var7

Задание 1:

Определим количество точек N. Нужно, чтобы частота целое количество раз умещалось в периоде. Так как f_1 = 300, N = 2400 / 300 = 8.0

Задание 2:

s1 = (cos(600*pi*t + 7*pi/4))

s2 = (cos(1200*pi*t + 0))

s1 + s2 = (cos(600*pi*t + 7*pi/4)) + (cos(1200*pi*t + 0)) Отсчеты максимумов:

x1 = 300 * 8 / 2400 = 1

x1 = 600 * 8 / 2400 = 2

Амплитуды максимумов: A1: 4.0*T, A2: 4.0*T

Re = A*cos(phi)

Im = A*sin(phi)

Задание 3:

s1 + s2 = cos(600 * pi * t + 7*pi/4 + cos(1200 * pi * t + 0) t->nT

s1 + s2 = cos(600 * pi * (1 / 2400) * n+ 7*pi/4) + cos(1200 * pi * (1 / 2400) * n+ 0) sin(0.25*pi*n + pi/4)

s1 + s2 = sin(0.25*pi*n + pi/4) + cos(pi*n/2)

Получены точки: [sqrt(2)/2 + 1, 1, -1 + sin(0.75*pi), 0, 1 - sqrt(2)/2, -1, -1 + sin(1.75*pi), 0]

Задание 4:

ΩT = 2 * pi / N = pi/4

W = e^(i * pi/4) - оператор единичного поворота вектора на угол pi/4. S(mΩ) = Σ(0-7) sin(0.25*pi*n + pi/4) + cos(pi*n/2) * W ^ -nm (sin(0.25*pi*n + pi/4), cos(pi*n/2))

m = 0: Расчет:

n = 0, W^0 n = 1, W^0 n = 2, W^0 n = 3, W^0 n = 4, W^0 n = 5, W^0 n = 6, W^0 n = 7, W^0

S(0*Ω) = sqrt(2)/2 + 1 + 1 + -1 + sin(0.75*pi) + 0 + 1 - sqrt(2)/2 + -1 + -1 + sin(1.75*pi) + 0 = sin(1.75*pi) + sin(0.75*pi)

m = 1: Расчет:

n = 0, W^0 n = 1, W^1 n = 2, W^2 n = 3, W^3 n = 4, W^4 n = 5, W^5 n = 6, W^6 n = 7, W^7

S(1*Ω) = sqrt(2)/2 + 1 + exp(-I*pi/4) + I*(1 - sin(0.75*pi)) + 0 + -1 + sqrt(2)/2 + -(-1)**(3/4) + I*(-1 + sin(1.75*pi)) + 0 = sqrt(2)*(2 - I) + I*sin(1.75*pi) - I*sin(0.75*pi)

m = 2: Расчет:

n = 0, W^0 n = 1, W^2 n = 2, W^4 n = 3, W^6 n = 4, W^0 n = 5, W^2 n = 6, W^4 n = 7, W^6

S(2*Ω) = sqrt(2)/2 + 1 + -I + 1 - sin(0.75*pi) + 0 + 1 - sqrt(2)/2 + I + 1 - sin(1.75*pi) + 0 = -sin(0.75*pi) - sin(1.75*pi) + 4

m = 3: Расчет:

n = 0, W^0 n = 1, W^3 n = 2, W^6 n = 3, W^1 n = 4, W^4 n = 5, W^7 n = 6, W^2 n = 7, W^5

S(3*Ω) = sqrt(2)/2 + 1 + exp(-3*I*pi/4) + I*(-1 + sin(0.75*pi)) + 0 + -1 + sqrt(2)/2 + -(-1)**(1/4) + I*(1 - sin(1.75*pi)) + 0 = I*(-sqrt(2) - sin(1.75*pi) + sin(0.75*pi))

m = 4: Расчет:

n = 0, W^0 n = 1, W^4 n = 2, W^0 n = 3, W^4 n = 4, W^0 n = 5, W^4 n = 6, W^0 n = 7, W^4

S(4*Ω) = sqrt(2)/2 + 1 + -1 + -1 + sin(0.75*pi) + 0 + 1 - sqrt(2)/2 + 1 + -1 + sin(1.75*pi) + 0 = sin(1.75*pi) + sin(0.75*pi)

m = 5: Расчет:

n = 0, W^0 n = 1, W^5 n = 2, W^2 n = 3, W^7 n = 4, W^4 n = 5, W^1 n = 6, W^6 n = 7, W^3

S(5*Ω) = sqrt(2)/2 + 1 + exp(3*I*pi/4) + I*(1 - sin(0.75*pi)) + 0 + -1 + sqrt(2)/2 + (-1)**(3/4) + I*(-1 + sin(1.75*pi)) + 0 = I*(-sin(0.75*pi) + sin(1.75*pi) + sqrt(2))

m = 6: Расчет:

n = 0, W^0 n = 1, W^6 n = 2, W^4 n = 3, W^2 n = 4, W^0 n = 5, W^6 n = 6, W^4 n = 7, W^2

S(6*Ω) = sqrt(2)/2 + 1 + I + 1 - sin(0.75*pi) + 0 + 1 - sqrt(2)/2 + -I + 1 - sin(1.75*pi) + 0 = -sin(0.75*pi) - sin(1.75*pi) + 4

m = 7: Расчет:

n = 0, W^0 n = 1, W^7 n = 2, W^6 n = 3, W^5 n = 4, W^4 n = 5, W^3 n = 6, W^2 n = 7, W^1

S(7*Ω) = sqrt(2)/2 + 1 + exp(I*pi/4) + I*(-1 + sin(0.75*pi)) + 0 + -1 + sqrt(2)/2 + (-1)**(1/4) + I*(1 - sin(1.75*pi)) + 0 = I*sin(0.75*pi) - I*sin(1.75*pi) + sqrt(2)*(2 + I)

Получены данные: [sin(1.75*pi) + sin(0.75*pi), sqrt(2)*(2 - I) + I*sin(1.75*pi) - I*sin(0.75*pi), -sin(0.75*pi) - sin(1

Задание 5:

S(nT) = 1 / N * S(m * Ω * W ^ -nm n = 0:

Расчет: m= 0, W^0 m= 1, W^0 m= 2, W^0 m= 3, W^0 m= 4, W^0 m= 5, W^0 m= 6, W^0 m= 7, W^0

0T = (sin(1.75*pi) + sin(0.75*pi)+sqrt(2)*(2 - I) + I*sin(1.75*pi) - I*sin(0.75*pi)+-sin(0.75*pi) - sin(1.75*pi) + 4+I*(-sqrt(2) - sin(1.75*pi) + sin(0.75*pi))+sin(1.75*pi) + sin(0.75*pi)+I*(-sin(0.75*pi) + sin(1.75*pi) + sqrt(2))+-sin(0.75*pi) - sin(1.75*pi) + 4+I*sin(0.75*pi) - I*sin(1.75*pi) + sqrt(2)*(2 + I) ) / 8 = 0.5*sqrt(2) + 1.0

n = 1: Расчет: m= 0, W^0 m= 1, W^1 m= 2, W^2 m= 3, W^3 m= 4, W^4 m= 5, W^5 m= 6, W^6 m= 7, W^7

1T = (sin(1.75*pi) + sin(0.75*pi)+(-1)**(1/4)*(sqrt(2)*(2 - I) + I*sin(1.75*pi) - I*sin(0.75*pi))+I*(-sin(0.75*pi) - sin(1.75*pi) + 4)+(-1)**(1/4)*(-sin(0.75*pi) + sin(1.75*pi) + sqrt(2))+-sin(0.75*pi) - sin(1.75*pi)+(-1)**(3/4)*(-sqrt(2) - sin(1.75*pi) + sin(0.75*pi))+I*(-4 + sin(1.75*pi) + sin(0.75*pi))+(-1)**(3/4)*(-sqrt(2)*(2 + I) + I*sin(1.75*pi) - I*sin(0.75*pi)) ) / 8 = 1.00000000000000

n = 2: Расчет: m= 0, W^0 m= 1, W^2 m= 2, W^4 m= 3, W^6 m= 4, W^8 m= 5, W^10 m= 6, W^12 m= 7, W^14

2T = (sin(1.75*pi) + sin(0.75*pi)+-sin(1.75*pi) + sin(0.75*pi) + sqrt(2)*(1 + 2*I)+-4 + sin(1.75*pi) + sin(0.75*pi)+-sqrt(2) - sin(1.75*pi) + sin(0.75*pi)+sin(1.75*pi) + sin(0.75*pi)+-sqrt(2) - sin(1.75*pi) + sin(0.75*pi)+-4 + sin(1.75*pi) + sin(0.75*pi)+-sin(1.75*pi) + sin(0.75*pi) + sqrt(2)*(1 - 2*I) ) / 8 = -1.0 + 1.0*sin(0.75*pi)

n = 3: Расчет: m= 0, W^0 m= 1, W^3 m= 2, W^6 m= 3, W^9 m= 4, W^12 m= 5, W^15 m= 6, W^18 m= 7, W^21

3T = (sin(1.75*pi) + sin(0.75*pi)+(-1)**(3/4)*(sqrt(2)*(2 - I) + I*sin(1.75*pi) - I*sin(0.75*pi))+I*(-4 + sin(1.75*pi) + sin(0.75*pi))+(-1)**(3/4)*(-sqrt(2) - sin(1.75*pi) + sin(0.75*pi))+-sin(0.75*pi) - sin(1.75*pi)+(-1)**(1/4)*(-sin(0.75*pi) + sin(1.75*pi) + sqrt(2))+I*(-sin(0.75*pi) - sin(1.75*pi) + 4)+(-1)**(1/4)*(-sqrt(2)*(2 + I) + I*sin(1.75*pi) - I*sin(0.75*pi)) ) / 8 = 0

n = 4: Расчет: m= 0, W^0 m= 1, W^4 m= 2, W^8 m= 3, W^12 m= 4, W^16 m= 5, W^20 m= 6, W^24 m= 7, W^28

4T = (sin(1.75*pi) + sin(0.75*pi)+I*sin(0.75*pi) - I*sin(1.75*pi) + sqrt(2)*(-2 + I)+-sin(0.75*pi) - sin(1.75*pi) + 4+I*(-sin(0.75*pi) + sin(1.75*pi) + sqrt(2))+sin(1.75*pi) + sin(0.75*pi)+I*(-sqrt(2) - sin(1.75*pi) + sin(0.75*pi))+-sin(0.75*pi) - sin(1.75*pi) + 4+-sqrt(2)*(2 + I) + I*sin(1.75*pi) - I*sin(0.75*pi) ) / 8 = 1.0 - 0.5*sqrt(2)

n = 5: Расчет: m= 0, W^0 m= 1, W^5 m= 2, W^10 m= 3, W^15 m= 4, W^20 m= 5, W^25 m= 6, W^30 m= 7, W^35

5T = (sin(1.75*pi) + sin(0.75*pi)+(-1)**(1/4)*(I*sin(0.75*pi) - I*sin(1.75*pi) - sqrt(2)*(2 - I))+I*(-sin(0.75*pi) - sin(1.75*pi) + 4)+(-1)**(1/4)*(-sqrt(2) - sin(1.75*pi)

+sin(0.75*pi))+-sin(0.75*pi) - sin(1.75*pi)+(-1)**(3/4)*(-sin(0.75*pi) + sin(1.75*pi) + sqrt(2))+I*(-4 + sin(1.75*pi) + sin(0.75*pi))+(-1)**(3/4)*(I*sin(0.75*pi) - I*sin(1.75*pi)

+sqrt(2)*(2 + I)) ) / 8 = -1.00000000000000

n = 6: Расчет: m= 0, W^0 m= 1, W^6 m= 2, W^12 m= 3, W^18 m= 4, W^24 m= 5, W^30 m= 6, W^36 m= 7, W^42

6T = (sin(1.75*pi) + sin(0.75*pi)+-sin(0.75*pi) + sin(1.75*pi) - sqrt(2)*(1 + 2*I)+-4 + sin(1.75*pi) + sin(0.75*pi)+-sin(0.75*pi) + sin(1.75*pi) + sqrt(2)+sin(1.75*pi) + sin(0.75*pi)+-sin(0.75*pi) + sin(1.75*pi) + sqrt(2)+-4 + sin(1.75*pi) + sin(0.75*pi)+-sin(0.75*pi) + sin(1.75*pi) + sqrt(2)*(-1 + 2*I) ) / 8 = -1.0 + 1.0*sin(1.75*pi)

n = 7: Расчет: m= 0, W^0 m= 1, W^7 m= 2, W^14 m= 3, W^21 m= 4, W^28 m= 5, W^35 m= 6, W^42 m= 7, W^49

7T = (sin(1.75*pi) + sin(0.75*pi)+(-1)**(3/4)*(I*sin(0.75*pi) - I*sin(1.75*pi) - sqrt(2)*(2 - I))+I*(-4 + sin(1.75*pi) + sin(0.75*pi))+(-1)**(3/4)*(-sin(0.75*pi) + sin(1.75*pi) + sqrt(2))+-sin(0.75*pi) - sin(1.75*pi)+(-1)**(1/4)*(-sqrt(2) - sin(1.75*pi) + sin(0.75*pi))+I*(-sin(0.75*pi) - sin(1.75*pi) + 4)+(-1)**(1/4)*(I*sin(0.75*pi) - I*sin(1.75*pi) + sqrt(2)*(2 + I)) ) / 8 = 0

Полученные итоговые данные: [1.71, 1.00000000000000, -0.29, 0, 0.29, -1.00000000000000, -1.71, 0] Полученная кривая:

[0.5*sqrt(2) + 1.0, 1.00000000000000, -1.0 + 1.0*sin(0.75*pi), 0, 1.0 - 0.5*sqrt(2), -1.00000000000000, -1.0 + 1.

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