1、基本題2.12.20 見基本題ifxn 0Q linearTxn x1n Txn Tx1n Tx1nTxn 02.21 證明：yn 2 n 5 n 1 n 32.22 (a)(c)yn hn 1(b)yn n 2 2 n 3 3 n 4 4 n 5 5 n 6 5 n 7 4 n 8 3 n 9 2 n 10 2 n 11 2 n 12 3 n 13 4 n 14 5 n 15 5 n 16 4 n 17 3 n 18 2 n 19 n 20(d) yn n 2 n 1 n 3 n 3 3 n 4 2 n 5 n 6223 證明略2.242.250, n 01 an10, n 4,0 n N1

2、1, n 41 a1 ayn , N n NN 12, n 51121 ayn 3, n 64, n 72, n 8 2 a aN 1n1 N12, N2 n (N1 N2 )1 a 1 a N1 12, (N1 N2) n0, n 91 a2.26(a)NO(b)YES (c)NO(d)YES (e)YES(b)YES hn=2n, or, H (e j ) 2 ,unique2.27(a)NO(c)isnot unique, the only constrain isH (e j ) | 21 / 82.28(a)5(b)38(c)not (d)not229 畫圖略2.30 (a) Y,Y

3、,Y,N(b) Y,N,Y,N(c) Y,Y,Y,N(d) N,N,Y,Y(b)hccn 5 (1/ 3)nun 1 6 (2 / 5)nun 12.31(a) yhn A1(1/ 3)n A2 (2 / 5)n1111(d ) yn 25 (1/ 3)nun 55 (2 / 5)nun 27 (3 / 5)nun（c）證明略44122012.32yn 8e j / 4 cos(n / 2 / 2)yn cos(3n / 2 11 /12)2.33yn y0 n 2 2 y0 n 4 y0 n 6hn n 1 n 12.34深入題（B） T n y3n 4235（A）非線性（C）只有當(dāng)輸入是已

4、知三個輸入的移位時可以確定輸出（B） L n 1 y n 1 y n y n236（A）時變12322237證明略 1 n 1 n(a) y n A(b) A1 1 / 2, A2 1 / 2 A 238h1224 1 n 1 n(c) y n A nB (d ) A1 0, B1 1 / 2h11 2 2239（A）時變（B）非線性（C）線性時變(1)n2311yn cos(n) /(1 j / 2)241yn cos(n ）1681682401 j / 21 e jjnn1, | | 1（a)hn un un 1) j1e(b)H (e242(c) yn yn 1 xn xn 1while

5、| a | 1(d ) yes, stable243畫圖略（a) 1 X (e j ) X * (e j ) 2(c) X (e j ) X * (e j )1/ 21(b) X (e j ) X * (e j ) 2J(d )a tana sin /(1 a cos )（C） 2（D） 4（E） xn244245（A）6yn n（B）2(B) 1 (a|n1| a|n1|) |n0（A）a|n|2462(a)hn n 2 n 1 n 2247(b) yes2(c)H (e j ) 2e j (cos( ) 1)(e)(1) n hn(d )畫圖略(a)2 ( k )k(c)Y (e j )(

6、1 cos( )X：低通，截止頻率 / a(b) X (e j ) X (e j( ) )2.48(d )a 2較好近似Y：a2 時帶阻W：a2 時紅虛線249（A）長度 3，n=0,1,2(B) hn 2,4,2(a)qn (un un 6) (2un 2 2un 8) (un 4 un 10) (b)rn un 1* wn（C）YES2.50(a) y1n e jn / 2 /(1 ja)(b) y2 n (1) n /(1 a 2 )251(c) y n e jn / 2 1 ( ja) n1 /(1 ja)3(d )相同sin(0.5 (n 5) (n 5)sin(0.5 (n 6)

7、(n 6)cos( (n 1/ 4)22.522.53 33e j / 4 cos(n / 4 5 / 24)254255YES(d)乘以e j0n256(a)YES(b)NO(c)YES1,| | 0.8j257(a)高通H (e ) 0,| | 0.810,| | 0.3j | | 0.7(b)帶通H (e ) 1,0.320,| | 0.70.1,| | 0.1jH (e ) 0.15 | | / 2 ,0.1 | |(c)低通0.330,| | 0.3j2 X (e ),| |0j258W (e ) 0,| | 03(a)gn x *n259(b)證明略1, n 0,24(b)hn 2

8、, n 1(a) y n yn k 26020, otherk 0 xn n 1yn (1 / 2) n1un 1 (1 / 2) n1lim yn n261N0例如：擴充題：262證明略hn (1 / 2) n263系統(tǒng)可能是 LTI264NO1( ) 1.5 2 ( ) 3 / 2265(a)E(e j ) X (e j )H1(e j )F (e j ) X (e j )H1(e j )G(e j ) X (e j )H1(e j )H1(e j )Y (e j ) X (e j )H1(e j )H1(e j )266(b)H (e j ) H1(e j )H1(e j )(c)hn h1n* h1n(a)H (e j ) H1(e j( ) )267(b)高通268不一定（B） 0,.0.6269（A）NO270（A）證明略(C)H (e j ) 1 e j（E）hi n u