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Intuitive impementation of discrete Fourier transform (and inverse DFT) in Python (without numpy)
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#!/usr/bin/env python3 | |
import math | |
# >> Discrete Fourier transform for sampled signals | |
# x [in]: sampled signals, a list of magnitudes (real numbers) | |
# yr [out]: real parts of the sinusoids | |
# yi [out]: imaginary parts of the sinusoids | |
def dft(x): | |
N, yr, yi = len(x), [], [] | |
for k in range(N): | |
real, imag = 0, 0 | |
for n in range(N): | |
theta = -k * (2 * math.pi) * (float(n) / N) | |
real += x[n] * math.cos(theta) | |
imag += x[n] * math.sin(theta) | |
yr.append(real / N) | |
yi.append(imag / N) | |
return yr, yi | |
# >> Inverse discrete Fourier transform | |
# yr [in]: real parts of the sinusoids | |
# yi [in]: imaginary parts of the sinusoids | |
# x [out]: sampled signals (real parts only), a list of magnitude | |
def idft(yr, yi): | |
N, x = len(yr), [] | |
for n in range(N): | |
real, imag = 0, 0 | |
for k in range(N): | |
theta = k * (2 * math.pi) * (float(n) / N) | |
real += (yr[k] * math.cos(theta)) - (yi[k] * math.sin(theta)) | |
# imag += (yr[k] * math.sin(theta)) + (yi[k] * math.cos(theta)) | |
x.append(real) | |
return x | |
if __name__ == '__main__': | |
x = [1, 2, 3, 5] | |
yr, yi = dft(x) # y=[2.75+0j, -0.5+0.75j, 0.75+0j, -0.5-0.75j] | |
x2 = idft(yr, yi) # x2=[1, 2, 3, 5] |
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