (tt-tt)) # assume uniform spacing Please see the TI-83 Plus and TI-84 Plus Family guidebooks for additional information.Here is a parameter-free fitting function fit_sin() that does not require manual guess of frequency: import numpy, scipy.optimize ģ) Press the key to graph the function.Ĥ) To display a better graph of the sin(x) function, press and select 7:ZTrig.Ĥ) To display a better graph of the cos(x) function, press and select 7:ZTrig.Ĥ) To display a better graph of the tan(x) function, press and select 7:ZTrig. Degree Mode can be used as well but may not match the images below until the fourth step to use ZOOM Ztrig is used.Ģ) Highlight Radian and press the key.ģ) Press the to return to the home screen.ġ) Press the key to access the Y= Editor.Ģ) With the cursor next to Y1, press. Radian mode is recommended when graphing a trigonometric and an algebraic function on the same screen. Please Note: The example functions below use Radian mode. Each device has the ability to graph trigonometric function in either degrees or radians. The following examples will demonstrate how to graph sine, cosine and tangent functions on the TI-83 Plus and TI-84 Plus family of graphing calculators. How do I graph sine, cosine, and tangent functions on the TI-83 Plus and TI-84 Plus family of graphing calculators? Solution 34673: Graphing Sine, Cosine, and Tangent Functions on the TI-83 Plus and TI-84 Plus Family of Graphing Calculators.
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