拟合傅立叶函数时，scipy curve_fit无法生成平滑图形

Question

I'm getting a strange result when using scipy curve_fit when fitting my data to this function.

def func(t, freq, offset, a0, b0, a1, b1, a2, b2, a3, b3):
    return (
        + a0*np.sin(2.*0*np.pi*freq*t)
        + b0*np.cos(2.*0*np.pi*freq*t)    
        + a1*np.sin(2.*1*np.pi*freq*t)
        + b1*np.cos(2.*1*np.pi*freq*t)    
        + a2*np.sin(2.*2*np.pi*freq*t)
        + b2*np.cos(2.*2*np.pi*freq*t)    
        + a3*np.sin(2.*3*np.pi*freq*t)
        + b3*np.cos(2.*3*np.pi*freq*t)
        + offset)

This is the result of the fit plotted

The fit itself is okay, the only problem being is that the line is bumpy. Since I am only fitting sines and cosines with a constant, how could this be happening? Is this happening in matplotlib or in the curve_fitting function? Another thing is that depending on whether I add more or less terms to the function, the function will either smooth itself out, or get bumpy again.

Answer 1

You may leave the a0 term out, as this is constant zero. You may also leave b0 out as this is the same as offset. This is not the cause of the bumps, but removes two redundant fitting parameters.

def func(t, freq, offset, a1, b1, a2, b2, a3, b3):
    return (   
        + a1*np.sin(2.*1*np.pi*freq*t)
        + b1*np.cos(2.*1*np.pi*freq*t)    
        + a2*np.sin(2.*2*np.pi*freq*t)
        + b2*np.cos(2.*2*np.pi*freq*t)    
        + a3*np.sin(2.*3*np.pi*freq*t)
        + b3*np.cos(2.*3*np.pi*freq*t)
        + offset)

Apart from that the result is expected. The more frequencies you allow, the more frequencies you have in your plot. The bumps are the sin or cos functions with low amplitude and high frequency. Using more datapoints on the x-axis when plotting the fit curve will allow you to observe that the bumps are smooth like sin functions as well.