ChTheo/FFT_and_FP_math
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implemented FFT_naive function. It just calculated DFT inside. But DFT should be substituted by FFT function (its only arg -- inp arr. It returns F(k))

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Theodor Chikin
2025-10-08 15:55:22 +03:00
parent 03486b80e0
commit d15f940da6
1 changed files with 46 additions and 8 deletions
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54
naive_DFT.py
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@ -5,7 +5,7 @@ from plotly.subplots import make_subplots
FP_acc = 1e3 FP_acc = 1e3
INP_L = 1000 INP_L = 1024
F_nyquist = INP_L//2 F_nyquist = INP_L//2
@ -22,7 +22,7 @@ def abs_FP(re, im):
return int(sqrt(re*re + im*im)) return int(sqrt(re*re + im*im))
def sqrt_FP(val): def sqrt_FP(val):
print(val) #print(val)
return int(sqrt(val)) return int(sqrt(val))
def DFT_naive(inp, out): def DFT_naive(inp, out):
@ -41,7 +41,7 @@ def DFT_naive(inp, out):
def abs_FP(re, im): def abs_FP(re, im):
# return sqrt(re*re + im*im) # return sqrt(re*re + im*im)
return int(sqrt(re*re + im*im)) return int(sqrt(re*re + im*im)/FP_acc)
trigon_debug = 0 trigon_debug = 0
@ -89,7 +89,7 @@ def sin_FP(phi_fp):
return sin_FP_constrained(phi_fp) return sin_FP_constrained(phi_fp)
sin_05_debug = 1 sin_05_debug = 0
def sin_FP_constrained(phi_fp): def sin_FP_constrained(phi_fp):
phi_trh = pi_FP/16 phi_trh = pi_FP/16
@ -141,7 +141,7 @@ def DFT_naive_FP(inp_float, out):
phi = 2*pi_FP*f*n/INP_L phi = 2*pi_FP*f*n/INP_L
phi_sin = sin_FP(phi) phi_sin = sin_FP(phi)
phi_cos = cos_FP(phi) phi_cos = cos_FP(phi)
print(phi, phi_sin, phi_cos) #print(phi, phi_sin, phi_cos)
val_re += inp[n] * phi_sin /INP_L val_re += inp[n] * phi_sin /INP_L
val_im += inp[n] * phi_cos /INP_L val_im += inp[n] * phi_cos /INP_L
@ -149,21 +149,57 @@ def DFT_naive_FP(inp_float, out):
print("F, val_abs:",f, val_abs) print("F, val_abs:",f, val_abs)
out[f] = val_abs out[f] = val_abs
def FFT_naive(inp, out):
for f in range(len(out)):
val_re = 0
val_im = 0
for n in range(len(inp)):
phi = 2*pi*f*n/INP_L
val_re += inp[n] * sin(phi) /INP_L
val_im += inp[n] * cos(phi) /INP_L
val_abs = abs_f(val_re, val_im)
print("F, val_abs:",f, val_abs)
out[f] = val_abs
def FFT_tester():
inp = [-1 + 0.01*i + sin(2*pi*i/10) + cos(2*pi*i/20) + sin(2*pi*i/250) + sin(2*pi*i/2.001) for i in range(INP_L)]
# inp = [sin(2*pi*i/2.001)for i in range(INP_L)]
out_DFT = [0 for i in range(F_nyquist + 1)]
out_FFT = [0 for val in range(F_nyquist + 1)]
DFT_naive(inp, out_DFT)
FFT_naive(inp, out_FFT)
Fourier_error = []
for a,b in zip(out_FFT, out_DFT):
Fourier_error.append(a - b)
chart = make_subplots(rows=3, cols=1)
chart.add_trace(go.Scatter(x=[i for i in range(len(inp))], y=inp, name="inp", mode="markers+lines"), row=1, col=1)
chart.add_trace(go.Scatter(x=[i for i in range(len(out_DFT))], y=out_DFT, name="out_DFT", mode="markers+lines"), row=2, col=1)
chart.add_trace(go.Scatter(x=[i for i in range(len(out_FFT))], y=out_FFT, name="out_FFT", mode="markers+lines"), row=2, col=1)
chart.add_trace(go.Scatter(x=[i for i in range(len(Fourier_error))], y=Fourier_error, name="error", mode="markers+lines"), row=3, col=1)
chart.show()
def main():
def DFT_tester():
inp = [-1 + 0.01*i + sin(2*pi*i/10) + cos(2*pi*i/20) + sin(2*pi*i/250) + sin(2*pi*i/2.001) for i in range(INP_L)] inp = [-1 + 0.01*i + sin(2*pi*i/10) + cos(2*pi*i/20) + sin(2*pi*i/250) + sin(2*pi*i/2.001) for i in range(INP_L)]
# inp = [sin(2*pi*i/2.001)for i in range(INP_L)] # inp = [sin(2*pi*i/2.001)for i in range(INP_L)]
out_float = [0 for i in range(F_nyquist + 1)] out_float = [0 for i in range(F_nyquist + 1)]
out_FP = [0 for val in out_float] out_FP = [0 for val in out_float]
DFT_naive(inp, out_float) DFT_naive(inp, out_float)
DFT_naive_FP(inp, out_FP) DFT_naive_FP(inp, out_FP)
chart = make_subplots(rows=2, cols=1) FP_error = []
for a,b in zip(out_float, out_FP):
FP_error.append(a - b/FP_acc)
chart = make_subplots(rows=3, cols=1)
chart.add_trace(go.Scatter(x=[i for i in range(len(inp))], y=inp, name="inp", mode="markers+lines"), row=1, col=1) chart.add_trace(go.Scatter(x=[i for i in range(len(inp))], y=inp, name="inp", mode="markers+lines"), row=1, col=1)
chart.add_trace(go.Scatter(x=[i for i in range(len(out_float))], y=out_float, name="out_float", mode="markers+lines"), row=2, col=1) chart.add_trace(go.Scatter(x=[i for i in range(len(out_float))], y=out_float, name="out_float", mode="markers+lines"), row=2, col=1)
chart.add_trace(go.Scatter(x=[i for i in range(len(out_FP))], y=[val/FP_acc for val in out_FP], name="out_FP", mode="markers+lines"), row=2, col=1) chart.add_trace(go.Scatter(x=[i for i in range(len(out_FP))], y=[val/FP_acc for val in out_FP], name="out_FP", mode="markers+lines"), row=2, col=1)
chart.add_trace(go.Scatter(x=[i for i in range(len(out_FP))], y=FP_error, name="FP_error", mode="markers+lines"), row=3, col=1)
chart.show() chart.show()
@ -196,4 +232,6 @@ def sin_tester():
if __name__ == "__main__": if __name__ == "__main__":
#main() #main()
sin_tester() # DFT_tester()
FFT_tester()
#sin_tester()