def compute_inv_dft(x_val, y_val, zeropad_num=0):
""" Compute the inverse Discrete fourier Transform
@param numpy.array x_val: 1D array
@param numpy.array y_val: 1D array of same size as x_val
@param int zeropad_num: zeropadding (adding zeros to the end of the array).
zeropad_num >= 0, the size of the array, which is
add to the end of the y_val before performing the
dft. The resulting array will have the length
(len(y_val)/2)*(zeropad_num+1)
Note that zeropadding will not change or add more
information to the dft, it will solely interpolate
between the dft_y values.
@return: tuple(dft_x, dft_y):
be aware that the return arrays' length depend on the zeropad
number like
len(dft_x) = len(dft_y) = (len(y_val)/2)*(zeropad_num+1)
"""
x_val = np.array(x_val)
y_val = np.array(y_val)
corrected_y = np.abs(y_val - y_val.max())
# The absolute values contain the fourier transformed y values
# zeropad_arr = np.zeros(len(corrected_y)*(zeropad_num+1))
# zeropad_arr[:len(corrected_y)] = corrected_y
fft_y = np.fft.ifft(corrected_y)
# Due to the sampling theorem you can only identify frequencies at half
# of the sample rate, therefore the FT contains an almost symmetric
# spectrum (the asymmetry results from aliasing effects). Therefore take
# the half of the values for the display.
middle = int((len(corrected_y)+1)//2)
# sample spacing of x_axis, if x is a time axis than it corresponds to a
# timestep:
x_spacing = np.round(x_val[-1] - x_val[-2], 12)
# use the helper function of numpy to calculate the x_values for the
# fourier space. That function will handle an occuring devision by 0:
fft_x = np.fft.fftfreq(len(corrected_y), d=x_spacing)
# return abs(fft_x[:middle]), fft_y[:middle]
return fft_x[:middle], fft_y[:middle]
# return fft_x, fft_y
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