impemented FFT with numpy and recursion

FFT.py

@@ -3,10 +3,30 @@ import numpy as np
 
 
 
-def FFT(inp):
+def FFT_backup(inp):
   inp = np.array(inp)
   out = np.fft.fft(inp)
   out = [val for val in np.abs(out)]
   print(out)
   return out
 
+
+def FFT_real(inp):
+  inp = np.array(inp)
+  out = FFT(inp)
+  out = [val for val in np.abs(out)]
+  print(out)
+  return out
+
+
+def FFT(inp):
+  inp = np.array(inp)
+  N = inp.shape[0]
+  if N == 1:
+    return inp
+  X_even = FFT(inp[::2])
+  X_odd  = FFT(inp[1::2])
+  k = np.arange(N // 2)
+  tw = np.exp(-2j * np.pi * k / N) * X_odd
+  return np.concatenate((X_even + tw, X_even - tw))
+