- 在线时间
- 123 小时
- 最后登录
- 2015-5-27
- 注册时间
- 2008-9-18
- 听众数
- 11
- 收听数
- 0
- 能力
- 0 分
- 体力
- 5215 点
- 威望
- 12 点
- 阅读权限
- 200
- 积分
- 2119
- 相册
- 3
- 日志
- 3
- 记录
- 49
- 帖子
- 785
- 主题
- 42
- 精华
- 1
- 分享
- 2
- 好友
- 245

di_dar
TA的每日心情 | 无聊 2015-1-15 22:05 |
|---|
签到天数: 79 天 [LV.6]常住居民II
- 自我介绍
- 隐秘盛开
 群组: Matlab讨论组 群组: 数学趣味、游戏、IQ等 群组: 数学建模 群组: SIMULINK 群组: LINGO |
本帖最后由 大笨象 于 2011-6-7 12:26 编辑 % h- }' I" s J8 C/ B+ m6 U
% K3 V- g: S9 M$ A
不知道有木有人研究这个,比较偏向于硬件描述。2 M# h- f* v/ u; @4 J
今天先发一个sine cose函数的实现。 {/ u9 ?/ B5 t8 F
有兴趣的可以看一下,m文件见附件。' k H4 r& d& l3 [4 n5 ?
function v=f_cordic(beta,n)4 x$ N& X+ {, }4 B
if beta < -pi/2 || beta > pi/2
/ C3 L7 G! d; x4 j7 \3 {; u! c if beta < 0/ x8 u. G7 D" R: f0 G- h
v=f_cordic(beta + pi,n);
% Z$ j4 @8 l3 o0 ^9 h# I else
; ?' U. p3 D6 L" z) q/ N8 i v=f_cordic(beta - pi,n);& j$ X4 \; j" {8 y% B
end4 ?9 H, Z4 ^6 W
v = -v;% flip the sign for second or third quadrant
) ?; K" {. v: |2 e, W1 r return3 ?, k5 Q& h5 l
end
7 ?1 g2 w7 h4 q4 n6 S' |% Initialization of tables of constants used by CORDIC0 B% a* x6 C! G- J- m2 K
% need a table of arctangents of negative powers of two, in radians:
# H u1 a7 z* P% E6 A/ R$ \; ~% angles = atan(2.^-(0:27));
& J' I2 _1 K& E/ L% Q1 Zangles = [ ...
. b" G+ T2 f- E 0.78539816339745 0.46364760900081 0.24497866312686 0.12435499454676 ...
" X, O( f3 I9 ~7 p- ?- ~& N6 _ 0.06241880999596 0.03123983343027 0.01562372862048 0.00781234106010 ...
; T' {8 K' [$ Y& c* X% f( p+ [ 0.00390623013197 0.00195312251648 0.00097656218956 0.00048828121119 ...
0 n. l, v0 ^1 a6 `* Y1 b9 {9 N 0.00024414062015 0.00012207031189 0.00006103515617 0.00003051757812 ...2 R- z' j1 _6 ?; D! o3 ^6 f$ P
0.00001525878906 0.00000762939453 0.00000381469727 0.00000190734863 ...& g3 h; w/ c8 U3 {
0.00000095367432 0.00000047683716 0.00000023841858 0.00000011920929 ...
6 d# F6 t+ v0 k! S 0.00000005960464 0.00000002980232 0.00000001490116 0.00000000745058 ];
v( i& q9 v3 [2 v- K' V" W5 l# ^% and a table of products of reciprocal lengths of vectors [1, 2^-j]:
1 W7 `: Z$ `, rKvalues = [ ...
) R7 J5 T1 R) ?1 x- t5 o% L 0.70710678118655 0.63245553203368 0.61357199107790 0.60883391251775 ...9 G* h3 I$ ~! w d
0.60764825625617 0.60735177014130 0.60727764409353 0.60725911229889 ...$ P/ y2 O8 B4 {8 H# {
0.60725447933256 0.60725332108988 0.60725303152913 0.60725295913894 ...# x0 [& f# A! _/ z1 A [0 \) B! z8 s
0.60725294104140 0.60725293651701 0.60725293538591 0.60725293510314 ...5 F; f! T/ k7 \" J
0.60725293503245 0.60725293501477 0.60725293501035 0.60725293500925 ...
, h k4 S6 D9 U) M4 N9 i 0.60725293500897 0.60725293500890 0.60725293500889 0.60725293500888 ];' `( Z v/ V; k! s6 ]# c- m
Kn = Kvalues(min(n, length(Kvalues)));& Z. l( n q" ]4 x
" k! g$ @) P9 @
% Initialize loop variables:
4 p2 t! ^% V; r7 _5 v( d: E1 Iv = [1;0]; % start with 2-vector cosine and sine of zero+ I9 F* G1 c# A7 L, O
poweroftwo = 1;
9 O9 u3 `1 Y/ @+ Z7 h! z% Iterations$ A+ H8 `- R3 B' e
for j = 1:n;
! X C! b2 B- P( I1 J if beta < 0' L |+ @* Q6 x! B0 v1 q% ]1 l
sigma = -1;
/ j" l/ I; r' E else9 X& |6 \" D% C, E0 r1 V+ ^
sigma = 1;1 y- d9 k" b# ~) N$ ~# s5 u
end
: t: L$ p: b) S1 {$ Y % update the angle from table, or eventually by just dividing by two' a- j" _5 R/ b/ _& y
if j <= length(angles)0 i, @+ `; p3 R! b1 t( E- e
angle = angles(j);' p# c* ~5 U) l
else
+ V. H. Q5 l' e& A4 v2 L0 w angle = angle/2;# K* H& p2 `$ p$ ^" s
end U' j+ e4 N- c; U$ c
factor = sigma * poweroftwo;) Z/ ^' \; F7 D5 N5 q7 f. \
R = [1, -factor; factor, 1];
) y& j! B# h1 v v = R * v; % 2-by-2 mtrix multiply; u, [+ y- b8 f, E, z N
beta = beta - sigma * angle; % update the remaining angle3 P: G2 j a; L5 ~: B, R
poweroftwo = poweroftwo / 2;$ p* o, @, [6 C( G; C1 ?6 h0 M7 H
end
# Z3 k! w% v, _% Adjust length of output vector to be [cos(beta), sin(beta)]:
) Z" v2 t' y" r8 Hv = v * Kn;
! i% H1 [2 }$ j+ ]/ b' W W. z$ Zreturn) {4 h1 C E9 M+ C0 E
3 H! N; B; _7 B# ]7 G0 ?使用20位寄存器,仿真波形如下:6 f( i' M; E: X( v! M* v, s
. m9 {: s/ z9 I K% } |
-
-
f_cordic.m
2.25 KB, 下载次数: 21, 下载积分: 体力 -2 点
CORDIC算法
zan
-
总评分: 体力 + 10
查看全部评分
|