diff --git a/FFT.py b/FFT.py
index 45ebfb5..61ec9a0 100644
--- a/FFT.py
+++ b/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))
+
diff --git a/__pycache__/FFT.cpython-312.pyc b/__pycache__/FFT.cpython-312.pyc
index 90dfc2c..7ed90aa 100644
Binary files a/__pycache__/FFT.cpython-312.pyc and b/__pycache__/FFT.cpython-312.pyc differ
diff --git a/naive_DFT.py b/naive_DFT.py
index 65ae0ad..f00483e 100755
--- a/naive_DFT.py
+++ b/naive_DFT.py
@@ -3,7 +3,7 @@ from math import sin, cos, pi, sqrt
 import plotly.graph_objs as go
 from plotly.subplots import make_subplots
 
-from FFT import FFT
+from FFT import FFT_real
 
 FP_acc = 1e3
 
@@ -156,7 +156,7 @@ def DFT_naive_FP(inp_float, out):
 
   
 def FFT_naive(inp, out):
-  fft_out = FFT(inp)
+  fft_out = FFT_real(inp)
   for i in range(len(fft_out)):
     val = fft_out[i]/len(inp)
     if (i < len(out)):