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作为 A 和 B 两个余弦数据系列（相同的 X 值，不同的 Y 值），我想确定第三个余弦函数（及其参数），以便： A(x) = B(x) + C(x) [A 是蓝色曲线，B是下面的红色曲线]

我只想发现我必须将哪个余弦函数（或 N 个余弦函数）添加到 B(x) 以产生 A(x)（或尽可能接近）。

插入图像描述

到目前为止，我已经设法读取了 A(x) 和 B(x) 的数据点，并用于scipy.optimize.curve_fit()恢复每个系列的余弦函数参数。

    def fit_cos1(angles,energy):

        ang = numpy.array(angles)
        energy = numpy.array(energy)
        ff = numpy.fft.fftfreq(len(ang), (ang[1]-ang[0]))   # assume uniform spacing
        Fenergy = abs(numpy.fft.fft(energy))

        guess_freq = abs(ff[numpy.argmax(Fenergy[1:])+1])   # excluding the zero frequency peak, which is related to offset
        guess_amp = numpy.std(energy) * 2.**0.5
        guess_offset = numpy.mean(energy)
        guess = numpy.array([guess_amp, 2.*numpy.pi*guess_freq, 0., guess_offset])

        def cosfunc(t, K, N, Y, c):
            return K*(1 - numpy.cos(N*t + Y)) + c

        popt, pcov = scipy.optimize.curve_fit(cosfunc, ang, energy, p0=guess)
        K, N, Y, c = popt


        fitfunc = lambda t: K*(1 - numpy.cos(N*t + Y)) + c

        return {"amp": round(K,2), "omega": round(N*57.2958,2), "phase": round(Y*57.2958,2), "coeff": round(c,2), "fitfunc": fitfunc, "maxcov": numpy.max(pcov), "rawres": (guess,popt,pcov)} # outputing in degrees


angles = [0,30,60,90,120,150,180,210,240,270,300,330,360]
energyA = [0,3.3908, 10.7669, 14.9809, 11.526, 3.9065, 0.0016, 3.9057, 11.5265, 14.9811, 10.7667, 3.39, 0]
energyB = [4.679575, 3.251112, 0.951731, 0.0, 1.047923, 3.352932, 4.688559, 3.31077, 1.047938, 0.00, 0.951859, 3.25869, 4.679554]

A = fit_cos1(angles, energyA)
print( "CurveA: Amplitude=%(amp)s, Periodicity=%(omega)s, Phase=%(phase)s, V-shift=%(coeff)s, Max. Cov.=%(maxcov)s" % A )

B = fit_cos1(angles, energyB)
print( "CurveB: Amplitude=%(amp)s, Periodicity=%(omega)s, Phase=%(phase)s, V-shift=%(coeff)s, Max. Cov.=%(maxcov)s" % B )

获得的余弦参数似乎没问题，并且在我期望的误差范围内。

CurveA: Amplitude=7.48, Periodicity=2.03, Phase=-5.31, V-shift=0.04, Max. Cov.=0.00130465635936
CurveB: Amplitude=-2.35, Periodicity=1.98, Phase=4.31, V-shift=4.6, Max. Cov.=0.00214051830825

从那里，有没有人知道如何找到第三个余弦函数，以便 A(x) = B(x) + C(x)？

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