Initial commit

fft/real_fft_test.py

@@ -0,0 +1,83 @@
+"""This script is used to visualize the behavior of the fft if the input is
+purely real."""
+
+import numpy as np
+import seaborn as sns
+import matplotlib.pyplot as plt
+
+
+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
+
+    # fig, axes = plt.subplots(2, int(np.log2(N0)))
+
+    N = 2
+    while N <= N0:
+        first_subfft_index = 0
+        while first_subfft_index < N0:
+            temp = x[first_subfft_index + N // 2]
+            x[first_subfft_index + N // 2] = x[first_subfft_index] - temp
+            x[first_subfft_index] = x[first_subfft_index] + temp
+
+            for k in range(1, N // 2):
+                factor = np.exp(-2j * np.pi * k / N)
+
+                x[first_subfft_index + k] \
+                    = x[first_subfft_index + k] \
+                      + factor * x[first_subfft_index + k + N // 2]
+
+            for k in range(1, N // 2):
+                x[first_subfft_index + N - k] \
+                    = x[first_subfft_index + k].conj()
+            #      \
+            #         = x[first_subfft_index + k] + temp
+            # for k in range(N // 2):
+            #     factor = np.exp(- 2j * np.pi * k / N)
+            #
+            #     temp = factor * x[first_subfft_index + k + N // 2]
+            #     x[first_subfft_index + k + N // 2] \
+            #         = x[first_subfft_index + k] - temp
+            #     x[first_subfft_index + k] \
+            #         = x[first_subfft_index + k] + temp
+
+            first_subfft_index += N
+        # axes[0][int(np.log2(N)) - 1].plot(x.real[1:])
+        # axes[1][int(np.log2(N)) - 1].plot(x.imag[1:])
+        N *= 2
+
+    plt.show()
+
+    return x
+
+
+def main():
+    sns.set_theme()
+
+    x = np.arange(16) + 1
+    X = fft(x)
+    X_reference = np.fft.fft(x)
+
+    for X_i, X_ref_i in zip(X, X_reference):
+        print(
+            f"{X_i.real:06.2f} + j({X_i.imag:06.2f})\t\t{X_ref_i.real:06.2f} "
+            f"+ j({X_ref_i.imag:06.2f})")
+
+    print(np.allclose(X, X_reference, rtol=1e-05, atol=1e-08))
+
+
+if __name__ == "__main__":
+    main()