78 lines
2.7 KiB
Python
78 lines
2.7 KiB
Python
import numpy as np
|
|
import sympy as sp
|
|
import matplotlib.pyplot as plt
|
|
|
|
t = sp.symbols('t')
|
|
T = 4 # Perioda funkce
|
|
to = 1/2
|
|
omega = 2 * sp.pi / T
|
|
|
|
f = 1 + sp.exp(-t)
|
|
|
|
def fc(x):
|
|
return 1 + sp.exp(-x)
|
|
|
|
def get_tabulka():
|
|
print(f"a_0 = {a_0: .2f}")
|
|
print(f"c_0 = {((1 / T) * sp.integrate(f, (t, 0, to))):.2f}")
|
|
print(f"A_0 = {(a_0 / 2):.2f}")
|
|
|
|
pa_coeffs = [((2 / T) * sp.integrate(f * sp.cos(n * omega * t), (t, 0, to)).evalf(), n) for n in range(1, n_max + 1)]
|
|
pb_coeffs = [((2 / T) * sp.integrate(f * sp.sin(n * omega * t), (t, 0, to)).evalf(), n) for n in range(1, n_max + 1)]
|
|
pc_coeffs = [((1 / T) * sp.integrate(f * sp.exp(1j * n * omega * t), (t, 0, to)).evalf(), n) for n in range(1, n_max + 1)]
|
|
for a, b, c in zip(pa_coeffs, pb_coeffs, pc_coeffs):
|
|
print(f"n= {a[1]}")
|
|
print(f"a= {a[0]:.2f}")
|
|
print(f"b= {b[0]:.2f}")
|
|
print(f"A= {(a[0]**2+b[0]**2)**(1/2):.2f}")
|
|
print(f"c_n= {np.absolute(c[0]):.2f}")
|
|
print(f"phi= {np.angle(float(a[0])+float(b[0])*1j, deg=True):.2f}")
|
|
|
|
def calculate_coefficients(n_max):
|
|
a_0 = (2 / T) * sp.integrate(f, (t, 0, to))
|
|
a_coeffs = [((2 / T) * sp.integrate(f * sp.cos(n * omega * t), (t, 0, to)), n) for n in range(1, n_max + 1)]
|
|
b_coeffs = [((2 / T) * sp.integrate(f * sp.sin(n * omega * t), (t, 0, to)), n) for n in range(1, n_max + 1)]
|
|
return a_0, a_coeffs, b_coeffs
|
|
|
|
def cosinus_series(x, a_0, a_coeffs):
|
|
cosinus = a_0 / 2
|
|
for a_n, n in a_coeffs:
|
|
cosinus += a_n * sp.cos(omega * n * x)
|
|
return cosinus
|
|
|
|
def sinus_series(x, b_coeffs):
|
|
sinus = 0
|
|
for b_n, n in b_coeffs:
|
|
sinus += b_n * sp.sin(omega * n * x)
|
|
return sinus
|
|
|
|
# Předpočítat koeficienty
|
|
n_maxs = [5, 10, 20, 30]
|
|
|
|
for n_max in n_maxs:
|
|
a_0, a_coeffs, b_coeffs = calculate_coefficients(n_max)
|
|
|
|
# Definujte interval pro vykreslení
|
|
t_values = np.linspace(-4, 6, 200)
|
|
|
|
cosinus = [cosinus_series(x, a_0, a_coeffs) for x in t_values]
|
|
cosinus_scaled = [2 * y for y in cosinus]
|
|
original = [fc(-x % (2*2)) if (-x % (2*2)) < to else fc(x % (2*2)) if (x % (2*2)) < to else 0 for x in t_values]
|
|
plt.plot(t_values, original, label="f(t)")
|
|
plt.plot(t_values, cosinus_scaled, label="CŘ")
|
|
plt.title(f"n={n_max}")
|
|
plt.legend()
|
|
plt.xlabel("t")
|
|
plt.ylabel("f(t)")
|
|
plt.show()
|
|
|
|
sinus = [sinus_series(x, b_coeffs) for x in t_values]
|
|
sinus_scaled = [2 * y for y in sinus]
|
|
original = [-fc(-x % (2*2)) if (-x % (2*2)) < to else fc(x % (2*2)) if (x % (2*2)) < to else 0 for x in t_values]
|
|
plt.plot(t_values, original, label="f(t)")
|
|
plt.plot(t_values, sinus_scaled, label="SŘ")
|
|
plt.title(f"n={n_max}")
|
|
plt.legend()
|
|
plt.xlabel("t")
|
|
plt.ylabel("f(t)")
|
|
plt.show()
|