信号与线性系统
课后答案_吴大正
第一章
r(t),t,(t)1-1画出下列各信号的波形(式中)为斜升函数。
解:各信号波形为
,t (2)f(t),e,,,,t,,
(3) f(t),sin(,t),(t)
(4) f(t),,(sint)
(5) f(t),r(sint)
k(7) f(t),2,(k)
k(10) f(k),[1,(,1)],(k)
r(t),t,(t)1-2 画出下列各信号的波形[为斜升函数]。
f(t),r(t),2r(t,1),r(t,2)f(t),2,(t,1),3,(t,1),,(t,2) (1) (2)
f(k),k[,(k),,(k,5)]f(t),r(2t),(2,t) (5) (8)
,kkf(k),sin()[,(k),,(k,7)]f(k),2[,(3,k),,(,k)](11) (12) 6
解:各信号波形为
f(t),2,(t,1),3,(t,1),,(t,2) (1)
f(t),r(t),2r(t,1),r(t,2) (2)
f(t),r(2t),(2,t) (5)
f(k),k[,(k),,(k,5)] (8)
,k
f(k),sin()[,(k),,(k,7)](11) 6
kf(k),2[,(3,k),,(,k)](12)
1-3 写出图1-3所示各波形的
达式。
1-4 写出图1-4所示各序列的闭合形式表达式。
1-5 判别下列各序列是否为周期性的。如果是,确定其周期。
3,,,,f(t),3cost,2sin(,t)f(k),cos(k,),cos(k,) (2) (5) 524436
解:
f(t)1-6 已知信号的波形如图1-5所示,画出下列各函数的波形。
f(0.5t,2)f(1,2t)f(t,1),(t)f(t,1),(t,1) (1) (2) (5) (6)
tdf(t)
f(x)dx (7) (8) ,,,dt
解:各信号波形为
f(t,1),(t) (1)
f(t,1),(t,1) (2)
f(1,2t) (5)
f(0.5t,2) (6)
df(t)
(7) dt
t
f(x)dx (8) ,,,
f(k)1-7 已知序列的图形如图1-7所示,画出下列各序列的图形。
f(k,2),(k)f(k,2),(k,2) (1) (2)
f(,k,2)f(k,2)[,(k),,(k,4)] (3) (4) f(,k,2),(,k,1)f(k),f(k,3) (5) (6) 解:
df(t)f(t)1-9 已知信号的波形如图1-11所示,分别画出和的波形。 dt
f(3,2t)f(3,t)f(3,t)解:由图1-11知,的波形如图1-12(a)所示(波形是由对的波形展宽为原来f(3,t)f(t,3)f(t,3)的两倍而得)。将的波形反转而得到的波形,如图1-12(b)所示。再将的波形右
df(t)f(t)移3个单位,就得到了,如图1-12(c)所示。的波形如图1-12(d)所示。 dt
1-10 计算下列各题。
2d,td(1,t)[e,(t)],,,,cost,sin(2t),(t) (1) (2) 2dtdt
t,,t2(1,x),'(x)dx[t,sin()],(t,2)dt (5) (8) ,,,,,,4
1-12 如图1-13所示的电路,写出
u(t)(1)以为响应的微分方程。 C
i(t)(2)以为响应的微分方程。 L
1-20 写出图1-18各系统的微分或差分方程。
y(,)f(,)x(0)1-23 设系统的初始状态为,激励为,各系统的全响应与激励和初始状态的关系如下,试分
析各系统是否是线性的。
tt,ty(t),f(t)x(0),f(x)dxy(t),ex(0),sinxf(x)dx (1) (2) ,,00
tky(k),(0.5)x(0),f(k)f(k,2)y(t),sin[x(0)t],f(x)dx (3) (4) ,0
k
y(k),kx(0),f(j), (5)
,0j
y(,)f(,)1-25 设激励为,下列是各系统的零状态响应。判断各系统是否是线性的、时不变的、因果的、zs
稳定的,
dft()y(t),f(t)y(t),f(t)cos(2,t)yt(), (1) (2) (3) zszszsdt
y(t),f(,t)y(k),f(k)f(k,1)y(k),(k,2)f(k) (4) (5) (6) zszszs
k
y(k),f(j)y(k),f(1,k)(7) (8) ,zszs,0j
1-28 某一阶LTI离散系统,其初始状态为。已知当激励为时,其全响应为 y(k),,(k)x(0)1
k若初始状态不变,当激励为时,其全响应为 y(k),[2(0.5),1],(k),f(k)2
若初始状态为,当激励为时,求其全响应。 2x(0)4f(k)
第二章
2-1 已知描述系统的微分方程和初始状态如下,试求其零输入响应。
(1) y''(t),5y'(t),6y(t),f(t),y(0),1,y'(0),,1,
(4) y''(t),y(t),f(t),y(0),2,y'(0),0,
y(0)y'(0)02-2 已知描述系统的微分方程和初始状态如下,试求其值和。 ,,,
(2) y''(t),6y'(t),8y(t),f''(t),y(0),1,y'(0),1,f(t),,(t),,
2t (4) y''(t),4y'(t),5y(t),f'(t),y(0),1,y'(0),2,f(t),e,(t),,
解:
2-4 已知描述系统的微分方程和初始状态如下,试求其零输入响应、零状态响应和全响应。
,ty''(t),4y'(t),4y(t),f'(t),3f(t),y(0),1,y'(0),2,f(t),e,(t) (2) ,,
解:
i(t)u(t)2-8 如图2-4所示的电路,若以为输入,为输出,试列出其微分方程,并求出冲激响应和阶跃响SR
应。
u(t)2-12 如图2-6所示的电路,以电容电压为响应,试求其冲激响应和阶跃响应。 C
2-16 各函数波形如图2-8所示,图2-8(b)、(c)、(d)均为单位冲激函数,试求下列卷积,并画出波形图。
f(t)*f(t)f(t)*f(t)f(t)*f(t) (1) (2) (3) 131412
f(t)*f(t)*f(t)f(t)*[2f(t),f(t,3) (4) (5) 143122
波形图如图2-9(a)所示。
波形图如图2-9(b)所示。
波形图如图2-9(c)所示。
波形图如图2-9(d)所示。
波形图如图2-9(e)所示。
f(t),t,(t)y(t),f(t)*f(t,1)*,'(t,2)f(t),,(t),,(t,2)2-20 已知,,求 1122
,2(tx),,y(t),ef(x,2)dxy(t)f(t)2-22 某LTI系统,其输入与输出的关系为 ,t1,
h(t)求该系统的冲激响应。
f(t),,(t)2-28 如图2-19所示的系统,试求输入时,系统的零状态响应。
2-29 如图2-20所示的系统,它由几个子系统组合而成,各子系统的冲激响应分别为
h(t),,(t),,(t,3)h(t),,(t,1) ba
求复合系统的冲激响应。
第三章习题
0,,k,k1f(i)3.1、试求序列 的差分、和。 f(k)=,,,f(k),f(k),,,,i=-,,2,,,
3.6、求下列差分方程所描述的LTI离散系统的零输入相应、零状态响应和全响应。
ykykfkfkky()-2(-1)(),()2(),(-1)-1,,,,1)
ykykfkfkkky()2(-1)(),()(34)(),(-1)-1,,,,,,3)
5)
1kykykykfkfkkyy,,,,,,,()2(-1)(-2)(),()3()(),(-1)3,(-2)-52
3.8、求下列差分方程所描述的离散系统的单位序列响应。
ykykfk()-(-2)(), 2)
ykykykfk()-4(-1)8(-2)(),, 5)
3.9、求图所示各系统的单位序列响应。
(a)
(c)
3.10、求图所示系统的单位序列响应。
3.11、各序列的图形如图所示,求下列卷积和。
fkfkfk()-()(),(1)(2)(3)(4) fkfk()(),fkfk()(),fkfk()(),,,213122334
3.13、求题3.9图所示各系统的阶跃响应。
3.14、求图所示系统的单位序列响应和阶跃响应。
kgkk()0.5,,3.15、若LTI离散系统的阶跃响应,求其单位序列响应。 ,,,,
kfkk()0.5(),,3.16、如图所示系统,试求当激励分别为(1) (2)时的零状态响应。 fkk()(),,,,
k,khkk=,fkkak=--1,,3.18、如图所示的离散系统由两个子系统级联组成,已知,,激励,hk=2cos,,,,,,,,,,,,21a4
求该系统的零状态响应。(提示:利用卷积和的结合律和交换律,可以简化运算。) ()kyzs
hkk=,hkk=-5,3.22、如图所示的复合系统有三个子系统组成,它们的单位序列响应分别为,,求复合,,,,,,,,12
系统的单位序列响应。
第四章习题 4.6 求下列周期信号的基波角频率Ω和周期T。
,j100t (1) (2) cos[(t,3)]e2
cos(2t),sin(4t)cos(2,t),cos(3,t),cos(5,t) (3) (4)
,,,,, (5) (6) cos(t),sin(t)cos(t),cos(t),cos(t)24235
4.7 用直接计算傅里叶系数的
,求图4-15所示周期函数的傅里叶系数(三角形式或指数形式)。
图4-15
4.10 利用奇偶性判断图4-18示各周期信号的傅里叶系数中所含有的频率分量。
图4-18
4-11 某1Ω电阻两端的电压如图4-19所示, u(t)
(1)求的三角形式傅里叶系数。 u(t)
1(2)利用(1)的结果和,求下列无穷级数之和 u(),12
111 S,1,,,,......357(3)求1Ω电阻上的平均功率和电压有效值。 (4)利用(3)的结果求下列无穷级数之和
111 S,1,,,,......222357
图4-19
4.17 根据傅里叶变换对称性求下列函数的傅里叶变换
,sin[2(t,2)] (1)f(t),,,,,t,, ,(t,2)
,2f(t),,,,,t,,22 (2) ,,t
2,sin(2t),, f(t),,,,,t,, (3),,,2t,,
4.18 求下列信号的傅里叶变换
,jt,3(t,1)(1) (2) f(t),e,(t,2)f(t),e,'(t,1)
2,2t(3) (4) f(t),sgn(t,9)f(t),e,(t,1)
t(5) f(t),,(,1)2
4.19 试用时域微积分性质,求图4-23示信号的频谱。
图4-23
F[f(t)],F(j,)4.20 若已知,试求下列函数的频谱:
df(t)tf(2t)(1-t)f(1-t) (1) (3) (5) tdt
dft()1jt (8) (9) ef(3-2t)*dt,t
4.21 求下列函数的傅里叶变换
,,,,1,0,,(j) (1)F ,,0,,,0,
F(j,),2cos(3,) (3)
2,2sin-j(2n,1),,F,e(5)(j) ,,n,0
4.23 试用下列方式求图4-25示信号的频谱函数
(1)利用延时和线性性质(门函数的频谱可利用已知结果)。 (2)利用时域的积分定理。
,(t,2),(t,2)(3)将看作门函数与冲激函数、的卷积之和。 g(t)f(t)2
图4-25
4.25 试求图4-27示周期信号的频谱函数。图(b)中冲激函数的强度均为1。
图4-27
F(j,)F(j,)4.27 如图4-29所示信号的频谱为,求下列各值[不必求出] f(t)
, (1) (2) F(j,)d,F(0),F(j,)|,,0,,,
2, (3) F(j,)d,,,,
图4-29
4.28 利用能量等式
2,,12 f(t)dt,F(j,)d,,,,,,,2,
计算下列积分的值。
2,,dxsin(t) (1)[]dt (2) 22,,,,,,(1,x)t
4.29 一周期为T 的周期信号,已知其指数形式的傅里叶系数为,求下列周期信号的傅里叶系数 Ff(t)n
(1) (2) f(t),f(t,t)f(t),f(,t)102
df(t)f(t) (3) (4) ,f(t),f(at),a,034dt
,U(j)2,4.31 求图4-30示电路中,输出电压电路中,输出电压对输入电流的频率响应H(j),为了能,i(t)u(t)S2I(j,)S
无失真的传输,试确定R、R的值。 12
图4-30
4.33 某LTI系统,其输入为,输出为 f(t)
,1x,a y(t),s()f(x,2)dx,,,aa
s(t),S(j,)H(j,)式中a为常数,且已知,求该系统的频率响应。
,2,j,H(j),f(t),cos(2t)4.34 某LTI系统的频率响应,若系统输入,求该系统的输出。 y(t)2,j,
4.35 一理想低通滤波器的频率响应
,,,,1,,,3rad/s,H(j), ,3
,,0,,3rad/s,
4.36 一个LTI系统的频率响应
,,j2,,,,,6/0erads,,,,j2,,, (),06/Hj,e,rads,
,0,其他,
,
sin(3t)若输入,求该系统的输出。 f(t),cos(5t)y(t)t
24.39 如图4-35的系统,其输出是输入的平方,即(设为实函数)。该系统是线性的吗, y(t),f(t)f(t)
sintf(t), (1)如,求的频谱函数(或画出频谱图)。 y(t)t
1 (2)如,求的频谱函数(或画出频谱图)。 f(1),,cost,cos(2t)y(t)2
4.45 如图4-42(a)的系统,带通滤波器的
,(,),0频率响应如图(b)所示,其相频特性,若输入
,sin(2t) f(t),,s(t),cos(1000t),2t
求输出信号。 y(t)
图4-42
4.48 有限频带信号的最高频率为100Hz,若对下列信号进行时域取样,求最小取样频率。 ff(t)s
2f(3t) (1) (2) f(t)
2f(t)*f(2t) (3) (4) f(t),f(t)
4.50 有限频带信号,其中,求的冲激函数序列进行取样(请f,800Hzf(t),5,2cos(2,ft),cos(4,ft)f,1kHz,(t)sT111
注意)。 f,fs1
(1)画出及取样信号在频率区间(-2kHz,2kHz)的频谱图。 f(t)f(t)s
(2)若将取样信号输入到截止频率,幅度为的理想低通滤波器,即其频率响应 f(t)f,500Hzsc
,T,f,500HzsHj,Hjf,(,)(2,) ,0,f,500Hz,
画出滤波器的输出信号的频谱,并求出输出信号。 y(t)
图4-47
图4-48
图4-49
4.53 求下列离散周期信号的傅里叶系数。
1k (2) f(k),()(0,k,3)(N,4)2
第五章
5-2 求图5-1所示各信号拉普拉斯变换,并注明收敛域。
,atsin(,t),(t)cos(,t),(t),(t)e,(t)5-3 利用常用函数(例如,,,等)的象函数及拉普拉斯
F(s)f(t)变换的性质,求下列函数的拉普拉斯变换。
,t,(t,2)sin(,t)[,(t),,(t,1)]e,(t),e,(t,2) (1) (3)
,
sin(2t,),(t),(4t,2) (5) (7) 4
2tdsin(,t)dx[sin(,t),(t)](9) (11) 2,0dt
2,2t,(t,3)te(t),te,(t,1) (13) (15)
123
1
F(s),y(t)Y(s)f(t)5-4 如已知因果函数的象函数,求下列函数的象函数。 2s,s,1
t,t
ef()tf(2t,1) (1) (4) 2
f(0)F(s)f(,)5-6 求下列象函数的原函数的初值和终值。 ,
3s,12s,3F(s),F(s),2 (1) (2) s(s,1)(s,1)
f(t)F(s)t,05-7 求图5-2所示在时接入的有始周期信号的象函数。
图5-2
f(t)F(s)5-8 求下列各象函数的拉普拉斯变换。
21s,4s,52s,4
22 (1) (3) (5) (s,2)(s,4)s(s,4)s,3s,2
1s,5
22 (7) (9) s(s,1)s(s,2s,5)
F(s)f(t)5-9 求下列象函数的拉普拉斯变换,并粗略画出它们的波形图。
2,s,Ts,2(s,3),,e(1)1,ee
22 (1) (3) (6) s,,s,1s,3
其波形如下图所示:
其波形如下图所示:
其波形如下图所示:
f(t)t,0F(s)5-10 下列象函数的原函数是接入的有始周期信号,求周期T并写出其第一个周期
f(t)0,t,T()的时间函数表达式。 o
1
1
,s,2s (1) (2) s(1,e)1,e
y''(t),5y'(t),6y(t),3f(t)5-12 用拉普拉斯变换法解微分方程 的零输入响应和零状态响应。
f(t),,(t),y(0),1,y'(0),2(1)已知。 ,,
,tf(t),e,(t),y(0),0,y'(0),1(2)已知。 ,,
y(t)y(t)5-13 描述某系统的输出和的联立微分方程为 12
'(),(),2(),4()ytytytft,112
,
'(),(),2(),,()ytytytft212,
y(t)y(t)y(0),1f(t),0y(0),2(1)已知,,,求零状态响应,。 zs1zs21,2,
y''(t),3y'(t),2y(t),f'(t),4f(t)5-15 描述某LTI系统的微分方程为 求在下列条件下的零输入响应和零状态响应。
f(t),,(t),y(0),0,y'(0),1 (1)。 ,,
,2tf(t),e,(t),y(0),1,y'(0),1(2)。 ,,
y''(t),3y'(t),2y(t),f'(t),4f(t)5-16 描述描述某LTI系统的微分方程为 求在下列条件下的零输入响应和零状态响应。
f(t),,(t),y(0),1,y'(0),3 (1)。 ,,
,2tf(t),e,(t),y(0),1,y'(0),2 (2)。 ,,
h(t)g(t)5-17 求下列方程所描述的LTI系统的冲激响应和阶跃响应。
y''(t),4y'(t),3y(t),f'(t),3f(t) (1)
y(t)5-18 已知系统函数和初始状态如下,求系统的零输入响应。 zi
s,6
H(s),y(0),y'(0),1 (1), 2,s,5s,6
s,4
H(s),y(0),y'(0),y''(0),12 (3), ,,s(s,3s,2)
5-22 如图5-5所示的复合系统,由4个子系统连接组成,若各子系统的系统函数或冲激响应分别为
11,2tH(s),H(s),h(t),,(t)h(t)h(t),e,(t)21,,,,求复合系统的冲激响应。 34s,2s,1
,2t,3ty(t),(1,5e,5e),(t)f(t),,(t)5-26 如图5-7所示系统,已知当时,系统的零状态响应,zs
求系数a、b、c。
f(t),,(t)5-28 某LTI系统,在以下各种情况下起初始状态相同。已知当激励时,其全响应1
,t,tf(t),,(t)y(t),3e,(t)y(t),,(t),e,(t);当激励时,其全响应。 221
,2tf(t),e,(t) (1)若,求系统的全响应。3
,(t)u(t)5-29 如图5-8所示电路,其输入均为单位阶跃函数,求电压的零状态响应。
,1,jf(t),y(t)H(j),5-42 某系统的频率响应,求当输入为下列函数时的零状态响应。 zs1,j,
f(t),,(t)f(t),sint,(t) (1) (2)
5-50 求下列象函数的双边拉普拉斯变换。
2,2
,,3,Re[s],,1,1,Re[s],3 (1) (2) (s,1)(s,3)(s,1)(s,3)4,s,4
,,1,Re[s],0,Re[s],022 (3) (4) (s,4)(s,1)s,4
第六章
6.4 根据下列象函数及所标注的收敛域,求其所对应的原序列。
F(z),1 (1),全z平面
3F(z),z,z,, (2)
,1F(z),z,z,0 (3)
,2F(z),2z,1,z,0,z,, (4)
1 (5) F(z),,z,a,11,az
1 (6) F(z),,z,a,11,az
zzk,(k),1k,(k),6.5 已知,a(k),,,试利用z变换的性质求下列序列的z变换并注明收敛域。 ,2(z,1)z,a
1kk (1) (3) [1,(,1)],(k)(,1)k,(k)2
k(k,1),(k,1)k[,(k),,(k,4)] (5) (7)
,1kk (9) ()cos(),(k)22
limf(k)6.8 若因果序列的z变换如下,能否应用终值定理,如果能,求出。 F(z)k,,
22zz,1F(z), (1) (3) F(z),11(z,1)(z,2)(z,)(z,)23
6.10 求下列象函数的双边逆z变换。
211z, (1)F(z),,z, 113(z,)(z,)23
21zF(z),,z, (2) 112(z,)(z,)23
31zF(z),,z, (3) 122(z,)(z,1)2
311z (4) F(z),,,z,1322(z,)(z,1)2
6.11 求下列象函数的逆z变换。
1 (1) F(z),,z,12z,1
2z,zF(z),,z,1 (2) 2(z,1)(z,z,1)
zF(z),,z,1 (5) 2(z,1)(z,1)
2z,azF(z),,z,a (6) 3(z,a)
f(k),F(z)6.13 如因果序列,试求下列序列的z变换。
kkikaf(i)af(i) (1) (2) ,,i,0i,0
6.15 用z变换法解下列齐次差分方程。
y(k),0.9y(k,1),0,y(,1),1 (1)
y(k,2),y(k,1),2y(k),0,y(0),0,y(1),3 (3)
6.17 描述某LTI离散系统的差分方程为
y(k),y(k,1),2y(k,2),f(k)
1 已知,求该系统的零输入响应,零状态响应及全响应。 y(k)y(k)y(,1),,1,y(,2),,f(k),,(k)y(k)zizs4
6.19 图6-2为两个LTI离散系统框图,求各系统的单位序列响应和阶跃响应。 h(k)g(k)
6.20 如图6-2的系统,求激励为下列序列时的零状态响应。
1kf(k),k,(k) (1) (3) f(k),(),(k)3
6.23 如图6-5所示系统。
(1)求该系统的单位序列响应。 h(k)
1k (2)若输入序列,求零状态响应。 y(k)f(k),(),(k)zs2
6.24 图6-6所示系统,
(1)求系统函数; H(z)
(2)求单位序列响应; h(k)
(3)列写该系统的输入输出差分方程。
1kf(k),(),(k)6.26 已知某LTI因果系统在输入时的零状态响应为
2
11kk y(k),[2(),2()],(k)zs23求该系统的系统函数,并画出它的模拟框图。 H(z)
图6-12
y(,1),1y(,1),,16-29 已知某一阶LTI系统,当初始状态,输入时,其全响应;当初始状态,f(k),,(k)y(k),2,(k)11
11k输入时,其全响应。求输入时的零状态响应。 f(k),k,(k)f(k),(),(k)y(k),(k,1),(k)2222
k6.31 如图6-10所示的复合系统由3个子系统组成,已知子系统2的单位序列响应,子系统3h(k),(,1),(k)2
zf(k),,(k)的系统数,当输入时复合系统的零状态响应。求子系统1的单位序H(k),y(k),3(k,1),(k)31z,1
列响应。 h(k)1
6.33 设某LTI系统的阶跃响应为,已知当输入为因果序列时,其零状态响应 g(k)f(k)
k
y(k),g(i) ,zki,0求输入。 f(k)
6.34 因果序列满足方程 f(k)
k
f(k),k,(k),f(i) ,,0i求序列 。 f(k)
以下是大学体验英语综合教程2(第三版)课后翻译答案
Unit1
1. 任何年满18岁的人都有资格投票。(be eligible to, vote)
Answer:Anyone over the age of 18 is eligible to vote.
2. 每学期开学前,这些奖学金的申请
就会由学校发给每一个学生。(apply for, scholarship)
Answer:A form to apply for these scholarships is sent by the university to every student before the start of every semester.
3. 遵照医生的建议,我决定戒烟。(on the advice of)
Answer:On the advice of my doctor, I decided to give up smoking.
4. 公园位于县城的正中央。(be located in)
Answer:The park is located right in the center of town.
5. 这所大学提供了我们所需的所有材料和设备。(facilities)
Answer:The university provides all the materials and facilities we desire.
1. 他们花了多年的时间寻找内心的平静,但是收效甚微。(search for)
Answer:They spent many years searching for peace of mind, but with little success. 2. 这种新药的成功研制已经使许多疾病的治疗发生了根本性的变革。(revolutionize)
Answer:The successful development of the new drug has revolutionized the treatment of many diseases.
3. 由于这个国家的经济不景气,这家公司濒于破产。(on the edge of)
Answer:The company is on the edge of bankruptcy due to the economic depression in the country. 4. 大学毕业后他成为了一名护士。他认为护士这一职业可能很有发展前途。(rewarding)
Answer:He became a nurse after college. He thought nursing could be a very rewarding career. 5. 他像往常一样在文件上签了名。(just as)
Answer:He signed his name on the paper just as he has always done it.
Unit2
1. 警察们正忙着填写关于这场事故的各种表格。(fill out)
Answer:The policemen are busy fi lling out forms about the accident. 2. 我想在还车之前把油箱加满。(fill up, fuel tank)
Answer:I want to fi ll up the fuel tank before returning the car.
3. 如果你要投诉,最好遵循正确的程序。(follow the procedure)
Answer:If you want to make a complaint, you’d better follow the correct procedure.
4. 要不是约翰帮忙,我们绝不会这么快就完成实验。(without)
Answer:We couldn’t have fi nished the experiment so soon without John’s help.
5. 暴风雨之后,岸边的人们焦急地搜索湖面以期发现小船的踪迹。(scan for)
Answer:After the storm, the people on the shore anxiously scanned the lake for any sign of the boat.
1. 这个国家不大,但是在国际事务中它却发挥着重要作用。(play a role)
Answer:This country is not big, but it plays an important role in international affairs. 2. 正是在我叔叔的帮助下,我得以克服困难,按时完成了任务。(it is ... that)
Answer:It was with the help of my uncle that I overcame the difficulty and completed the assignment in time.
3. 毕业时他决定留在北京,而他最好的朋友却选择了去西藏。(while)
Answer:While he decided to stay in Beijing upon graduation, his best friend chose to go to Tibet. 4. 在这次校园英语演讲比赛中,我们班的玛丽获得了第三名。(come in)
Answer:In this Campus English Speaking Contest, Mary from our class came in third. 5. 你应该知道学习弹钢琴需要有时间,有金钱,还要有毅力。(as well as)
Answer:You should know that it takes time, money as well as perseverance to learn to play the piano.
Unit3
1. 我发现量入为出地过日子越来越难了。(increasingly)
Answer:I find it increasingly difficult to live within my income.
2. 现代政治家们都试图以电视
来影响普通百姓。(reach out)
Answer:Modern politicians try to reach out to ordinary people in their TV speeches. 3. 应该帮助学生对人生采取积极的态度。(adopt)
Answer:Pupils should be helped to adopt a positive attitude to life.
4. 希望全班同学参加这些讨论。(participate in)
Answer:Everyone in the class is expected to participate in these discussions. 5. 如果你犯了罪就必须受到惩罚。(crime)
Answer:If you commit a crime you must expect to be punished.
1.儿子的死让老妇人变得麻木痴呆了。(numb)
Answer:The old woman was numbed by her son’s death.
2.身处所有这些烦恼之中,他依然能保持乐观。(in the midst)
Answer:In the midst of all troubles, he managed to remain cheerful. 3. 虽有困难,他们还是设法坚持试验下去。(carry on)
Answer:They managed to carry on their experiments in spite of the difficulties.
4.我们必须淘汰不合格的申请人。(weed out)
Answer:We have to weed out unqualified applicants. 5. 医生要他减少抽烟。(cut down on)
Answer:The doctor told him to cut down on smoking.
Unit4
1.她在公共汽车站一直等到末班车进站。(come in)
Answer:She waited at the bus stop until the last bus came in. 2.如果我们能帮得上忙,尽管和我们联系。(contact)
Answer:If there is any way we can be of assistance, please do not hesitate to contact us.
3 .他需要多少船务人员才能使他的游艇航行,(crew, yacht)
Answer:How many crew does he need to sail his yacht? 4 .虽然她的新书没有上一本好,但是我还是喜欢它。(not quite as)
Answer:I enjoyed her new book though it’s not quite as good as her last one.
5 .我从未遇到过如此善良的人。(never before)
Answer:Never before have I met such a kind person. 1.公共汽车放慢速度并停下,让那位乘客上车。(slow down)
Answer:The bus slowed down and stopped to allow the passenger to get on board.
2.许多车子都驶过去了,可是没有一辆愿意让我们搭便车。(roll by)
Answer:Many vehicles rolled by, but no one offered us a ride. 3 .请勿践踏草地。(get off)
Answer:Please get off the grass.
4.他按妻子的吩咐,一下班就去了市场。(make one’s way)
Answer:He made his way to the marketplace right after work, as his wife had asked him to do. 5 .值得庆幸的是,史蒂夫 (Steve) 从自行车上摔下来时没有摔断骨头。(luckily)
Answer:Luckily, Steve didn’t break any bones when he fell off his bike.
Unit5
1. 我们得把感情放在一边,从专业的角度来对待这件事。(from a professional standpoint)
Answer:We have to put aside our emotions and take it from a professional standpoint. 2. 这部戏非常精彩,我很快就沉浸于激动人心的剧情之中。(lose oneself in)
Answer:The play was so wonderful that I soon lost myself in the excitement of it. 3 .她没有什么爱好——除非你把看电视也算是一种爱好。(unless)
Answer:She hasn’t got any hobbies — unless you call watching TV a hobby.
4. 他说他是直接从市长本人那里得到这个信息的。(first-hand)
Answer:He said that he had got the information first-hand from the Mayor himself. 5 .既然你不能回答这个问题,我们最好问问别人。(since)
Answer:Since you can’t answer the question, perhaps we’d better ask someone else.
1. 由于公共汽车司机突然刹车,旅客们都不由自主地向前摔倒。(brake, pitch forward)
Answer:All the passengers pitched forward because the bus driver braked sharply. 2. 这个协议将冲破对自由贸易设置的障碍。(break through, obstacle)
Answer:This agreement will break through the obstacles to free trade. 3 .我刚放下叫出租车的电话,车就来了。(soon after)
Answer:The taxi arrived soon after I rang for it.
4. 在过去,不管我什么时候到家,我父母总会等我。(no matter)
Answer:My parents always waited up for me no matter what time I got home. 5 .由于没有一方愿意让步,两个公司之间的对话完全破裂了。(break down)
Answer:Talks between the two companies completely broke down, because neither of them wanted to give in.
Unit6
1. 那件工作很难做,不过我想试试看。(have a shot)
Answer:It’s a difficult job, but I’d like to have a shot.
2. 这是一本关于商务实践而非理论的书。(as opposed to)
Answer:This is a book about business practice as opposed to theory. 3. 社会活动从未耽误她的学习。(in the way)
Answer:Social activities never get in the way of her studies. 4. 直到1911年人们才发现第一种维生素。(It is not until ... that)
Answer:It was not until 1911 that the first of the vitamins was identified. 5. 尽管年事已高,爷爷每天还帮忙做家务。(despite)
Answer:Despite advanced years, Grandpa helps do housework every day.
1. 我们的婚姻很幸福,但我们也曾经历过许多坎坷。(ups and downs)
Answer:Our marriage is happy but we’ve had many ups and downs.
2. 许多外语教师常常在课堂上自顾自地讲得太多。(be inclined to)
Answer:Many teachers of foreign languages are inclined to talk too much themselves in class.
3. 那位著名演员每天早晨锻炼一小时以保持健康。(work out)
Answer:The famous actor keeps fit by working out for an hour every morning. 4. 与他促膝长谈之后,她的怀疑消失了。(melt away)
Answer:After a long heart-to-heart talk with him, her suspicion melted away. 5. 目前我们没有职位空缺,但我们肯定会记住您的申请。(keep in mind)
Answer:We have no vacancies now, but we’ll certainly keep your application in mind.
Unit7
1. 他并不后悔说过的话,只是觉得他完全可以不用这种方式表达。(could have done)
Answer:He did not regret what he had said but felt that he could have expressed it differently.
2. 我们最好等到12月14日。那时大卫已考完试,就能和我们一起去度假了。(will have done)
Answer:We’d better wait till 14 December. David will have had his exam by then, so he’ll be able to go on holiday with us. 3. 他正在做一个新项目,年底前必须完成。(work on)
Answer:He’s working on a new project which has to be finished by the end of the year.
4. 他们让我们使用他们的实验室,作为回报,我们则让他们分享研究成果。(in return)
Answer:They are letting us use their lab, and in return, we are sharing with them the results of our research.
5. 诸如打电话、听电话一类的事情占用了这位秘书的大部分时间。(take up)
Answer:Such things as making and answering telephone calls take up most of the secretary’s time.
1. 他们把房子卖了后就到加拿大和女儿住在一起。(go off)
Answer:They sold their house and went off to live in Canada with their daughter. 2. ——你下星期这个时候会在干什么,
——还是像平常一样干活。(will be doing)
Answer:What will you be doing this time next week?I’ll be working as usual.
3. 他既聪明又勤奋,不久就接管了杂志的编辑工作。(editing; before long)
Answer:He was intelligent and hard-working and before long he took over the editing of the magazine.
4. 你话还没说完别人就挂断电话,难道你不恼火吗,(hang up)
Answer:Don’t you hate it when someone hangs up on you before you finish speaking?
5. 让他们感到惊恐的是,他们的房顶着火了。(to one’s horror)
Answer:To their horror, the roof of their house caught fire.