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 (symbol, nexpr, delta, H, sign, rect, sinc, sincu, n, sin, cos, exp, j, Omega) 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) ]
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, n, k, rect, sinc, sign, sin, cos, exp, dt, j, pi, delta, H) alpha = symbol('alpha') m = symbol('m', integer=True) N = symbol('N', integer=True, positive=True) f0 = symbol('f0') w0 = 2 * pi * f0 sigs = [nexpr('x(n)'), nexpr('x(a * n)'), nexpr('x(n - m)'), nexpr(1), delta(n), delta(n - m), H(n), n * H(n), alpha**-n * H(n), exp(j * 2 * pi * n / N), cos(2 * pi * n / N), sin(2 * pi * n / N)] sigs2 = [n, n**2, 1 / n, rect(n), sinc(n), alpha**-abs(n), sign(n), cos(w0 * n * dt), sin(w0 * n * dt), exp(j * w0 * n * dt)] for sig in sigs: print(':math:`%s \\longleftrightarrow %s`\n' % (sig.latex(), sig(k, N=N).simplify().latex()))