added codes

1 files changed, 92 insertions, 0 deletions

diff --git a/FSF-2020/calculus/series-and-transformations/Fourier Transform/video4_FourierSeriesOfSquarePulse.py b/FSF-2020/calculus/series-and-transformations/Fourier Transform/video4_FourierSeriesOfSquarePulse.py
new file mode 100644
index 0000000..5d33fbe
--- /dev/null
+++ b/FSF-2020/calculus/series-and-transformations/Fourier Transform/video4_FourierSeriesOfSquarePulse.py
@@ -0,0 +1,92 @@
+from manimlib.imports import *
+import numpy as np
+
+def returnSum(k,x):
+    summ=0
+    for i in range(1,k+1,2):
+        summ+=((np.sin(2*np.pi*i*x))/i)
+    return summ
+
+def returnFunc(self,k):
+    graph=self.get_graph(lambda x:(4/np.pi)*returnSum(k,x),color=WHITE,x_max=1,x_min=-1)
+    return graph
+
+class fourierSeries(GraphScene,MovingCameraScene):
+    CONFIG = {
+        "x_min": -3,
+        "x_max": 3,
+        "x_axis_width": 13,
+        "y_min": -3,
+        "y_max": 3,
+        "graph_origin": ORIGIN,
+        "function_color": RED,
+        "axes_color": BLUE,
+        "x_axis_label": "$x$",
+        "y_axis_label": "$y$",
+        "exclude_zero_label": True,
+        "x_labeled_nums": range(-2, 3, 1),
+    }
+    def setup(self):
+        GraphScene.setup(self)
+        MovingCameraScene.setup(self)
+    def construct(self):
+        x_each_unit = self.x_axis_width / (self.x_max - self.x_min)
+        y_each_unit = self.y_axis_height / (self.y_max - self.y_min)   
+
+        equation=TextMobject("$f(x)=\\frac { 4 }{ \pi  } \sum _{ k=1,3,5.. }^{ \infty  }{ \\frac { 1 }{ k } \sin { 2\pi kx }  }$").shift(5*RIGHT+3*UP).set_color(RED).scale(0.4)
+        self.add(equation)
+        self.setup_axes(animate=True)
+        line1=Line(start=(-x_each_unit,y_each_unit,0),end=(-(1/2)*x_each_unit,y_each_unit,0),color=RED)
+        line2=Line(start=(-(1/2)*x_each_unit,y_each_unit,0),end=(-(1/2)*x_each_unit,-y_each_unit,0),color=RED)
+        line3=Line(start=(-(1/2)*x_each_unit,-y_each_unit,0),end=(0,-y_each_unit,0),color=RED)
+        line4=Line(start=(0,-y_each_unit,0),end=(0,y_each_unit,0),color=RED)
+        line5=Line(start=(0,y_each_unit,0),end=((1/2)*x_each_unit,y_each_unit,0),color=RED)
+        line6=Line(start=((1/2)*x_each_unit,y_each_unit,0),end=((1/2)*x_each_unit,-y_each_unit,0),color=RED)
+        line7=Line(start=((1/2)*x_each_unit,-y_each_unit,0),end=(x_each_unit,-y_each_unit,0),color=RED)
+        self.play(ShowCreation(line1))
+        self.play(ShowCreation(line2))
+        self.play(ShowCreation(line3))
+        self.play(ShowCreation(line4))
+        self.play(ShowCreation(line5))
+        self.play(ShowCreation(line6))
+        self.play(ShowCreation(line7))
+        self.wait(0.5)
+
+        labels=[
+            TextMobject("$f_{ k=1 }(x)$"),
+            TextMobject("$f_{ k=3 }(x)$"),
+            TextMobject("$f_{ k=5 }(x)$"),
+            TextMobject("$f_{ k=7 }(x)$"),
+            TextMobject("$f_{ k=9 }(x)$"),
+            TextMobject("$f_{ k=11 }(x)$"),
+            TextMobject("$f_{ k=13 }(x)$"),
+            TextMobject("$f_{ k=15 }(x)$"),
+            TextMobject("$f_{ k=17 }(x)$"),
+            TextMobject("$f_{ k=19 }(x)$"),
+            TextMobject("$f_{ k=85 }(x)$")
+        ]
+        p=0
+        for i in range(1,20,2):
+            if(i==1):
+                graphInitial=returnFunc(self,1)
+                label=labels[p].scale(0.5).shift(y_each_unit*1.5*UP+RIGHT*x_each_unit*0.3)
+                self.play(ShowCreation(graphInitial),Write(labels[0]))
+                old=graphInitial
+                oldLabel=label
+            else:
+                graph=returnFunc(self,i)
+                graphLabel=labels[p].scale(0.5).shift(y_each_unit*1.5*UP+RIGHT*x_each_unit*0.3)
+                self.play(ReplacementTransform(old,graph),ReplacementTransform(oldLabel,graphLabel))
+                old=graph
+                oldLabel=graphLabel
+            p+=1
+        graphFinal=returnFunc(self,85)
+        labelFinal=labels[10].scale(0.5).shift(y_each_unit*1.5*UP+RIGHT*x_each_unit*0.3)
+        self.play(FadeOut(old),FadeOut(oldLabel))
+        self.play(ShowCreation(graphFinal),Write(labelFinal))
+        self.wait(1)
+        self.camera_frame.save_state()
+        self.play(self.camera_frame.set_width, 2.25,self.camera_frame.move_to, y_each_unit*UP+RIGHT*x_each_unit*0.3)
+        self.wait(1)
+        self.play(self.camera_frame.set_width,14,self.camera_frame.move_to,0)
+        self.wait(2)