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Uncertainty progress
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Grant Sanderson
parent
321a5ccc1e
commit
36a4aacdf9
2 changed files with 131 additions and 11 deletions
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@ -45,7 +45,7 @@ def get_fourier_graph(
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# T = time_range/n_samples
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time_range = float(t_max - t_min)
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time_step_size = time_range/n_samples
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time_samples = time_func(np.linspace(t_min, t_max, n_samples))
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time_samples = np.vectorize(time_func)(np.linspace(t_min, t_max, n_samples))
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fft_output = np.fft.fft(time_samples)
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frequencies = np.linspace(0.0, n_samples/(2.0*time_range), n_samples//2)
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# #Cycles per second of fouier_samples[1]
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@ -1685,9 +1685,8 @@ class MentionDopplerRadar(TeacherStudentsScene):
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class IntroduceDopplerRadar(Scene):
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def construct(self):
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self.setup_axes()
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# self.measure_distance_with_time()
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self.measure_distance_with_time()
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self.show_frequency_shift()
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self.shift_time_graph()
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self.show_frequency_shift_in_fourier()
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def setup_axes(self):
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@ -1761,8 +1760,9 @@ class IntroduceDopplerRadar(Scene):
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randy_look_at = ContinualUpdateFromFunc(
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randy, lambda pi : pi.look_at(pulse.mobject)
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)
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axes_anim = ContinualAnimation(axes)
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self.add(randy_look_at, ContinualAnimation(axes), graph_draw)
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self.add(randy_look_at, axes_anim, graph_draw)
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self.wait(0.5)
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self.add(pulse)
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self.play(
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@ -1784,7 +1784,8 @@ class IntroduceDopplerRadar(Scene):
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)
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self.wait()
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self.remove(graph_draw, pulse, randy_look_at)
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self.remove(graph_draw, pulse, randy_look_at, axes_anim)
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self.add(axes)
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self.play(LaggedStart(FadeOut, VGroup(
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sum_graph, randy,
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pulse_graph.arrow, pulse_graph.label,
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@ -1854,25 +1855,144 @@ class IntroduceDopplerRadar(Scene):
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self.wait()
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self.remove(graph_draw, pulse, plane_flight)
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pulse_graph.set_stroke(width = 0)
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echo_graph.set_stroke(width = 0)
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self.time_graph_group = VGroup(
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axes, pulse_brace, pulse_text,
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echo_brace, echo_text, echo_subtext,
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sum_graph
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pulse_graph, echo_graph, sum_graph,
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)
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self.set_variables_as_attrs(*self.time_graph_group)
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def show_frequency_shift_in_fourier(self):
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sum_graph = self.sum_graph
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pulse_graph = self.pulse_graph
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pulse_label = VGroup(self.pulse_brace, self.pulse_text)
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echo_graph = self.echo_graph
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echo_label = VGroup(
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self.echo_brace, self.echo_text, self.echo_subtext
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)
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#Setup all fourier graph stuff
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f_max = 0.02
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frequency_axes = Axes(
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x_min = 0, x_max = 20,
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x_axis_config = {"unit_size" : 0.5},
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y_min = -f_max, y_max = f_max,
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y_axis_config = {
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"unit_size" : 50,
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"tick_frequency" : 0.01,
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},
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)
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frequency_axes.move_to(self.axes, LEFT)
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frequency_axes.to_edge(DOWN)
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frequency_label = TextMobject("Frequency")
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frequency_label.next_to(
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frequency_axes.x_axis.get_right(), UP,
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)
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frequency_label.to_edge(RIGHT)
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frequency_axes.add(frequency_label)
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for graph in pulse_graph, echo_graph, sum_graph:
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graph.fourier_transform = get_fourier_graph(
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frequency_axes, graph.underlying_function,
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frequency_axes.x_min, 25,
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complex_to_real_func = abs,
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)
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#Braces labeling F.T.
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original_fourier_brace = Brace(
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Line(
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frequency_axes.coords_to_point(7, 0.9*f_max),
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frequency_axes.coords_to_point(9, 0.9*f_max),
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),
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UP,
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).highlight(BLUE)
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echo_fourier_brace = Brace(
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Line(
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frequency_axes.coords_to_point(14, 0.4*f_max),
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frequency_axes.coords_to_point(18, 0.4*f_max),
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),
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UP,
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).highlight(YELLOW)
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# braces = [original_fourier_brace, echo_fourier_brace]
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# words = ["original signal", "echo"]
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# for brace, word in zip(braces, words):
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# brace.add(brace.get_text("F.T. of \\\\ %s"%word))
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fourier_label = TexMobject("||\\text{Fourier transform}||")
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# fourier_label.next_to(sum_graph.fourier_transform, UP, MED_LARGE_BUFF)
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fourier_label.next_to(frequency_axes.y_axis, UP, buff = SMALL_BUFF)
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fourier_label.shift_onto_screen()
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fourier_label.highlight(RED)
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#v_lines
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v_line = DashedLine(
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frequency_axes.coords_to_point(8, 0),
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frequency_axes.coords_to_point(8, 1.2*f_max),
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color = YELLOW,
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dashed_segment_length = 0.025,
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)
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v_line_pair = VGroup(*[
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v_line.copy().shift(u*0.6*RIGHT)
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for u in -1, 1
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])
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v_line = VGroup(v_line)
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double_arrow = DoubleArrow(
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frequency_axes.coords_to_point(8, 0.007),
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frequency_axes.coords_to_point(16, 0.007),
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buff = 0,
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color = WHITE
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)
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self.pulse_echo_graph = sum_graph
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def shift_time_graph(self):
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self.play(
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self.time_graph_group.to_edge, UP,
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ApplyMethod(
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self.dish.shift, 2*UP,
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remover = True
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)
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),
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FadeIn(frequency_axes)
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)
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self.wait()
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self.play(
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FadeOut(sum_graph),
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FadeOut(echo_label),
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pulse_graph.set_stroke, {"width" : 3},
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)
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self.play(
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ReplacementTransform(
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pulse_label[0].copy(),
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original_fourier_brace
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),
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ShowCreation(pulse_graph.fourier_transform)
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)
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self.play(Write(fourier_label))
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self.wait()
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self.play(ShowCreation(v_line))
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self.wait()
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self.play(ReplacementTransform(v_line, v_line_pair))
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self.wait()
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self.play(FadeOut(v_line_pair))
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self.wait()
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self.play(
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FadeOut(pulse_graph),
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FadeIn(sum_graph),
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ReplacementTransform(
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pulse_graph.fourier_transform,
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sum_graph.fourier_transform
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)
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)
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self.play(FadeIn(echo_label))
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self.play(ReplacementTransform(
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echo_label[0].copy(),
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echo_fourier_brace,
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))
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self.wait(2)
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self.play(GrowFromCenter(double_arrow))
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self.wait()
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def show_frequency_shift_in_fourier(self):
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pass
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###
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