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