如何使用python-scipy消除余弦函数中的可变幅度？

Question

after a complex FFT analysis, I got my data as `

y=np.array([-0.31757207, -0.759897  , -0.97481323, -0.90067096, -0.56201419,
   -0.06141066,  0.45184696,  0.82654122,  0.95429599,  0.80098432,
    0.41565507, -0.08528661, -0.55350349, -0.85289024, -0.89924892,
   -0.6838725 , -0.27446443,  0.20632688,  0.61789554,  0.84295248,
    0.82091852,  0.56394004,  0.15139964, -0.29481341, -0.64650262,
   -0.80602096, -0.73317927, -0.45486384, -0.0552602 ,  0.3498015 ,
    0.64649953,  0.75486814,  0.64997615,  0.36696461, -0.01077531,
   -0.37629244, -0.62928397, -0.70331519, -0.58277349, -0.30541445,
    0.04956568,  0.38413122,  0.60823604,  0.66362602,  0.53848173,
    0.26941065, -0.06930203, -0.38601383, -0.59612545, -0.6442082 ,
   -0.5182447 , -0.25246689,  0.08181356,  0.39497462,  0.60264688,
    0.6480463 ,  0.51731067,  0.24376628, -0.10019951, -0.42181997,
   -0.63254052, -0.67215727, -0.52601037, -0.23032442,  0.13622702,
    0.47298468,  0.68464621,  0.70816855,  0.53165966,  0.19956061,
   -0.19797826, -0.54920882, -0.75206661, -0.74391156, -0.52103408,
   -0.14180003,  0.28818356,  0.64528143,  0.82341019,  0.76573576,
    0.48295615,  0.05224223, -0.40355087, -0.75089961, -0.88488436,
   -0.76111445, -0.41051563,  0.06797007,  0.53521743,  0.85248562,
    0.92285209,  0.72105995,  0.30251038, -0.21178154, -0.67024193,
   -0.935627  , -0.92637938, -0.64190028, -0.16383967,  0.36735054,
    0.79386302,  0.98768951,  0.88930233,  0.52608786,  0.00477518,
   -0.52006527, -0.89210845, -1.00012051, -0.8114311 , -0.3818889 ,
    0.16075761,  0.65507887,  0.95427369,  0.97001733,  0.69866763,
    0.22200955])

Which, when plotted produces this:

This is a cosine function with variable amplitude. I'm looking for a way to get rid of the amplitude envelope to obtain normal cosine function which I can fit.

Answer 1

from matplotlib.pyplot import plot, figure

from numpy import array, exp, arange, real, append

from scipy.fftpack import fft, ifft

w = fft(y)

f = arange(0,y.size)

cf = 10 #central freq

wd = 0.5 #width

gate1 = exp(-((f-cf)/(0.707106*wd))**(2*2))

gate2 = append([0],gate1[::-1])[:-1] #symmetrize

gate = gate1+gate2

w_f = w*gate

figure(1)

plot(abs(w))

plot(abs(w_f))

figure(2)

plot(real(ifft(w_f)))