real_forward_fft.py

import numpy as np

def real_forward_fft(x):
    N = len(x) # length of input signal
    K = N // 2 + 1 # length of resulting FFT

    result = np.zeros(K, dtype=np.complex64)

    for k in range(K):
        val = 0.0

        for n in range(N): # note, in Python j is the imaginary number sqrt(-1)
            val += x[n] * np.exp(-1j * 2 * np.pi / N * k * n)

        result[k] = val

    return result