![1 Convolutional Polar Codes - arXiv · 1 Convolutional Polar Codes Andrew James Ferris, Christoph Hirche and David Poulin Abstract Arikan’s Polar codes [1] attracted much attention](https://static.fdocument.org/doc/165x107/5f07505c7e708231d41c5eb5/1-convolutional-polar-codes-arxiv-1-convolutional-polar-codes-andrew-james-ferris.jpg)
“Neat” Polar Graphs page 1 of 4 - greenleecds.comgreenleecds.com/rgbest/polar.pdf · ♦R....
4
♦ ♦ ♦ R. Greenlee Wheaton Warrenville South High School Wheaton Il. 07/22/00 ∗ ∗ ∗ “Neat” Polar Graphs page 1 of 4 0) Setup (unless specified differently): MODE: Pol & Radian (for TI82 or TI83 calculators) ZOOM: 6 (ZStandard) FORMAT: AxisOff & PolarGC (optional) 1) Y= : r 1 = 4 cos(64θ θ θ) Window: [θmin, θmax] θstep: θ [0,39] 0.1 [Xmin, Xmax] Xstep: X [-6,6] 0 [Ymin, Ymax] Ystep: Y [-4,4] 0 2) Y= : r 1 = 4 cos(64θ θ θ) Window: θ [0,2π] π/24 X [-6,6] 0 Y [-4,4] 0 3) Y= : r 1 = 4 cos(3θ θ θ) r 2 = 4 sin(3θ θ θ) r 3 = -4 sin(3θ θ θ) r 4 = 4 cos(6θ θ θ) r 5 = 4 cos(3(θ θ θ − π π π π/3)) r 6 = 4 Window: θ [0,2π] π/24 X [-6,6] 0 Y [-4,4] 0 4) Y= : r 1 = 4 cos(8θ θ θ) r 2 = 4 cos(2θ θ θ) r 3 = 4 cos(4θ θ θ) r 4 = 4 sin(8θ θ θ) r 5 = 4 sin(4θ θ θ) r 6 = 4 sin(2θ θ θ) Window: θ [0,2π] π/24 X [-6,6] 0 Y [-4,4] 0
Transcript of “Neat” Polar Graphs page 1 of 4 - greenleecds.comgreenleecds.com/rgbest/polar.pdf · ♦R....
♦♦♦♦ R. Greenlee Wheaton Warrenville South High School Wheaton Il. 07/22/00 ∗∗∗∗
“Neat” Polar Graphs page 1 of 4
0) Setup (unless specified differently): MODE: Pol & Radian (for TI82 or TI83 calculators) ZOOM: 6 (ZStandard) FORMAT: AxisOff & PolarGC (optional) 1) Y= : r1 = 4 cos(64θθθθ) Window: [θmin, θmax] θstep: θ [0,39] 0.1 [Xmin, Xmax] Xstep: X [-6,6] 0 [Ymin, Ymax] Ystep: Y [-4,4] 0 2) Y= : r1 = 4 cos(64θθθθ) Window: θ [0,2π] π/24 X [-6,6] 0 Y [-4,4] 0 3) Y= : r1 = 4 cos(3θθθθ) r2 = 4 sin(3θθθθ) r3 = -4 sin(3θθθθ) r4 = 4 cos(6θθθθ) r5 = 4 cos(3(θθθθ −−−− π π π π/3)) r6 = 4 Window: θ [0,2π] π/24 X [-6,6] 0 Y [-4,4] 0 4) Y= : r1 = 4 cos(8θθθθ) r2 = 4 cos(2θθθθ) r3 = 4 cos(4θθθθ) r4 = 4 sin(8θθθθ) r5 = 4 sin(4θθθθ) r6 = 4 sin(2θθθθ) Window: θ [0,2π] π/24 X [-6,6] 0 Y [-4,4] 0
♦♦♦♦ R. Greenlee Wheaton Warrenville South High School Wheaton Il. 07/22/00 ∗∗∗∗
“Neat” Polar Graphs continued page 2 of 4 5) Y= : r1 = 3 sin((1/3)θθθθ) r2 = -3 sin((1/3)θθθθ) Window: θ [0,2π] π/24 X [-6,6] 0 Y [-4,4] 0 6) Y= : r1 = 3 sin(10θθθθ) Window: θ [0,2π] π/24 X [-4.7,4.7] 0 Y [-3.1,3.1] 0 7) Y= : r1 = θθθθ Window: θ [0,157] 0.8 X [-155,155] 0 Y [-140,140] 0 8) Y= : r1 = 2θθθθ r2 = -2θθθθ Window: θ [0,40] 0.2 X [-60,60] 0 Y [-40,40] 0 9) Y= : r1 = 0.25θθθθ Window: θ [0,600] 0.5 X [-60,60] 0 Y [-40,40] 0
a) graph with a θ step of 0.5 b) graph with a θ step of 1.0 c) graph with a θ step of 1.5 d) graph with a θ step of 2.0 e) graph with a θ step of 2.5 (best one?) f) graph with a θ step of 3.0 g) graph with a θ step of 3.5
♦♦♦♦ R. Greenlee Wheaton Warrenville South High School Wheaton Il. 07/22/00 ∗∗∗∗
“Neat” Polar Graphs continued page 3 of 4 10) Y= : r1 = 4 cos(4sin(4 cos(4sin(cos(4 sin(cos(4sin( tan(θθθθ))))))))) r2 = 4 cos(cos(cos( tan(tan(tanθθθθ)))))) r3 = r1 + r2 Note: r1 & r2 are not turned on only r3 is turned on Window: θ [0,2π] π/24 X [-7,7] 0 Y [-4,4] 0 11) Y= : r1 = 4 cos(2cosθθθθ)) Window: θ [0,2π] π/24 X [-6,6] 0 Y [-4,4] 0 12) Y= : r1 = 4 cos(4cosθθθθ)) Window: θ [0,2π] π/24 X [-6,6] 0 Y [-4,4] 0 13) Y= : r1 = 4 cos(10cosθθθθ)) Window: θ [0,2π] π/24 X [-6,6] 0 Y [-4,4] 0 14) Y= : r1 = 4 cos(θθθθ)*4 sin(θθθθ) r2 = 0.5 sin(θθθθ) r3 = 1 sin(θθθθ) r4 = -3 sin(θθθθ) r5 = -2 sin(θθθθ) r6 = -1 sin(θθθθ) Window: θ [0,2π] π/24 X [-6,6] 0 Y [-4,4] 0
♦♦♦♦ R. Greenlee Wheaton Warrenville South High School Wheaton Il. 07/22/00 ∗∗∗∗
“Neat” Polar Graphs continued page 4 of 4 15) Y= : r1 = 184 tan(465θθθθ) r2 = 842 sin(372θ)θ)θ)θ) r3 = 52 cos(12θ)θ)θ)θ) Window: θ [0,2π] π/24 X [-6,6] 0 Y [-4,4] 0
