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标题: 序列的奇偶分解的 MATLAB 函数编写实践 [打印本页]

作者: mytomorrow    时间: 2020-5-18 10:19
标题: 序列的奇偶分解的 MATLAB 函数编写实践
序列 x(n)的奇偶分解的公式为:5 z* u3 z  q3 u* U+ @# ^2 W
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/ k0 I% \# ~6 ?6 o* B编写一个序列 x(n) 的奇偶分解式 xe(n) 和 xo(n),需要考虑的问题是序列长度,下标的变化。
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, G4 x+ p+ f4 H0 y# ]9 V% ?  O* }% ^这里必须做个声明,下面的程序中用到了前几篇博客中的几个函数,这里给贴出来:0 m) Q+ A; Y0 c- U( K) h/ l, I
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信号相加:+ f3 p2 c+ p0 ?# p4 E
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function [y,n] = sigadd(x1,n1,x2,n2)2 J8 E$ n5 t: v' k( m8 @4 m
% implements y(n) = x1(n) + x2(n)
4 I2 x  B1 l7 G2 Y6 ]- O% [y,n] = sigadd(x1,n1,x2,n2)% D/ E* h8 Z8 U& }4 ]! ?9 \& j
%____________________________________+ k/ k: E9 P) p# D
% y = sum sequence over n, which includes n1 and n2; h, J  E% W0 \
% x1 = first sequence over n1
3 J4 w' U1 z8 a; n  H3 m( K* M( d% x2 = second sequence over n2( n2 can be different from n1)* l. N5 ~: t: w6 \9 x
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n = min( min(n1), min(n2) ):max( max(n1), max(n2) ); %duration of y(n)
9 [5 N  p  P1 D% Q. by1 = zeros(1,length(n)); y2 = y1; %initialization
8 G2 [' ?7 W5 q5 ]1 w6 y1 \% ]0 hy1( find( ( n >= min(n1) )&( n <= max(n1) ) == 1  )  ) = x1; %x1 with duration of y1
. a% S7 H; m7 D8 Q6 sy2( find( ( n >= min(n2) )&( n <= max(n2) ) == 1  )  ) = x2; %x2 with duration of y2: K" U) j) k, `, a2 }
y = y1 + y2;
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# U1 D/ z. L# h1 t1 ]信号移位:; ]5 Z  Z9 U3 h! G' [4 m
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function [y,n] = sigshift(x,m,k)3 i( W! R! U- b9 u; {2 d1 w
%implements y(n) = x(n - k): Z' u7 h! I' k. l
%_________________________
0 l' o" E4 G! J%[y,n] = sigshift(x,m,k)9 L' @$ @* }3 g6 s4 j4 Q
%  v0 c' v7 z" l, M
n = m+k;- A) r" A2 p8 D' X' u
y = x;
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) b4 R$ L. ]$ O& W1 a% F单位阶跃序列:: F7 l0 d5 `. `% [& Z

3 G3 ~; I1 l  A5 t. d2 u( tfunction [x,n]=stepseq(n0,n1,n2);- r2 N1 V) Z2 i8 F% Q7 o# M# ?
% generate x(n) = u(n - n0); n1 <= n <= n28 k) v9 r' I( Z- g1 ~2 j0 Y% F" J
%_____________________________________________5 }1 z3 Y7 o: z& h
%[x,n] = stepseq(n0, n1, n2);
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/ m! M1 y9 ]: gn = [n1:n2];
6 \! s3 @- G& N+ I) `8 Q7 @$ Nx = [(n-n0) >= 0];
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" f: B, h9 i3 p' C' {8 I; }* K' d下面给出函数程序:
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function [xe, xo, m] = evenodd(x, n)
) p# L1 G  P2 h# t* T/ k! k% Real signal decomposition into even and odd parts: o- _  K4 z2 R8 E& Y8 J- ]
%__________________________________________________
0 ], E+ l/ _- p- X8 L%[xe, xo, m] = evenodd(x, n)
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if any( imag(x) ), N, S5 ~! B5 @5 S
    error('x is not a real sequence!');
! x) T" r7 @% M' m' g+ Lend
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% Ensure m of xe and xo! w* o- }( f2 F' C- x$ {
m = - fliplr(n);& \$ \0 Q5 Y2 a% c6 Y2 r
m1 = min([m,n]);5 a4 W4 @6 r% j5 g: r& ~
m2 = max([m,n]);& |9 A9 U! I% n3 z* _$ x
m = m1:m2;2 d8 \7 F! r8 J6 O' C& }

4 j' {: O  r- t2 d+ @3 g% Ensure x over m
) |2 w2 `" {0 x  t/ P1 X# ]  h# d4 Ynm = n(1) - m(1);
/ l% ^1 z# P% t+ W( V8 e' Cn1 = 1:length(n);# m1 U2 e8 z$ A4 X4 E) [
x1 = zeros(1,length(m)); % initialization- c! a; w/ L% U+ {/ A5 O
x1(nm + n1) = x;$ j6 f  s7 a( n. g1 U4 \+ s3 C
x = x1; % new x which enlarge index n
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- U  H( C) ^- i7 H5 w% xe and xo
, w/ m4 t: d% n# s8 p- Exe = 0.5*(x + fliplr(x));
/ h1 e- w6 ]+ W+ I' V3 Wxo = 0.5*(x - fliplr(x));4 G; e; @5 T+ [: v
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序列和及其位置分别装入 x 和 n 数组。首先确认是否已知序列是实序列并在m数组中确定偶部和奇部分量的位置,最后将所得奇偶分量存入xe和xo数组中。
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下面以一个实例来验证上述函数:
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将x(n)分解为奇偶分量。
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5 B; ~+ ]3 ~$ t% i! f7 q# Cclc
/ ]+ i4 M) k. {! aclear
! T/ ?& u$ c+ |! w) j" Tclose all
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. U( @# x. I: Z' K3 D  h$ N4 {$ ^n = 0:10;
, B* O9 D9 V. I1 g1 h. b6 C! fx = stepseq(0,0,10) - stepseq(10,0,10);1 B: D* `9 K# f7 W
[xe, xo, m] = evenodd(x,n);) b7 t4 v5 {0 H# S" h( W5 N

3 d/ N& ~- r- _9 f! csubplot(2,2,1);
7 k) d) u* m2 i" Cstem(n,x,'filled');# \7 R" p+ }" V& |$ a1 s
title('Rectangular pulse');% _" [) R6 K* b1 M/ x
xlabel('n');ylabel('x(n)'); 5 Y1 N0 a8 \4 R" ^
axis([-10,10,0,1.2]);5 E! E% Z2 e+ h9 ^" g) P6 V
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subplot(2,2,2);
9 b) A2 i8 W" ~stem(m,xe,'filled');
1 F% z, o; W0 w" W7 Dtitle('Even part');
6 ~% P" C: O1 k* K0 Lxlabel('n');ylabel('xe(n)');
# P4 a' _0 e) R( O( W8 y) laxis([-10,10,0,1.2]);  a" B# _6 @6 b' w: T2 |& D6 \9 Z5 h

- K7 G; _1 g+ tsubplot(2,2,4);6 K9 T; I# i1 [! Q
stem(m,xo,'filled');  u8 P$ b7 m7 E  a5 t
title('Odd part');
1 `1 q1 ]3 I/ p+ Kxlabel('n');ylabel('xo(n)');$ q# Q( N' S2 C1 [. _9 S
axis([-10,10,-0.6,0.6]);
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事实上,这篇博文到这里已经结束了,那我还想看看序列x(n)= u(n) - u(n-10)的合成过程:) b: M1 R. X: A3 I3 s  |
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clc9 Z2 S2 s* P) V& }) S5 c
clear1 J4 ]2 y8 Q4 n+ A% ]+ F4 S
close all
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: i+ L. f, ~  T/ M5 _* X* L) Q[u1,n1] = stepseq(0,0,10);( \7 p8 y! s! l/ n( ]8 P+ @  ^

: m. ^/ T+ C+ d# D" W$ i# rsubplot(3,1,1)0 p' s. o+ F  l5 K' o5 ]
stem(n1,u1,'filled');
' t/ A7 ^6 ^, \  `% w& mtitle('u(n)');
2 m  @0 U) b% Tylabel('u(n)');xlabel('n');& L* H* ~# x- X! c+ N; }2 C
axis([-10,10,0,1.2]);
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[u2,n2] = sigshift(u1,n1,10);
& H; v# n& a" _. O9 H3 \6 Bsubplot(3,1,2)1 J4 C& ^! N' i% p+ C
stem(n2,u2,'filled');# u" g! n+ S8 H+ o4 n
title('u(n-10)')
. c9 s. T! T% k3 E: L% N+ zxlabel('n');ylabel('u(n - 10)');
8 \# j) j! O2 |7 k4 zaxis([0,20,0,1.2]);
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0 `/ L* n' K4 B8 s6 v8 x0 k: R[x,n] = sigadd(u1,n1,-u2,n2);1 q& N* N3 H6 P) l* B9 r, q
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subplot(3,1,3)- l0 w, o6 W' n3 A
stem(n,x,'filled');
1 [8 o8 f& c  i8 ?title('Rectangular sequence');
1 M0 R" z0 Y& i0 n  o9 jxlabel('n');ylabel('x(n)= u(n) - u(n -10)');
6 y4 u3 C( m# U1 Y0 n6 gaxis([-10,10,0,1.2]);2 j) C- u. s' L( r; G: v5 |1 ]1 X

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作者: yin123    时间: 2020-5-18 11:10
序列的奇偶分解的 MATLAB 函数编写实践




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