from lcapy import (symbol, texpr, cos, sin, exp,
expr, pi, rect, sinc, tri, trap, delta, sign, H, j, t, f)
alpha = symbol('alpha')
t0 = symbol('t0')
f0 = symbol('f0')
w0 = 2 * pi * f0
sigs = [texpr('x(t)'), texpr('x(a * t)'), texpr('x(t - tau)'),
cos(w0 * t), sin(w0 * t), exp(j * w0 * t),
texpr(1), t, t**2, 1 / t, delta(t), delta(t - t0),
H(t), t * H(t), sign(t),
rect(t), sinc(t), tri(t), trap(t, alpha),
exp(-abs(t)), exp(-t) * H(t)]
for sig in sigs:
print(':math:`%s \\longleftrightarrow %s`\n' %
(sig.latex(), sig(f).latex()))
from lcapy import delta
from lcapy.discretetime import n, dt
from matplotlib.pyplot import savefig
x = delta(n) + delta(n - 2)
x.DTFT().subs(dt, 1).plot(figsize=(6, 3))
savefig('dt1-DTFT-plot1.png', bbox_inches='tight')
alpha = symbol('alpha')
m = symbol('m', integer=True)
W0 = symbol('Omega_0')
No = symbol('N_o', odd=True)
Ne = symbol('N_e', even=True)
K = symbol('K')
sigs = [
nexpr('x(n)'),
nexpr('x(a * n)'),
nexpr('x(n - m)'),
cos(W0 * n),
sin(W0 * n),
exp(j * W0 * n),
nexpr(1),
delta(n),
delta(n - m),
H(n), n * H(n),
sign(n), alpha**-n * H(n),
rect(n),
rect(n / No),
rect(n / Ne),
sinc(n),
sinc(K * n),
sinc(K * n)**2,
sincu(K * n)
]
for sig in sigs:
print(':math:`%s \\longleftrightarrow %s`\n' %
(sig.latex(), sig(Omega).latex()))
from lcapy import symbol, nexpr, delta, cos, sin, exp, H, n, dt, pi, j, z
alpha = symbol('alpha')
p = symbol('p')
a = symbol('a')
f0 = symbol('f0')
w0 = 2 * pi * f0
sigs = [nexpr('x(n)'), nexpr('x(n - m)'),
cos(w0 * n * dt), sin(w0 * n * dt), exp(j * w0 * n * dt),
nexpr(1), delta(n), delta(n - p), a**n, a**-n, n * a**n, n * a**-n,
H(n), exp(-n * dt) * H(n)]
for sig in sigs:
print(':math:`%s \\longleftrightarrow %s`\n' %
(sig.latex(), sig(z).latex()))
from lcapy import (symbol, nexpr, cos, sin, exp, j, sinc,
rect, sincu, n, dt, delta, sign, H, pi, f)
alpha = symbol('alpha')
m = symbol('m', integer=True)
f0 = symbol('f0')
w0 = 2 * pi * f0
No = symbol('N_o', odd=True)
Ne = symbol('N_e', even=True)
K = symbol('K')
sigs = [nexpr('x(n)'), nexpr('x(a * n)'), nexpr('x(n - m)'),
cos(w0 * n * dt), sin(w0 * n * dt), exp(j * w0 * n * dt),
nexpr(1), delta(n), delta(n - m),
H(n), n * H(n), sign(n),
alpha**-n * H(n), rect(n), rect(n / No), rect(n / Ne),
sinc(n), sinc(K * n), sinc(K * n)**2, sincu(K * n)]
for sig in sigs:
print(':math:`%s \\longleftrightarrow %s`\n' %
(sig.latex(), sig(f).latex()))