implemented in-place FFT c-style. (by ChatGPT)

FFT.py

@@ -1,5 +1,5 @@
 import numpy as np
-
+from math import sin, cos, pi, sqrt
 
 
 
@@ -12,17 +12,38 @@ def FFT_backup(inp):
 
 
 def FFT_real(inp):
-  inp = np.array(inp)
+  
-  out = FFT(inp)
+  mode = 2
-  out = [val for val in np.abs(out)]
+  if (mode == 0):
+    inp = np.array(inp)
+    out = FFT_np(inp)
+    out = [np.abs(val) for val in out]
+  if (mode == 1):
+    
+    out = FFT_arr([[val, 0] for val  in inp])
+    #out = [val for val in np.abs(out)]
+    print("FFT_calculated!")
+    print("output:", out)
+    out = [sqrt(val[0]**2 + val[1]**2) for val in out]
+#    out = [2 for val in out]
+  if (mode == 2):
+  
+  
+    out = FFT_arr_inplace([[val, 0] for val  in inp])
+    #out = [val for val in np.abs(out)]
+    print("FFT_calculated!")
+    print("output:", out)
+    out = [sqrt(val[0]**2 + val[1]**2) for val in out]
+    
   print(out)
   return out
 
 
 def FFT(inp):
-  return FFT_np(inp)
+  return FFT_arr([[val, 0] for val  in inp])
 
 def FFT_np(inp):
+  print("inp:", inp)
   inp = np.array(inp)
   N = inp.shape[0]
   if N == 1:
@@ -33,3 +54,143 @@ def FFT_np(inp):
   tw = np.exp(-2j * np.pi * k / N) * X_odd
   return np.concatenate((X_even + tw, X_even - tw))
 
+def FFT_arr(x):
+  print("x:", x)
+
+  N = len(x)
+  print("len(x):", N)
+  if N == 1:
+    print("As len(x) == 1, return it`s value")
+    return x
+  X_even = FFT_arr(x[::2])
+  X_odd = FFT_arr(x[1::2])
+  print("X_even:",X_even)
+  
+  tw = []
+  for k in range(len(X_odd)):
+    a = cos(2*pi * k/N) #real
+    b = -sin(2*pi * k/N) #imag
+    
+    c = X_odd[k][0]  # real
+    d = X_odd[k][1]  # imag
+    
+    print("a,b,c,d:", a,b,c,d)
+    
+    tw.append([a*c - b*d, b*c + a*d])   #(a + ib)(c + id) =  (ac - bd) + i(bc + ad)
+  res = [0 for i in range(len(X_even)*2)]
+  for i in range(len(X_even)):
+    res[i] = [X_even[i][0] + tw[i][0], X_even[i][1] + tw[i][1]]
+    res[i+len(X_even)] = [X_even[i][0] - tw[i][0], X_even[i][1] - tw[i][1]]
+  return res
+
+
+
+
+import math
+
+def FFT_arr_inplace(buf):
+  """
+    In-place radix-2 DIT FFT для списка buf длины N=2^m, где каждый элемент — [re, im].
+    Без массивов twiddle: твиддл на уровне обновляется рекуррентно.
+    """
+  N = len(buf)
+  # --- bit-reverse перестановка (чтобы бабочки шли последовательно) ---
+  j = 0
+  for i in range(1, N):
+    bit = N >> 1
+    while j & bit:
+      j ^= bit
+      bit >>= 1
+    j |= bit
+    if i < j:
+      buf[i], buf[j] = buf[j], buf[i]
+
+  # --- уровни бабочек ---
+  m = 2
+  while m <= N:
+    half = m // 2
+    # шаг угла Δ = 2π/m, базовый твиддл w_m = e^{-jΔ} => (cw, sw)
+    cΔ = math.cos(2.0 * math.pi / m)
+    sΔ = -math.sin(2.0 * math.pi / m)
+
+    for start in range(0, N, m):
+      # w = e^{-j*0*Δ} = 1 + j0
+      wr, wi = 1.0, 0.0
+      for k in range(half):
+        u_re, u_im = buf[start + k]
+        v_re, v_im = buf[start + k + half]
+
+        # t = w * v
+        t_re = wr * v_re - wi * v_im
+        t_im = wr * v_im + wi * v_re
+
+        # верх/низ
+        buf[start + k][0]        = u_re + t_re
+        buf[start + k][1]        = u_im + t_im
+        buf[start + k + half][0] = u_re - t_re
+        buf[start + k + half][1] = u_im - t_im
+
+        # w *= w_m  (поворот на Δ с помощью рекуррентной формулы)
+        # (wr + j wi) * (cΔ + j sΔ)
+        wr, wi = wr * cΔ - wi * sΔ, wr * sΔ + wi * cΔ
+
+    m <<= 1
+  return buf
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+def FFT_arr_for_C(x):
+  print("x:", x)
+
+  N = len(x)
+  print("len(x):", N)
+  if N == 1:
+    print("As len(x) == 1, return it`s value")
+    return x
+  X_even = FFT_arr_for_C(x[::2])
+  X_odd = FFT_arr_for_C(x[1::2])
+  print("X_even:",X_even)
+  
+  tw = []
+  for k in range(len(X_odd)):
+    a = cos(2*pi * k/N) #real
+    b = -sin(2*pi * k/N) #imag
+    
+    c = X_odd[k][0]  # real
+    d = X_odd[k][1]  # imag
+    
+    print("a,b,c,d:", a,b,c,d)
+    
+    tw.append([a*c - b*d, b*c + a*d])   #(a + ib)(c + id) =  (ac - bd) + i(bc + ad)
+  res = [0 for i in range(len(X_even)*2)]
+  for i in range(len(X_even)):
+    res[i] = [X_even[i][0] + tw[i][0], X_even[i][1] + tw[i][1]]
+    res[i+len(X_even)] = [X_even[i][0] - tw[i][0], X_even[i][1] - tw[i][1]]
+  return res
+    
+
+    
+    
+    
+    
+    
+    
+    

naive_DFT.py

@@ -37,7 +37,7 @@ def DFT_naive(inp, out):
       val_im += inp[n] * cos(phi) /INP_L
       
     val_abs = abs_f(val_re, val_im)
-    print("F, val_abs:",f, val_abs)
+    #print("F, val_abs:",f, val_abs)
     out[f] = val_abs
 
 
@@ -148,7 +148,7 @@ def DFT_naive_FP(inp_float, out):
       val_im += inp[n] * phi_cos /INP_L
       
     val_abs = abs_FP(val_re, val_im)
-    print("F, val_abs:",f, val_abs)
+    #print("F, val_abs:",f, val_abs)
     out[f] = val_abs