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discrete fourier transform animation

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This commit is contained in:
Grant Sanderson 2020-12-08 09:26:45 -08:00
parent d650cfd3e7
commit 9dc4551685
1 changed files with 24 additions and 6 deletions
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30
from_3b1b/active/18S191/dft.py
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@ -237,7 +237,7 @@ class IntroduceDFT(Scene):
)
self.wait()
def change_signal(new_signal):
def change_signal(new_signal, omega=1):
side_vectors.generate_target()
vectors.generate_target()
for x, sv, v in zip(it.count(), side_vectors.target, vectors.target):
@ -247,7 +247,7 @@ class IntroduceDFT(Scene):
)
v.put_start_and_end_on(
plane.n2p(0),
plane.n2p(new_signal[x] * zeta**(-x)),
plane.n2p(new_signal[x] * zeta**(-omega * x)),
)
self.play(
MoveToTarget(vectors),
@ -321,13 +321,31 @@ class IntroduceDFT(Scene):
)
self.wait()
# Show cos(2x) example
cos2x_signal = np.cos(2 * np.arange(0, TAU, TAU / N)) + 1.5
sin2x_signal = np.sin(2 * np.arange(0, TAU, TAU / N)) + 1.5
VGroup(side_axes, side_vectors).shift(DOWN)
self.play(
FadeIn(side_axes),
FadeIn(side_vectors),
)
self.wait()
change_signal(cos2x_signal, omega=2)
self.wait()
change_signal(sin2x_signal, omega=2)
self.wait()
change_signal(signal, omega=2)
self.play(*map(FadeOut, (side_axes, side_vectors)))
self.wait()
# Show general formula
dots = TexMobject("\\vdots")
dots.next_to(lhs2[:-1], DOWN, MED_LARGE_BUFF)
formula = TexMobject(
"\\hat s[\\omega] = "
"\\sum_{n=0}^{N - 1} s[n] \\zeta^{\\omega \\cdot n}"
"\\hat s[f] = "
"\\sum_{n=0}^{N - 1} s[n] \\zeta^{f \\cdot n}"
)
formula.next_to(dots, DOWN)
formula.align_to(lhs2, LEFT)
@ -340,10 +358,10 @@ class IntroduceDFT(Scene):
# Cycle through
omega_label = VGroup(
TexMobject("\\omega = ", font_size=72),
TexMobject("f = ", font_size=72),
Integer(2),
)
omega_label.arrange(RIGHT, aligned_edge=DOWN)
omega_label.arrange(RIGHT)
omega_label.next_to(plane, LEFT, MED_LARGE_BUFF, aligned_edge=DOWN)
self.play(FadeIn(omega_label))