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-rw-r--r--video/qam.py104
1 files changed, 96 insertions, 8 deletions
diff --git a/video/qam.py b/video/qam.py
index 88096e9..711fb04 100644
--- a/video/qam.py
+++ b/video/qam.py
@@ -1,6 +1,18 @@
from manimlib import *
from scipy import signal as sig
+def square(t, slew_rate=.1):
+ t = t % 1
+
+ if t < .1:
+ return t * 1 / slew_rate
+ elif t < .5 - slew_rate / 2:
+ return 1
+ elif t < .5 + slew_rate / 2:
+ return 1 - (t - (.5 - slew_rate / 2)) * 1 / slew_rate
+ else:
+ return 0
+
class TimeDependentComplexPlane(ComplexPlane):
CONFIG = {
@@ -29,6 +41,9 @@ class TimeDependentComplexPlane(ComplexPlane):
def number_to_point(self, number, time=0):
return self.coords_to_point(number.real, number.imag, time)
+ def point_to_number(self, point, time=0):
+ return point[0] + 1j * point[1]
+
def n2p(self, number, time=0):
return self.number_to_point(number, time)
@@ -65,23 +80,96 @@ class QamModulation(Scene):
CONFIG = {}
def construct(self):
- cplane = TimeDependentComplexPlane()
+ self.camera.frame.reorient(0, 0, 0)
+ # create a complex plane
+ cplane = TimeDependentComplexPlane()
self.play(ShowCreation(cplane))
- self.play(self.camera.frame.animate.move_to(2 * OUT))
- graph_y = cplane.get_inphase_graph(lambda t: 2 * np.cos(2 * t), color=RED)
- graph_x = cplane.get_quadrature_graph(lambda t: 1 * sig.square(4 * t), color=BLUE)
+ # a complex number
+ dot = Dot(cplane.n2p(1 + 2j), color=GREEN)
+
+ number = DecimalNumber()
+
+ number.add_updater(lambda m: m.next_to(dot, RIGHT))
+
+ def update_nums(m):
+ x, y, z = dot.get_center()
+ num = cplane.p2n((x,y))
+ m.set_value(num)
+
+ number.add_updater(update_nums)
+
+ # create and move complex number around
+ self.play(ShowCreation(dot), ShowCreation(number))
+ self.play(dot.animate.move_to(cplane.n2p(-5+3j)), run_time=2)
+ self.play(dot.animate.move_to(cplane.n2p(-4-3j)), run_time=2)
+
+ # move the number according to a time dependend complex function
+ def signal_func(t):
+ real = -2 * np.cos(2 * t)
+ imag = 3 * (square(t / 2) - .5)
+
+ return real + 1j * imag
+
+ signal_func_at_zero = signal_func(0)
- self.play(self.camera.frame.animate.reorient(90, 90, 90))
+ self.play(dot.animate.move_to(cplane.n2p(signal_func_at_zero)), run_time=2)
+
+ def dot_update_func(m, dt):
+ m.move_to(cplane.n2p(signal_func(m.time)))
+ m.time = m.time + dt / 2
+
+ dot.time = 0
+ dot.add_updater(dot_update_func)
+ self.wait(5)
+
+ # get out and show time dependence
+ self.play(self.camera.frame.animate.shift(2 * OUT))
+
+ # show functions
+ graph_y = cplane.get_inphase_graph(lambda t: signal_func(t).real, color=RED)
+ graph_x = cplane.get_quadrature_graph(lambda t: signal_func(t).imag, color=BLUE)
+
+ self.play(self.camera.frame.animate.reorient(-90, 90, 90))
self.play(ShowCreation(graph_x))
self.play(self.camera.frame.animate.reorient(0, 90, 90))
self.play(ShowCreation(graph_y))
- self.play(self.camera.frame.animate.reorient(80, 90, 90))
+ self.play(self.camera.frame.animate.reorient(-100, 90, 90))
+ self.play(self.camera.frame.animate.rotate(40 * DEGREES, axis = UP))
+
+ # create arrow for complex value
+ dot.remove_updater(dot_update_func)
+ self.play(dot.animate.move_to(cplane.n2p(signal_func_at_zero)), run_time=2)
+
+ arr = Arrow(cplane.n2p(0), cplane.n2p(signal_func_at_zero))
+ self.play(ShowCreation(arr))
+
+ def arr_update_func(m, dt):
+ m.set_points_by_ends(
+ cplane.n2p(0, time=m.time),
+ cplane.n2p(signal_func(m.time), time=m.time)
+ )
+ m.time = m.time + dt / 2
+
+ dot.time = 0
+ arr.time = 0
+
+ dot.add_updater(dot_update_func)
+ arr.add_updater(arr_update_func)
+ self.wait(10)
+
+ self.play(*map(FadeOut, (arr, graph_x, graph_y)))
+ self.play(
+ self.camera.frame.animate.rotate(50 * DEGREES, axis = UP),
+ dot.animate.move_to(cplane.n2p(1+1j))
+ )
+ self.play(self.camera.frame.animate.shift(-2 * OUT))
- # arrow = Arrow(
+ dot.remove_updater(dot_update_func)
+ arr.remove_updater(arr_update_func)
# open an interactive IPython shell here
- self.embed()
+ # self.embed()