Initial commit

fft/iterative_fft.py

@@ -0,0 +1,48 @@
+import numpy as np
+
+
+def bit_reverse(val: int, num_bits: int) -> None:
+    b = '{:0{num_bits}b}'.format(val, num_bits=num_bits)
+    return int(b[::-1], 2)
+
+
+def fft_reorder(x: np.array) -> np.array:
+    result = np.zeros(x.size)
+    for i in range(x.size):
+        result[i] = x[bit_reverse(i, int(np.log2(x.size)))]
+    return result
+
+
+def fft(x: np.array) -> np.array:
+    x = fft_reorder(x).astype('complex64')
+
+    N0 = x.size
+    N = 2
+    # while N <= N0:
+    for N in [2, 4, 8]:
+        first_sub_fft_index = 0
+        while first_sub_fft_index < N0:
+            for k in range(N // 2):
+                factor = np.exp(-2j * np.pi * k / N)
+
+                temp = factor * x[first_sub_fft_index + N // 2 + k]
+
+                x[first_sub_fft_index + N//2 + k]\
+                    = x[first_sub_fft_index + k] - temp
+                x[first_sub_fft_index + k]\
+                    = x[first_sub_fft_index + k] + temp
+
+            first_sub_fft_index += N
+        # N *= 2
+
+    return x
+
+
+def main():
+    x = np.arange(8)
+    print(fft(x))
+    print(np.fft.fft(np.arange(8)))
+
+
+if __name__ == "__main__":
+    main()