do ifft using fft

do_ifft_using_fft.py

from scipy.fftpack import fft
import numpy as np

# random complex array of N = 4
a = np.array([11.+11.4j, 2.47+2.3j, 30.89+73.1j, 44.+16.3j])
print(a)

# do FFT to a to transform to frequency domain
da = fft(a)

# do ifft using fft
# beacuse the difference of idft and dft is just change of its imaginary part:
# see this:(https://www.dsprelated.com/showthread/comp.dsp/31758-1.php)
# just do some adjust and normalization and one can use fft for ifft
def do_ifft_using_fft(da):
    # get conjugation of freqency domain data
    da = np.conjugate(da)
    print(da)

    # do fft as ifft
    da = fft(da) 
    print(da)

    # normalization by 1/N
    N = len(a)
    da = da/ N

    # get conjugation of time domain data
    da = np.conjugate(da)
    print(da)
    return da

do_ifft_using_fft(da)

关于DFT和IDFT的相似性：
https://www.dsprelated.com/showthread/comp.dsp/31758-1.php
DFT和IDFT本质上相同，只是j前面的符号的不同，因此，IDFT可以在DFT上经过一些调整获得。
在FFT获得频域后，对频域进行共轭，就可以用DFT计算IDFT（指Type1型DFT或者FFT）
换回时域后需要除以1/N归一化，并且再求一次共轭