from base.sigadd import *
n1 = np.arange(-1, 3)
x1 = np.array([-4, 0, 2, 8])
n2 = np.arange(-1, 4)
x2 = np.array([-1, 1, 3, 7, 5])
n3 = np.arange(-1, 1)
x3 = np.array([7, 2])
# x3 = np.array([2, 7])
xtilde1 = periodic(x1, 10)
ntilde1 = np.arange(np.amin(n1), np.amin(n1) + len(n1) * 10)
xtilde2 = periodic(x2, 8)
ntilde2 = np.arange(np.amin(n2), np.amin(n2) + len(n2) * 8)
xtilde3 = periodic(x3, 20)
ntilde3 = np.arange(np.amin(n3), np.amin(n3) + len(n3) * 20)
xtilde, ntilde = sigadd(xtilde1, ntilde1, xtilde2, ntilde2)
xtilde, ntilde = sigadd(xtilde, ntilde, xtilde3, ntilde3)
plt.bar(ntilde, xtilde, width=0.1)
plt.xticks(range(np.amin(ntilde), np.amax(ntilde) + 1))
plt.xlabel('ntilde')
plt.ylabel('xtilde')
plt.title('periodic')
plt.show()
import matplotlib.pyplot as plt
import numpy as np
from base.stepseg import *
from base.sigshift import *
from base.sigadd import *
begin = -5
end = 25
step, m = stepseg(0, begin, end)
step_minus_5, m_minus_5 = sigshift(step, m, 5)
step_minus_10, m_minus_10 = sigshift(step, m, 10)
step_minus_15, m_minus_15 = sigshift(step, m, 15)
x, n = sigadd(10 * step, m, -5 * step_minus_5, m_minus_5)
x, n = sigadd(x, n, -10 * step_minus_10, m_minus_10)
x, n = sigadd(x, n, 5 * step_minus_15, m_minus_15)
plt.bar(n,x, width = 0.1)
plt.xticks(range(begin - 1, end + 1))
plt.xlim(begin - 1, end + 1)
plt.xlabel('n')
plt.ylabel('x')
plt.title('x(n)')
plt.show()
import matplotlib.pyplot as plt
import numpy as np
from base.sigadd import *
from base.sigshift import *
m_begin = -3
m_end = 3
x = np.array([2, 4, -3, 1, -5, 4, 7])
m = np.arange(m_begin, m_end + 1)
x_minus_3, m_minus_3 = sigshift(x, m, 3)
x_minus_3 = np.concatenate((x[0:3], x_minus_3))
m_minus_3 = np.concatenate((m[0:3], m_minus_3))
x_plus_4, m_plus_4 = sigshift(x, m, -4)
x1, n1 = sigadd(2 * x_minus_3, m_minus_3, 3 * x_plus_4, m_plus_4)
x1, n1 = sigadd(x1, n1, -1 * x, m)
plt.bar(n1, x1, width=0.1)
plt.xticks(range(np.amin(n1) - 1, np.amax(n1) + 1))
plt.xlabel('n1')
plt.ylabel('x1')
plt.title('x1(n1)')
plt.show()
import matplotlib.pyplot as plt
import numpy as np
from base.impseq import *
from base.sigshift import *
from base.sigadd import *
begin = -20
end = 20
delta, m = impseg(0, begin, end)
delta_plus_2, m_plus_2 = sigshift(delta, m, -2)
delta_plus_3, m_plus_3 = sigshift(delta, m, -3)
x1, nx1 = sigadd(delta_plus_2, m_plus_2, -1 * delta, m)
x1 = np.exp(0.2) * x1
x1, nx1 = sigadd(2 * delta_plus_3, m_plus_3, -1 * x1, nx1)
plt.bar(nx1, x1, width=0.1)
plt.xticks(range(begin, end))
plt.xlim(begin, end + 1)
plt.xlabel('nx1')
plt.ylabel('x1')
plt.title('x1(nx1)')
plt.show()
delta, n_delta = impseg(0, 0, 5)
delta = delta.astype('float64')
# left sided sequence
b1 = np.array([0, 2, 3])
a1 = np.array([1])
xb1 = signal.lfilter(b1, a1, delta, axis=0)
xb1 = np.flip(xb1)
n1 = -np.flip(n_delta)
# right sided sequence
b2 = np.array([1, -2, -3])
a2 = np.array([1])
xb2 = signal.lfilter(b2, a2, delta)
n2 = n_delta
xa1, na1 = sigadd(xb1, n1, xb2, n2)
print(xa1)
# x, nx
# plt.subplot(1, 2, 1)
# plt.bar(nx, x, width = 0.01)
# plt.xlabel('nx')
# plt.ylabel('x')
# plt.title('x(nx)')
# delta, n_delta
# plt.subplot(1, 2, 2)
# plt.bar(n_delta, delta, width = 0.01)
# plt.xlabel('n_delta')
# plt.ylabel('delta')
# plt.title('delta(n_delta)')
# plt.bar(m_minus_3,delta_minus_3, width = 0.1)
# plt.xticks(range(np.amin(m_minus_3) - 1, np.amax(m_minus_3) + 1))
# plt.xlabel('m_minus_3')
# plt.ylabel('delta_minus_3')
# plt.title('delta_minus_3')
# plt.subplot(2, 4, 4)
# plt.bar(m_minus_7,delta_minus_7, width = 0.1)
# plt.xticks(range(np.amin(m_minus_7) - 1, np.amax(m_minus_7) + 1))
# plt.xlabel('m_minus_7')
# plt.ylabel('delta_minus_7')
# plt.title('delta_minus_7')
delta = delta * 2
delta_plus_2 = delta_plus_2 * 3
delta_minus_3 = (-1) * delta_minus_3
delta_minus_7 = 5 * delta_minus_7
x, n = sigadd(delta_plus_2, m_plus_2, delta, m)
x, n = sigadd(x, n, delta_minus_3, m_minus_3)
x, n = sigadd(x, n, delta_minus_7, m_minus_7)
# plt.subplot(2, 4, 5)
plt.bar(n, x, width=0.1)
plt.xticks(range(np.amin(m) - 1, np.amax(m) + 1))
plt.xlim(np.amin(m) - 1, np.amax(m) + 1)
plt.xlabel('n')
plt.ylabel('x')
plt.title('x(n)')
plt.show()
import matplotlib.pyplot as plt
import numpy as np
from base.stepseg import *
from base.sigshift import *
from base.sigadd import *
from base.sigmult import *
begin = -25
end = 20
step, m = stepseg(0, begin, end + 20)
step_minus_10, m_minus_10 = sigshift(step, m, 10)
step_plus_20, m_plus_20 = sigshift(step, m, -20)
u, n = sigadd(step_plus_20, m_plus_20, -1 * step_minus_10, m_minus_10)
h = np.exp(0.1 * n)
x, n = sigmult(h, n, u, n)
# u, n
plt.subplot(2, 2, 1)
plt.bar(n, u, width=0.1)
# plt.xticks(range(begin, end))
plt.xlim(begin, end)
plt.ylim(0, 2)
plt.xlabel('n')
plt.ylabel('u')
plt.title('u(n)')
# h, n
plt.subplot(2, 2, 2)
plt.bar(n, h, width=0.1)
import matplotlib.pyplot as plt
import numpy as np
from base.sigshift import *
from base.sigadd import *
num1 = 100000
n1 = np.arange(0, num1)
x1 = 2 * np.random.rand(num1)
num2 = 10000
n2 = np.arange(0, num2)
x2 = np.random.normal(loc=10, scale=10, size=num2)
x11, n11 = sigshift(x1, n1, 1)
x3, n3 = sigadd(x1, n1, x11, n11)
num4 = 10000
n4 = np.arange(0, num4)
y1 = np.random.uniform(low=-0.5, high=0.5, size=num1)
y2 = np.random.uniform(low=-0.5, high=0.5, size=num1)
y3 = np.random.uniform(low=-0.5, high=0.5, size=num1)
y4 = np.random.uniform(low=-0.5, high=0.5, size=num1)
x4 = y1 + y2 + y3 + y4
# x1, n1
plt.subplot(2, 2, 1)
plt.hist(x1, bins=100)
plt.title('x1 histogram')
# x2, n2
plt.subplot(2, 2, 2)
import matplotlib.pyplot as plt
import numpy as np
from base.periodic import *
from base.sigadd import *
n = np.arange(0, 25)
x1 = np.arange(1, 4)
x2 = np.arange(1, 5)
P = 6
xtilde1 = periodic(x1, 9)
ntilde1 = np.arange(0, len(xtilde1))
xtilde2 = periodic(x2, 7)
ntilde2 = np.arange(0, len(xtilde2))
xtilde, ntilde = sigadd(xtilde1, ntilde1, xtilde2, ntilde2)
plt.bar(ntilde, xtilde, width = 0.1)
# plt.xlim(begin, end)
plt.xlabel('ntilde')
plt.ylabel('xtilde')
plt.title('periodic')
plt.show()