5 The discrete-time Fourier transform

《信号与系统》专业术语中英文对照表第 1 章绪论信号（signal）系统（system）电压（voltage）电流（current）信息（information）电路（circuit）网络（network）确定性信号（determinate signal）随机信号（random signal）一维信号（one–dimensional signal）多维信号（multi–dimensional signal）连续时间信号（continuous time signal）离散时间信号（discrete time signal）取样信号（sampling signal）数字信号（digital signal）周期信号（periodic signal）非周期信号（nonperiodic（aperiodic）signal）能量（energy）功率（power）能量信号（energy signal）功率信号（power signal）平均功率（average power）平均能量（average energy）指数信号（exponential signal）时间常数（time constant）正弦信号（sine signal）余弦信号（cosine signal）振幅（amplitude）角频率（angular frequency）初相位（initial phase）周期（period）频率（frequency）欧拉公式（Euler’s formula）复指数信号（complex exponential signal）复频率（complex frequency）实部（real part）虚部（imaginary part）抽样函数Sa(t)（sampling（Sa）function）偶函数（even function）奇异函数（singularity function）奇异信号（singularity signal）单位斜变信号（unit ramp signal）斜率（slope）单位阶跃信号（unit step signal）符号函数（signum function）单位冲激信号（unit impulse signal）广义函数（generalized function）取样特性（sampling property）冲激偶信号（impulse doublet 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half–cosine signal）周期全波余弦信号（periodic full–cosine signal）傅里叶逆变换（inverse Fourier transform）频谱密度函数（spectrum density function）单边指数信号（single–sided exponential signal）双边指数信号（two–sided exponential signal）对称矩形脉冲信号（symmetry rectangular pulse signal）线性（linearity）对称性（symmetry）对偶性（duality）位移特性（shifting）时移特性（time–shifting）频移特性（frequency–shifting）调制定理（modulation theorem）调制（modulation）解调（demodulation）变频（frequency conversion）尺度变换特性（scaling）微分与积分特性（differentiation and integration）时域微分特性（differentiation in the time domain）时域积分特性（integration in the time domain）频域微分特性（differentiation in the frequency domain）频域积分特性（integration in the frequency domain）卷积定理（convolution theorem）时域卷积定理（convolution theorem in the time domain）频域卷积定理（convolution theorem in the frequency domain）取样信号（sampling signal）矩形脉冲取样（rectangular pulse sampling）自然取样（nature sampling）冲激取样（impulse sampling）理想取样（ideal sampling）取样定理（sampling theorem）调制信号（modulation signal）载波信号（carrier signal）已调制信号（modulated signal）模拟调制（analog 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theorem）终值定理（expiration-value）复频域卷积定理（convolution theorem in the complex frequency domain）部分分式展开法（partial fraction expansion）留数法（residue method）第 5 章策动点函数（driving function）转移函数（transfer function）极点（pole）零点（zero）零极点图（zero-pole plot）暂态响应（transient response）稳态响应（stable response）稳定系统（stable system）一阶系统（first order system）高通滤波网络（high-low filter）低通滤波网络（low-pass filter）二阶系统（second system）最小相移系统（minimum-phase system）维纳滤波器（Winner filter）卡尔曼滤波器（Kalman filter）低通（low-pass）高通（high-pass）带通（band-pass）带阻（band-stop）有源（active）无源（passive）模拟（analog）数字（digital）通带（pass-band）阻带（stop-band）佩利－维纳准则（Paley-Winner criterion）最佳逼近（optimum approximation）过渡带（transition-band）通带公差带（tolerance band）巴特沃兹滤波器（Butterworth filter）切比雪夫滤波器（Chebyshew filter）方框图（block diagram）信号流图（signal flow graph）节点（node）支路（branch）输入节点（source node）输出节点（sink node）混合节点（mix node）通路（path）开通路（open path）闭通路（close path）环路（loop）自环路（self-loop）环路增益（loop gain）不接触环路（disconnect loop）前向通路（forward path）前向通路增益（forward path gain）梅森公式（Mason formula）劳斯准则（Routh criterion）第 6 章数字系统（digital system）数字信号处理（digital signal processing）差分方程（difference equation）单位样值响应（unit sample response）卷积和（convolution sum）Z 变换（Z transform）序列（sequence）样值（sample）单位样值信号（unit sample signal）单位阶跃序列（unit step sequence）矩形序列(rectangular sequence)单边实指数序列（single sided real exponential sequence）单边正弦序列（single sided exponential sequence）斜边序列（ramp sequence）复指数序列（complex exponential sequence）线性时不变离散系统（linear time-invariant discrete-time system）常系数线性差分方程（linear constant-coefficient difference equation）后向差分方程（backward difference equation）前向差分方程（forward difference equation）海诺塔（Tower of Hanoi）菲波纳西（Fibonacci）冲激函数串（impulse train）第7 章数字滤波器（digital filter）单边Z 变换（single-sided Z transform）双边Z 变换(two-sided (bilateral) Z transform)幂级数（power series）收敛（convergence）有界序列（limitary-amplitude sequence）正项级数（positive series）有限长序列（limitary-duration sequence）右边序列（right-sided sequence）左边序列（left-sided sequence）双边序列（two-sided sequence）Z 逆变换（inverse Z transform）围线积分法（contour integral method）幂级数展开法（power series expansion）z 域微分（differentiation in the z-domain）序列指数加权（multiplication by an exponential sequence）z 域卷积定理（z-domain convolution theorem）帕斯瓦尔定理（Parseval theorem）传输函数（transfer function）序列的傅里叶变换（discrete-time Fourier transform：DTFT）序列的傅里叶逆变换（inverse discrete-time Fourier transform：IDTFT）幅度响应（magnitude response）相位响应（phase response）量化（quantization）编码（coding）模数变换（A/D 变换：analog-to-digital conversion）数模变换（D/A 变换：digital-to- analog conversion）第8 章端口分析法（port analysis）状态变量（state variable）无记忆系统（memoryless system）有记忆系统（memory system）矢量矩阵（vector-matrix ）常量矩阵（constant matrix ）输入矢量（input vector）输出矢量（output vector）直接法（direct method）间接法（indirect method）状态转移矩阵（state transition matrix）系统函数矩阵（system function matrix）冲激响应矩阵（impulse response matrix）朱里准则（July criterion）。

137Chapter 7 Answers7.1 From the Nyquist sampling theorem , we know that only if X (j w)=0 for |w| > w s /2 will be signal be recoverable from its samples. Therefore, X(jw)>5000л.7.2 From the Nyquist theorem ,we know that the sampling frequency in this case must be at least w s =2000п.In other words ,the sampling period should be at most T=2п/ (w s )=1＊10-3.Clearly ,only (a) and (e) satisfy this condition.7.3 (a) We can easily show that X(j w)=0 for |w| >4000п.Therefore, the Nyquist rate for this signal is w N =2(4000п)=8000п.(b)From the Tables 4.1 and 4.2 we know that X(j w) is a rectangular pulse for which X(j w)=0 for |w| > 4000п.Therefore, the Nyquist rate for this signal is w N =2(4000п)=800п.(c) From the Tables 4.1 and 4.2 we know that X(j w) is the convolution of two rectangular pulses each of which is zero for |w| > 4000п.Therefore ,X(j w)=0 for |w| >8000пand the Nyquist rate for this signal is w N =2(8000п)=16000п.7.4 If the signal x(t) has a Nyquist rate of w o ,then its Fourier transform X (j w)=0 for |w| > w o /2. (a) From chapter 4,y(t) = x (t) + x (t-1) −→←FTY (jw) = X (jw) + e -jwt X (jw).Clearly, we can only guarantee that Y (jw) =0 for |w| > w o /2. Therefore, the Nyquist rate for y(t) is also w o . (b) From chapter 4,y(t) = dtt dx )( −→←FTY (jw)= jw X(jw).Clearly, we can only guarantee that Y (jw) =0 for |w| > w o /2. Therefore, the Nyquist rate for y(t) is also w o . (c) From chapter 4,y(t) =x 2(t) −→←FTY (jw)= (1/2п)[X(jw)*X(jw)]Clearly, we can only guarantee that Y (jw) =0 for |w| > w o . Therefore, the Nyquist rate for y(t) is also 2w o . (d) From chapter 4,y(t)=x(t)cos (w o t) −→←FTY (jw)= (1/2)X(j(w- w o )) +(1/2)X(j(w+ w o )).Clearly, we can guarantee that Y (jw) =0 for |w| > w o + w o /2. Therefore, the Nyquist rate for y(t) is 3w o. 7.5 Using Table 4.2,p(t) −→←FT Tπ2∑∞-∞=-K T K )/2(πωδFrom Table 4.1 p(t-1) −→←FT Tπ2 e -jw T jk k eTk ππωδ2)2(-∞-∞=∑-. Since y(t)=x(t)p(t-1),we haveY (jw)= (1/2п)[X(jw)*FT{P(t-1)}]=(1/T)T jk K e Tk j X ππω2))2((-∞-∞=∑-Therefore, Y(j ω) consists of replicates of X(j ω) shifted by k2π/T and added to earth other (see Figure⎩⎨⎧≤=otherwiseT j H c ,0||,)(ωωωWhere (2/0ω)<c ω<(2π/T) - (2/0ω).7.6 Consider the signal w(t)=x 1(t)x 2(t).The Fourier transform W(j ω) of w(t) is given by W(j ω)=π21[])(*)(21ωωj X j X .Since 0)(1=ωj X for |ω|≥1ωand X 2(j ω)=0 for |ω|≥2ω, we may conclude that W(j ω)=0 for |ω|≥1ω+2ω.Consequently ，the Nyquist rate for w(t) iss ω=2(1ω+2ω).Therefore ,the maximum sampling138period which would still allow w(t) to be recovered is T=2π/(s ω)=π/(1ω+2ω). 7.7 We note thatx 1(t) =h 1(t)*{∑∞-∞=-n nT t nT x )()(δ}Form Figure 7.7 in the book ,we know that the output of the zero-order hold may be written as x 0(t)=h 0(t)* {∑∞-∞=-n nT t nT x )()(δ}where h 0(t) is as shown in Figure S7.7 By taking the Fourier transform of the two above equations, we have X 1(j ω)=H 1( j ω)X p ( j ω)X 0(j ω)=H 0( j ω) X p ( j ω)We now need to determine a frequency response H d ( j ω) for a filter which produces x 1(t) at its output when x 0(t) is its input. Therefore, we needX 0(j ω) H d ( j ω)= X 1(j ω)The triangular function h 1(t) may be obtained by convolving two rectangular pulses as shown in Figure S7.7Therefore,h 1(t)={(1/T ) h 0(t+T/2)}*{( 1/T ) h 0(t+T/2)} Taking the Fourier transform of both sides of the above equation, H 1( j ω)=T1e T j ω H 0( j ω) H 0( j ω) ThereforeX 1(j ω)= H 1( j ω) X p ( j ω)=T 1e T j ω H 0( j ω) H 0( j ω) X p ( j ω) =T1e Tj ω H 0( j ω) X 0(j ω)ThereforeH d ( j ω)=T1eTj ω H 0( j ω)=e2/jwT TT ωω)2/sin(2 7.8 (a) Yes, aliasing does occur in this case .This may be easily shown by considering the sinusoidal term of x(t) for k=5. This term is a signal of the form y(t)=(1/2)5sin(5πt).If x(t) is sampled as T=0.2, then we will always be sampling y(t) at exactly its zero-crossings (This is similar to the idea presented in Figure 7.17 of your textbook). Therefore ,the signal y(t) appears to be identical to the signal (1/2)5sin(0πt) for frequency 5π is a liased into a sinusoid of frequency 0 in the sampled signal.(b) The lowpass filter performs band limited interpolation on the signal ∧x(t).But since aliasing has alreadyresulted in the loss of the sinusoid (1/2)5sin(5πt),the output will be of the formx γ(t)=k k )21(40∑= sin(k πt)The Fourier series representation of this signal is of the form139x γ(t)=∑-=44k k a e )/(t k j π-Where a k =-j(1/2)1+kj(1/2)1+-k7.9 The Fourier transform X(jWe know from the results on impulse-train sampling thatG(jw)=∑∞∞--ωωk j X T ((1s )),Where T=2π/s ω=1/75.therefore,G(jw) is as shown in Figure S7.9 .Clearly, G(jw)=(1/T)X(j ω)=75 X(j ω) for |ω|≤50π.7.10 (a) We know that x(t) is not a band-limited signal. Therefore, it cannot undergo impulse-train sampling without aliasing.(b) Form the given X(j ω) it is clear that the signal x(t) which is bandlimited. That is, X(j ω)=0 for |ω|>0ω.Therefore, it must be possible to perform impulse-train sampling on this signal without experiencing aliasing. The minimum sampling rate required would bes ω=20ω,This implies that thesampling period can at most be T=2π/s ω=π/0ω(c) When x(t) undergoes impulse train sampling with T=2π/0ω,we would obtain the signal g(t) with Fourier transformG(jw)= T1∑∞-∞=-k T k j X ))/2((πωFigure S7.10It is clear from the figure that no aliasing occurs, and that X(jw) can be recovered by using a filter with frequency response T 0≤ωω≤0 H(jw)= 0 otherwiseTherefore, the given statement is true. 7.11 We know from Section 7.4 thatX d (ωj e )= T1∑∞-∞=-k cT k j X ))/2((πω(a) Since X d (ωj e) is just formed by shifting and summing replicas of X(jw),we may argue that ifX d (ωj e ) is real , then X(jw) must also be real(b) X d (ωj e) consists of replicas of X(jw) which are scaled by 1/T,Therefore,if X d (ωj e) has amaximum of 1, then X(jw) must also be real.(c) The region πωπ≤≤||4/3in the discrete-time domain corresponds to the regionT T /||)4/(3πωπ≤≤ in the discrete-time domain. Therefore ,if X d (ωj e )=0 forπωπ≤≤||4/3,then X(jw)=0 for πωπ2000||1500≤≤,But since we already have X(jw)=0 for140πω2000||≥,we have X(jw)=0 for πω1500||≥(d) In this case, sinceπ in discrete-time frequency domain corresponds to 2000π in the continuous-time frequency domain, this condition translates to X(jw)=(j(ω-2000π))7.12 Form Section 7.4 ,we know that the discrete and continuous-time frequencies Ω and ω are related by Ω=ω.Therefore, in this case for Ω=43π,we find the corresponding value of ω toω=43πT1=3000π/4=7500π7.13 For this problem ,we use an approach similar to the one used in Example 7.2 .we assume thatx c (t)=tT t ππ)/sin(The overall output isy c (t)= x c (t-2T)= )2()]2)(/sin[(T t T t T --ππForm x c (t). We obtain the corresponding discrete-time signal x d [n] to be x d [n]= x c (nT)= T1][n δalso, we obtain from y c (t),the corresponding discrete-time signal y d [n] to be y d [n]= y c (nT) =)2()]2(sin[(--n T n ππWe note that the right-hand side of the above equation is always zero when n ≠2.When n=2 ,wemay evaluate the value of ratio using L ,Hospital ,s rule to be 1/T ,Thereforey d [n]= T1]2[-n δWe conclude that the impulse response of the filter is h d [n]= ]2[-n δ7.14 For this problem ,we use an approach similar to the one used in Example 7.2.We assume that x c (t)= tT t ππ)]/sin[(The overall output isy c (t)=)2(T t x dt d c -=)2/()]2/()/[()/(T t T t T COS T ---πππ-2))2/(()]2/)(/sin[(T t T t T --πππForm x c (t) , we obtain the corresponding discrete-time signal x d [n] to be x d [n]= x c (nT)= T1][n δAlso, we obtain from yc(t),the corresponding discrete-time signal y d [n] to beY d [n]=y c (nT)=)2/1()]2/1(cos[)/(--n T n T πππ- )2/1()]2/1(sin[--n T n ππThe first term in rig πht-hang side of the above equation is always zero because cos[π(n-1/2)]=0, therefore, y d [n]= )2/1()]2/1(sin[--n T n ππWe conclude that the impulse response of the filter is h d [n]= )2/1()]2/1(sin[--n T n ππ7.15. in this problem we are interested in the lowest rate which x[n] may be sampled without the possibility of aliasing, we use the approach used in Example 7.4 to solve this problem. To find the lowest rate at which x[n] may be sampled while avoiding the possibility of aliasing, we must find an N such that (22≥Nπ)73πN ≤7/37.16 Although the signal x 1[n]=2sin(πn/2)/( πn) satisfies the first tow conditions, it does not satisfy the thirdcondition . This is because the Flurries transform X 1(e j ω) of this signal is rectangular pulse which is zero for π/2<|ω|<π/2 We also note that the signal x[n]=4[sin(πn/2)/(πn)]2 satisfies the first tow conditions. Fromour numerous encounters with this signal, we know that its Fourier transform X(e j ω) is given by the periodic141convolution of X 1(e j ω) with itself. Therefore, X(e j ω) will be a triangular function in the range 0≤|ω|≤π. This obviously satisfies the third condition as well. T therefore, the desired signal is x[n]=4[sin(πn/2)/(πn)]2.7.17 In this problem .we wish to determine the effect of decimating the impulse response of the given filter by a factor of 2. As explained in Section 7.5.2 ,the process of decimation may be broken up into two steps. In the first step we perform impulse train sampling on h[n] to obtain H p [n]∑∞-∞=k h[2k]δ[n-2k]The decimated sequence is then obtained using h 1[n]=h[2n]=h p [2n]Using eq (7.37), we obtain the Fourier transform H p (e j ω) of h p [n] to beH 1(e j ω)=H p (e jω/2)In other words , H 1(e j ω) is H p (e j ω/2) expanded by a factor of 2. This is as shown in the figure above. Therefore, h 1[n]=h[2n] is the impulse response of an ideal lowpass filter with a passband gain of unity and a cutoff frequency of π/27.18 From Figure 7.37,it is clear interpolation by a factor of 2 results in the frequency response getting compressed by a factor of 2. Interpolation also results in a magnitude sealing by a factor of 2. Therefore, in this problem, the interpolated impulse response will correspond to an ideal lowpass filter with cutoff frequency π/ and a passband gain of 2.7.19 The Fourier transform of x[n] is given by1 |ω|≤ω1X(e j ω)= 0 otherwiseThis is as shown in Figure 7.19.(a) when ω1 ≤3π/5, the Fourier transform X 1(e j ω) of the output of the zero-insertion system is shown inFigure 7.19. The output w(e j ω) of the lowpass filter is as shown in Figure 7.19. The Fourier transform of theoutput of the decimation system Y(e j ω) is an expanded or stretched out version of W(e j ω). This is as shown in Figure 7.19.therefore, y[n]=51nn πω)3/5sin(1(b) When ω1＞3π/5, the Fourier’s transform X 1(e j ω) of the output of the zero-insertion system is as shownin Figure 7.19 The output W(e j ω142The Fourier transform of the output of the decimation system Y(e j ω) bis an expanded or stretched outversion of W(e j ω) .This is as shown in Figure S7.19. Therefore,y[n]=][51n δ7.20 Suppose that X(e j ω) is as shown in Figure S7.20, then the Fourier transform X A (e j ω) of the output of theoutput of S A , the Fourier transform X 1(e j ω) of the output of the lowpass filter , and the Fourier transform X B (e j ω) of the output of S B are all shown in the figures below. Clearly this system accomplishes the filtering task .Figure S7.20(b) Suppose that X(e j ω) is as shown in Figure S7.20 ,then the Fourier transform X B (e j ω) of the output ofS B ,the Fourier transform X 1(e j ω)of the output of the first lowpass filter ,the Fourier transfore X A (e j ω) of theoutput of S A ,the Fourier transform X 2(e j ω) of the output of the first lowpass filter are all shown in the figure below .Clearly this system does not accomplish the filtering task. 7.21(a) The Nyquist rate for the given signal is 2×5000π=10000π. Therefore in order to be able to recover x(t)from x p (t) ,the sampling period must at most be T max =2π/10000π=2×10-4 sec .Since the sampling period used is T=10-4＜T max ,x(t) can be recovered from x p (t).(b) The Nyquist rate for the given signal is 2×15000π=30000π. Therefore in order to be able to recover x(t)from x p (t) ,the sampling period must at most be T max =2π/30000π=0.66×10-4 sec .Since the sampling period used is T=10-4＞T max , x(t) can not be recovered from x p (t).(c) Here,I m {X(j ω)} is not specified. Therefore, the Nyquist rate for the signal x(t) is indeterminate. Thisimplies that one cannot guarantee that x(t) would be recoverable from x p (t).(d) Since x(t) is real,we may conclude that X(j ω)=0 for |ω|＞5000. Therefore the answer to this part isidentical to that of part (a)(e) Since x(t) is real, X(j ω)=0 for |ω|＞15000π. Therefore the answer to this part is identical to that of part(b)(f) If X(j ω)=0 for |ω|＞ω1,then X(j ω)*X(j ω)=0 for |ω|＞2ω1,Therefore in this part X(j ω)=0 for |ω|＞7500. The Nyquist rate for this signal is 2×7500π=15000π. Therefore in order to be able to recover x(t) from x p (t) ,the sampling period must at most be T max =2π/15000π=1.33×10-4 sec .Since the sampling period used is T=10-4＜T max , x(t) can be recovered from x p (t). (g)If |X(j ω)|=0 for ω＞5000π,then X(j ω)=0 for |ω|＞5000π. Therefore the answer to this part is identical to that of part (a).7.22 Using the properties of the Fourier transform, we obtain Y(j ω)=X 1(j ω)X 2(j ω).Therefore, Y(j ω)=0 for |ω|＞1000π.This implies that the Nyquist rate for y(t) is2×1000π=2000π.Therefore, the sampling period T can at most be 2π/(2000π)=10-3sec. Therefore we have to use T<10-3sec in order to be able to recover y(t) from y p (t). 7.23(a) We may express p(t) asP(t)=p 1(t)-p 1(t-△);Where p 1(t)=∑∞-∞=∆-k k t )2(δnow,143P 1(j ω)=∆π∑∞-∞=∆-k )/(πωδTherefore,P(j ω)= P 1(j ω)-e -j ω∆P 1(j )ωIs as shown in figure S7.23. Now,X p (j ω)=)](*)([21ωωπjP j XTherefore, X p (j ω) is as sketched below for △<π/(2ωM ),The corresponding Y(j ω) is also sketched in figure S7.23.(b) The system which can be used to recover x(t) from x p (t) is as shown in FigureS7.23. (c) The system which can be used to recover x(t) from x(t) is as shown in FigureS7.23.(d) We see from the figures sketched in part (a) that aliasing is avoided when ωM ≤π/△.therefore, △max =π/ωM.7.24 we may impress s(t) as s(t)=s(t)-1,where s(t) is as shown in Figure S7.24 we may easily show thats (j )ω= ∑∞-∞=-∆k T k kT k )/2()/2sin(4πωδπFrom this, we obtainS(j =-=)(2)()ωπδωωj S∑∞-∞=-∆k T k k T k )/2()/2sin(4πωδπ-2)(ωπδ Clearly, S(j ω) consists of impulses spaced every 2π/T.(a) If △=T/3, thenS(j =)ω∑∞-∞=-k T k kk )/2()3/2sin(4πωδπ-2)(ωπδNow, since w(t)=s(t)x(t),πω21)(=j W ∑∞-∞=--k X T k j X kk )(2))/2(()3/2sin(4ωππωπTherefore, W(j ω)consists of replicas of X(j ω) which are spaced 2π/T apart. Tn order to avoid aliasing,ωW should be less that π/T. Therefore, T max =2π/ωW. (b) If △=T/3, then(a)(b)()jw Figure S7.24x144S(j =)ω∑∞-∞=-k T k k k )/2()4/2sin(4πωδπ-2)(ωπδ we note that S(j ω)=0 for k=0,±2, ±4,…..This is as sketched in Figure S7.24.Therefore, the replicas of X(j ω)in W(j ω) are now spaced 4π/T apart. Tn order to avoid aliasing,ωW should be less that2π/T. Therefore, T max =2π/ωW. 7.25 Here, x T (kT) can be written asX T (kT)= ∑∞-∞=--k nT x n k n k )()()](sin[ππNote that when n ≠k,0)()](sin[=--n k n k ππAnd when n=k,1)()](sin[=--n k n k ππ Therefore,x τ(kT)=x(kT)7.26. We note thatp(j ω)=Tπ2δ(ω－k2π/T)Also, since x p (t)=x(t)p(t).X p (j ω)=12π{ x(j ω) * P(j ω)}=1Tx(j(ω－k2π/T))Figure S7.26Note that as T increase, Tπ2－ω2 approaches zero. Also, we note that there is aliasingWhen2ω1-ω2<Tπ2－ω2<ω2If 2ω1-ω2≥0(as given) then it is easy to see that aliasing does not occur when 0≤Tπ2－ω2≤2ω1－ω2For maximum T, we must choose the minimum allowable value for Tπ2－ω2 (which is zero).This implies that T max =2π/ω2. We plot x p (j ω) for this case in Figure S7.26. Therefore, A=T, ωb =2π/T, and ωa =ωb －ω11457.27.(a) Let x 1(j ω) denote the Fourier transform of the signal x 1(t) obtained by multiplyingx(t) with e -j ω0t Let x 2(j ω) be the Fourier transform of the signal x 2(t) obtained at the output of the lowpass filter. Then, x 1(j ω), x 2(j ω),and x p (j ω),are as shown in Figure S7.27(b) The Nyquist rate for the signal x 2(t) is 2×(ω2－ω1)/2=ω2－ω1.Therefore, thep 7.28. (a) The fundamental frequency of x(t) is 20π rad/sec.From Chapter 4 we know that the Fourier transform of x(t) is given byX(j ω)=2πk ∞=-∞∑a k δ(ω－20πk).This is as sketched below. The Fourier transform x c (j ω) of the signal x c (t) is also Sketched in Figure S7.28. Note thatP(j ω)=2510π⨯3(2/(510))k k δωπ∞-=-∞-⨯∑Andx p (j ω)=12π[ x c (j ω)* p(j ω)]Therefore, x p (j ω) is as shown in the Figure S7.28.Note that the impulses from adjacentReplicas of x c (j ω) add up at 200π.Now the Fourier transform x(e j Ω) of the sequence x[n] is given byx(e j Ω)= x p (j ω)|ω=ΩT. This is as shown in the Figure S7.28.Since the impulses in x(e j ω) are located at multiples of a 0.1π,the signal x[n] is146(b) The Fourier series coefficients of X[n] aT π2(12)k , k=0,±1,±2,….,±9 a k =4T π(12)10 , k=10 7.29. x p (j ω)=1T((2/))k x j k T ωπ∞=-∞-∑x(jwe ), Y(jwe ), Y p (j ω),and Y c (j ω) are as shown in Figure S7.29. 7.30. (a) Since x c (t)=δ(t),we have()c dy t dt+y c (t)= δ(t) Taking the Fourier transform we obtainj ωY(j ω)+ Y(j ω)=1 Therefore , Y c (j ω)=11j ω+, and y c (t) =e -t u(t). (b) Since y c (t) =e -tu(t) , y[n]= y c (nT)= e -nT u[n].Therefore, j ωH(e j ω)=()()j W e Y e ω=11/(1)T j e e ω---=1－e －T e －j ωTherefore,h[n]= δ[n]－e －T δ[n －1]7.31. In this problem for the sake of clarity we will use the variable Ωto denote discretefrequency. Taking the Fourier transform of both sides of the given difference equation we obtainH(j e Ω)=()()j j Y e X e ΩΩ=1112j e -Ω-Given that the sampling rate is greater than the Nyquist rate, we have147x(j eΩ)=1Tx c (j Ω/T), for －π≤Ω≤π Therefore,Y(j eΩ)=1(/)12c j x j T T e -ΩΩ-For －π≤Ω≤π.From this we getY(j ω)= Y(jw eT)= =1()12c j Tx j T e ωω--For －π/T ≤ω≤π/T. in this range, Y(j ω)= Y c (j ω).Therefore,H c (j ω)=()()c c Y j X j ωω=1/112j TT e ω--7.32. Let p[n]=[14]k n k δ∞=-∞--∑.Then from Chapter 5,p(jwe )= e -j ω24π(2/4)k k δωπ∞=-∞-∑=2π2/4(2/4)j k k k eπδωπ∞--=-∞∑Therefore, G(jw e )=()1()()2j j p e x e d πθωθπθπ--⎰=32/4(2/4)01()4j k j k k e x e πωπ--=∑jwjwFigure S7.32Clearly, in order to isolate just x(jwe ) we need to use an ideal lowpass filter with Cutoff frequency π/4 and passband gain of 4. Therefore, in the range |ω|<π, 4, |ω|<π/4H(e j ω)= 0, π/4≤|ω|≤π7.33. Let y[n]=x[n][3]k n k δ∞=-∞-∑.ThenY(e j ω)=3(2/3)1()3j k k x eωπ-=∑Note that sin(πn/3)/(πn/3) is the impulse response of an ideal lowpass filter with cutoff frequency π/3 and passband gain of 3.Therefore,we now require that y[n] when passed through this filter should yieldx[n].Therefore, the replicas of x(e j ω) contained in Y(e j ω) should not overlap with one another. This ispossible only if x(e j ω) =0 for π/3≤|ω|≤π.7.34. In order to make x(e j ω) occupy the entire region from －πto π,the signal x[n]148must be downsampled by a factor of 14/3.Since it is not possible to directly downsample by a noninteger factor, we first upsample the signal by a factor of 3. Therefore, after the upsampling we will need toreduce the sampling rate by 14/3× 3=14. Therefore, the overall system for performing the sampling rate conversion isy[n][]2nx ,n=0,±3,±6,… y[n]=p[14n] ω[n]= 0, otherwise Figure S7.34)(e xp)(ωj d e x 7.36. (a) Let us decnote the sampled signaled signal by x p (t). We have∑∞-∞=-=n pnT t nT x t x )()()(δSince the Nyquist rate for the signal x(t) is T /2π,we can reconstruct the signal from x p (t). From Section 7.2,we know that)(*)()(t h t x t x p = whereTt T t t h /)/sin()(ππ=Thereforedtt dh t x dtt dx p )(*)()(=Denoting dtt dh )( by g(t),we have∑∞-∞=-==n pnT t g nT x t g t x dtt dx )()()(*)()(Therefore,2)/sin()/cos()()(tT t T tT t dtt dh t g πππ-==(b) No.7.37. We may write p(t) asp(t)=p 1(t)+p 1(t-∆),where∑∞-∞=-=k W k t t p )/2()(1πδTherefore,)()1()(1ωωωj p e j p j ∆-+= where∑∞-∞=-=k kW w j p )()(1ωδω149Let us denote the product p(t)f(t) by g(t).Then,)()()()()()()(11t f t p t f t p t f t p t g ∆-+== This may be written as)()()(11∆-+=t bp t ap t g Therefore,)(()(1)ωωωj p be a j G j ∆-+= with )(1ωj p is specified in eq.(s7.37-1). Therefore [])()(kw be a w j G k w jk -+=∑∞-∞=∆-ωδωWe now have)()()()(1t f t p t x t y = Therefore,[])(*)(21)(1ωωπωj x j G j Y =This give us[]))((2)(1kW j x be a Wj Y wjk -+=∑∆-ωπωIn the range 0<ω<W, we may specify Y 1(j ω) as[]))(()()()(2)(1W j x be a j x b a w j Y w jk -+++=∆-ωωπωsince )()()(112ωωωj H j Y j Y =, in the range 0<ω<W we may specify Y 2(j ω) as []))(()()()(2)(2W j x be a j x b a jW j Y W j -+++=∆-ωωπωSince ),()()(3t p t x t y =in the range 0<ω<W we may specify Y 3(j ω) as []))(()1()(22)(3W j x e j x W j Y W j -++=∆-ωωπωGive that 0<W △<π,we require that )()()(32ωωωj kx j Y j Y =+ for 0<ω<W. That is[][])())(()1(2)()(2ωωπωπj kx W j x e W j x jb ja a Ww j =-++++∆-This implies that01=+++∆-∆-W j Wj jbe ja e Solving this we obtainA=1, b= -1, When W △=π/2. More generally, we also geta=sin(W △)+)tan())cos(1(∆∆+W W and )sin()cos(1∆∆+-=W W bexcept when 2/π=∆W Finally, we also get [])2/(12jb ja Wk ++=π。

《信号与系统》专业术语中英文对照表第 1 章绪论信号（signal）系统（system）电压（voltage）电流（current）信息（information）电路（circuit）网络（network）确定性信号（determinate signal）随机信号（random signal）一维信号（one –dimensional signal）多维信号（multi–dimensional signal）连续时间信号（continuous time signal）离散时间信号（discrete time signal）取样信号（sampling signal）数字信号（digital signal）周期信号（periodic signal）非周期信号（nonperiodic（aperiodic）signal）能量（energy）功率（power）能量信号（energy signal）功率信号（power signal）平均功率（average power）平均能量（average energy）指数信号（exponential signal）时间常数（time constant）正弦信号（sine signal）余弦信号（cosine signal）振幅（amplitude）角频率（angular frequency）初相位（initial phase）周期（period）频率（frequency）欧拉公式（Euler’s formula）复指数信号（complex exponential signal）复频率（complex frequency）实部（real part）虚部（imaginary part）抽样函数Sa(t)（sampling（Sa）function）偶函数（even function）奇异函数（singularity function）奇异信号（singularity signal）单位斜变信号（unit ramp signal）斜率（slope）单位阶跃信号（unit step signal）符号函数（signum function）单位冲激信号（unit impulse signal）广义函数（generalized function）取样特性（sampling property）冲激偶信号（impulse doublet signal）奇函数（odd function）偶分量（even component）奇分量（odd component）正交函数（orthogonal function）正交函数集（set of orthogonal function）数学模型（mathematics model）电压源（voltage source）基尔霍夫电压定律（Kirchhoff’s voltage law（KVL））电流源（current source）连续时间系统（continuous time system）离散时间系统（discrete time system）微分方程（differential function）差分方程（difference function）线性系统（linear system）非线性系统（nonlinear system）时变系统（time–varying system）时不变系统（time–invariant system）集总参数系统（lumped–parameter system）分布参数系统（distributed–parameter system）偏微分方程（partial differential function）因果系统（causal system）非因果系统（noncausal system）因果信号（causal signal）叠加性（superposition property）均匀性（homogeneity）积分（integral）输入–输出描述法（input–output analysis）状态变量描述法（state variable analysis）单输入单输出系统（single–input and single–output system）状态方程（state equation）输出方程（output equation）多输入多输出系统（multi–input and multi–output system）时域分析法（time domain method）变换域分析法（transform domain method）卷积（convolution）傅里叶变换（Fourier transform）拉普拉斯变换（Laplace transform）第 2 章连续时间系统的时域分析齐次解（homogeneous solution）特解（particular solution）特征方程（characteristic function）特征根（characteristic root）固有（自由）解（natural solution）强迫解（forced solution）起始条件（original condition）初始条件（initial condition）自由响应（natural response）强迫响应（forced response）零输入响应（zero-input response）零状态响应（zero-state response）冲激响应（impulse response）阶跃响应（step response）卷积积分（convolution integral）交换律（exchange law）分配律（distribute law）结合律（combine law）第3 章傅里叶变换频谱（frequency spectrum）频域（frequency domain）三角形式的傅里叶级数（trigonomitric Fourier series）指数形式的傅里叶级数（exponential Fourier series）傅里叶系数（Fourier coefficient）直流分量（direct composition）基波分量（fundamental composition）n 次谐波分量（nth harmonic component）复振幅（complex amplitude）频谱图（spectrum plot（diagram））幅度谱（amplitude spectrum）相位谱（phase spectrum）包络（envelop）离散性（discrete property）谐波性（harmonic property）收敛性（convergence property）奇谐函数（odd harmonic function）吉伯斯现象（Gibbs phenomenon）周期矩形脉冲信号（periodic rectangular pulse signal）周期锯齿脉冲信号（periodic sawtooth pulse signal）周期三角脉冲信号（periodic triangular pulse signal）周期半波余弦信号（periodic half–cosine signal）周期全波余弦信号（periodic full–cosine signal）傅里叶逆变换（inverse Fourier transform）频谱密度函数（spectrum density function）单边指数信号（single–sided exponential signal）双边指数信号（two–sided exponential signal）对称矩形脉冲信号（symmetry rectangular pulse signal）线性（linearity）对称性（symmetry）对偶性（duality）位移特性（shifting）时移特性（time–shifting）频移特性（frequency–shifting）调制定理（modulation theorem）调制（modulation）解调（demodulation）变频（frequency conversion）尺度变换特性（scaling）微分与积分特性（differentiation and integration）时域微分特性（differentiation in the time domain）时域积分特性（integration in the time domain）频域微分特性（differentiation in the frequency domain）频域积分特性（integration in the frequency domain）卷积定理（convolution theorem）时域卷积定理（convolution theorem in the time domain）频域卷积定理（convolution theorem in the frequency domain）取样信号（sampling signal）矩形脉冲取样（rectangular pulse sampling）自然取样（nature sampling）冲激取样（impulse sampling）理想取样（ideal sampling）取样定理（sampling theorem）调制信号（modulation signal）载波信号（carrier signal）已调制信号（modulated signal）模拟调制（analog modulation）数字调制（digital modulation）连续波调制（continuous wave modulation）脉冲调制（pulse modulation）幅度调制（amplitude modulation）频率调制（frequency modulation）相位调制（phase modulation）角度调制（angle modulation）频分多路复用（frequency–division multiplex（FDM））时分多路复用（time –division multiplex（TDM））相干（同步）解调（synchronous detection）本地载波（local carrier）系统函数（system function）网络函数（network function）频响特性（frequency response）幅频特性（amplitude frequency response）相频特性（phase frequency response）无失真传输（distortionless transmission）理想低通滤波器（ideal low–pass filter）截止频率（cutoff frequency）正弦积分（sine integral）上升时间（rise time）窗函数（window function）理想带通滤波器（ideal band–pass filter）第 4 章拉普拉斯变换代数方程（algebraic equation）双边拉普拉斯变换（two-sided Laplace transform）双边拉普拉斯逆变换（inverse two-sided Laplace transform）单边拉普拉斯变换（single-sided Laplace transform）拉普拉斯逆变换（inverse Laplace transform）收敛域（region of convergence（ROC））延时特性（time delay）s 域平移特性（shifting in the s-domain）s 域微分特性（differentiation in the s-domain）s 域积分特性（integration in the s-domain）初值定理（initial-value theorem）终值定理（expiration-value）复频域卷积定理（convolution theorem in the complex frequency domain）部分分式展开法（partial fraction expansion）留数法（residue method）第 5 章策动点函数（driving function）转移函数（transfer function）极点（pole）零点（zero）零极点图（zero-pole plot）暂态响应（transient response）稳态响应（stable response）稳定系统（stable system）一阶系统（first order system）高通滤波网络（high-low filter）低通滤波网络（low-pass filter）二阶系统（second system）最小相移系统（minimum-phase system）维纳滤波器（Winner filter）卡尔曼滤波器（Kalman filter）低通（low-pass）高通（high-pass）带通（band-pass）带阻（band-stop）有源（active）无源（passive）模拟（analog）数字（digital）通带（pass-band）阻带（stop-band）佩利－维纳准则（Paley-Winner criterion）最佳逼近（optimum approximation）过渡带（transition-band）通带公差带（tolerance band）巴特沃兹滤波器（Butterworth filter）切比雪夫滤波器（Chebyshew filter）方框图（block diagram）信号流图（signal flow graph）节点（node）支路（branch）输入节点（source node）输出节点（sink node）混合节点（mix node）通路（path）开通路（open path）闭通路（close path）环路（loop）自环路（self-loop）环路增益（loop gain）不接触环路（disconnect loop）前向通路（forward path）前向通路增益（forward path gain）梅森公式（Mason formula）劳斯准则（Routh criterion）第 6 章数字系统（digital system）数字信号处理（digital signal processing）差分方程（difference equation）单位样值响应（unit sample response）卷积和（convolution sum）Z 变换（Z transform）序列（sequence）样值（sample）单位样值信号（unit sample signal）单位阶跃序列（unit step sequence）矩形序列(rectangular sequence)单边实指数序列（single sided real exponential sequence）单边正弦序列（single sided exponential sequence）斜边序列（ramp sequence）复指数序列（complex exponential sequence）线性时不变离散系统（linear time-invariant discrete-time system）常系数线性差分方程（linear constant-coefficient difference equation）后向差分方程（backward difference equation）前向差分方程（forward difference equation）海诺塔（Tower of Hanoi）菲波纳西（Fibonacci）冲激函数串（impulse train）第7 章数字滤波器（digital filter）单边Z 变换（single-sided Z transform）双边Z 变换(two-sided (bilateral) Z transform) 幂级数（power series）收敛（convergence）有界序列（limitary-amplitude sequence）正项级数（positive series）有限长序列（limitary-duration sequence）右边序列（right-sided sequence）左边序列（left-sided sequence）双边序列（two-sided sequence）Z 逆变换（inverse Z transform）围线积分法（contour integral method）幂级数展开法（power series expansion）z 域微分（differentiation in the z-domain）序列指数加权（multiplication by an exponential sequence）z 域卷积定理（z-domain convolution theorem）帕斯瓦尔定理（Parseval theorem）传输函数（transfer function）序列的傅里叶变换（discrete-time Fourier transform：DTFT）序列的傅里叶逆变换（inverse discrete-time Fourier transform：IDTFT）幅度响应（magnitude response）相位响应（phase response）量化（quantization）编码（coding）模数变换（A/D 变换：analog-to-digital conversion）数模变换（D/A 变换：digital-to- analog conversion）第8 章端口分析法（port analysis）状态变量（state variable）无记忆系统（memoryless system）有记忆系统（memory system）矢量矩阵（vector-matrix ）常量矩阵（constant matrix ）输入矢量（input vector）输出矢量（output vector）直接法（direct method）间接法（indirect method）状态转移矩阵（state transition matrix）系统函数矩阵（system function matrix）冲激响应矩阵（impulse response matrix）朱里准则（July criterion）。

275个信号与系统常用词汇中英文对照表序号英文词汇中文翻译1 Absolutely summable impulse response 绝对可和的冲激响应2 Absolutely integrable impulse response 绝对积的冲激响应3 Accumulation property 累加性质4 Adder 加法器5 Additivity 可加性6 Aliasing 混叠7 Allpass system 全通系统8 Amplitude Modulation(AM) 幅度调制9 Amplifier 放大器10 Analog-to-Digital Conversion 模数转换11 Analysis equation 分析方程12 Aperiodic signal 非周期性信号13 Associative property 结合性质14 Audio system 音频系统15 Autocorrelation function 自相关函数16 Band-limited signal 带限信号17 Band-limited interpolation 带限内插18 Bandpass filter 带通滤波器19 Bandpass-sampling technique 带通抽样方法20 Bandpass signal 带通信号21 Bandwidth of an LTI system 线性时不变系统的带宽22 Bilinear transformation 双线性变换23 Block diagram 方框图24 Bode plot 波特图25 Butterworth filter 巴特沃斯滤波器26 Carrier frequency 载波频率27 Carrier signal 载波信号28 Cartesian (rectangular) form for complex number 复数的笛卡尔（直角坐标）形式29 Cascade-form block diagram 级联型方框图30 Cascade (series) interconnection 级联连接31 Causal LTI system 因果的线性时不变系统32 Channel equalization 信道均衡33 """Chirp"" transform algorithm" 线性调频变换算法34 Closed-loop system 闭环系统35 Coefficient multiplier 系数乘法器36 Communication system 通信系统37 Commutative property 交换性质38 Complex conjugate 复共轭39 Complex exponential 复指数40 Complex number 复数41 Continuous-time signal 连续时间信号42 Conjugate symmetry 共轭对称性43 Conjugation property 共轭性质44 Continuous-time Fourier series 连续时间傅里叶级数45 Continuous-time Fourier transform 连续时间傅里叶变换46 Continuous-time system 连续时间系统47 Convolution integral 卷积积分48 Convolution sum 卷积和49 Correlation function 相关函数50 Cross-correlation function 互相关函数51 Cutoff frequency 截止频率52 Digital signal 数字信号53 Demodulation 解调54 Discrete-time 离散时间55 Discrete-time Fourier series 离散傅里叶级数56 Distributive property 分配性质57 Damped sinusoid 阻尼正弦波58 Damping ratio 阻尼比59 DC offset 直流偏置60 Decibel (dB) 分贝61 Delay 延迟62 Delay time 延时63 Difference 差分64 Discrete-time Fourier series 离散时间傅里叶级数65 Discrete-time Fourier transform 离散时间傅里叶变换66 Differential equation 微分方程67 Differentiation 微分68 Digital-to-Analog converter 数模转换器69 Direct FormⅠrealization 直接Ⅰ型实现70 Direct FormⅡrealization 直接Ⅱ型实现71 Dirichlet conditions 狄里赫利条件72 Discontinuity 不连续73 Discrete-time Modulation 离散时间调制74 Discrete-time signal 离散时间信号75 Decimation 抽取76 Discrete-time system 离散时间系统77 Distortion 失真78 Distributive property 分配性质79 Double-sideband modulation 双边带调制80 Downsampling 降率抽样81 Duality 对偶性82 Eigenfunction 特征函数83 Eigenvalue 特征值84 Elliptic filter 椭圆滤波器85 Energy-density spectrum 能量密度谱86 Envelope 包络线87 Equalization 均衡88 Euler's relation 欧拉关系89 Exponential 指数函数90 Fast Fourier Transform (FFT) 快速傅里叶变换91 Feedback 反馈92 Feedback interconnection 反馈互联93 Filter 滤波器94 Finite Impulse Response (FIR) 有限冲激响应95 Forward path 前向通路96 Frequency-selective 频率选择97 Frequency-shaping 频率整形98 Final-value theorem 终值定理99 Finite-duration signal 有限持续时间信号,100 First harmonic component 一次谐波分量101 First-order continuous-time system 一阶连续时间系统102 First-order discrete-time system 一阶离散时间系统103 Forced response 强迫响应104 Frequency-Division Multiplexing (FDM) 频分复用105 Frequency response 频率响应106 Frequency scaling 频率尺度变换107 Frequency shifting property 频移性质108 Fundamental frequency 基本频率109 Fundamental period 基本周期110 Gain 增益111 General complex exponential 普通的复指数函数112 Generalized function 广义函数113 Gibbs phenomenon 吉布斯现象114 Group delay 群延时115 Hanning window 汉宁窗116 Harmonic analyzer 谐波分析器117 Harmonic component 谐波分量118 Highpass filter 高通滤波器119 Hilbert transform 希尔伯特变换120 Ideal frequency-selective filter 理想频率选择滤波器121 Image processing 图像处理122 Imaginary part 虚部123 Impulse response 冲激响应124 Impulse train 冲激串125 Impulse-train sampling 冲激串抽样126 Incrementally linear system 增量线性系统127 Independent variable 独立变量,自变量128 Infinite Impulse Response (IIR) 无限冲激响应129 Initial-value theorem 初值定理130 Instantaneous frequency 瞬时频率131 Integral 积分132 Integration property 积分性质133 Integrator 积分器134 Interconnection 互联135 Linear Time Invariant (LTI) system 线性时不变系统136 Interpolation 内插137 Inverse Fourier transform 逆傅里叶变换138 Inverse Laplace transform 逆拉普拉斯变换139 Inverse system 逆系统140 Inverse z-transform 逆z变换141 Laplace transform 拉普拉斯变换142 Left-half plane 左半平面143 Left-sided signal 左边信号144 Linear constant-coefficient differential equation 线性常系数微分方程145 Linear constant-coefficient difference equation 线性常系数差分方程146 Finite Impulse Response (FIR) 有限冲激响应147 Linear feedback system 线性反馈系统148 Linear interpolation 线性内插149 Linearity 线性150 Lowpass filter 低通滤波器151 Lowpass-to-highpass transformation 低通到高通的转换152 Magnitude of complex number 复数的幅值153 Matched filter 匹配滤波器154 Memoryless system 无记忆系统155 Modulating signal 调制信号156 Modulation 调制157 Modulation index 调制指数158 Modulation property 调制性质159 Multiplexing 多路复用160 Multiplication 乘法161 Natural frequency 自然频率162 Natural response 自然响应163 Negative feedback 负反馈164 Network 网络165 Noncausal system 非因果系统166 Nonideal filter 非理想滤波器167 Nonrecursive filter 非递归滤波器168 Normalized function 归一化函数169 Nyquist frequency 奈奎斯特频率170 Nyquist rate 奈奎斯特速率171 Operational amplifier 运算放大器172 Orthogonal function 正交函数173 Orthogonal signal 正交信号174 Oversampling 过抽样175 Parallel interconnection 并联连接176 Parseval's relation 帕塞瓦尔关系177 Partial-fraction expansion 部分分式展开178 Passband frequency 通带频率179 Passband ripple 通带纹波180 Periodic complex exponential 周期性复指数181 Periodic convolution 周期卷积182 Periodic signal 周期信号183 Power 功率184 Periodic square wave 周期性方波185 Periodic train of impulses 周期性冲激串186 Phase lag 相位滞后187 Phase lead 相位超前188 Phase modulation 相位调制189 Phase shift 相移190 Polar form for complex number 复数的极坐标形式191 Pole 极点192 Pole-zero plot 零极点图193 Power of signal 信号的功率194 Power-series expansion method 幂级数展开法195 Principal-phase function 主值相位函数196 Proportional feedback system 比例反馈系统197 Real part 实部198 Rectangular pulse 矩形脉冲199 Rectangular window 矩形窗200 Recursive filter 递归滤波器201 Region of Convergence (ROC) 收敛域202 Rational function 有理函数203 Right-sided signal 右边信号204 Right-sided sequence 右边序列205 Right-half plane 右半平面206 Rise time 上升时间207 Root-locus analysis 根轨迹分析法208 Running sum 流动和209 Sampled-data feedback system 抽样数据反馈系统210 Sampling frequency 抽样频率211 Sampling function 抽样函数212 Sampling period 抽样周期213 Sampling theorem 抽样定理214 Scaling (homogeneity) property 比例(齐次)性215 Scaling in the z-domain Z域尺度变换216 Second harmonic component 二次谐波分量217 Second-order system 二阶连续时间系统218 Series (cascade) interconnection 串联(级联)连接219 Sifting property 移位性质220 shifting property in the s-domain s域移位性质221 Single-sideband sinusoidal amplitude modulation 单边带正弦幅度调制222 Singularity function 奇异函数223 Synchronous 同步的224 Sinusoidal frequency modulation 正弦频率调制225 Sinusoidal signal 正弦信号226 Sliding 滑动227 Square wave 方波228 Step-invariant transformation 阶跃响应不变变换法229 Step response 阶跃响应230 Stopband edge 阻带边缘231 Stopband frequency 阻带频率232 Stopband ripple 阻带纹波233 Sufficiency 充分性234 Summer 加法器235 Superposition property 叠加性质236 Symmetry 对称性237 Synthesis equation 综合方程238 System function 系统函数239 Stability 稳定性240 Taylor series 泰勒级数241 Time constant 时间常数242 Time delay 时延243 Time-Division Multiplexing (TDM) 时分复用244 Time-domain 时域的245 Time reversal property 时间翻转性质246 Time scaling 时间尺度变换247 Time shifting property 时移性质248 Time window 时间窗249 Transition band 过渡带250 Triangular window 三角窗251 Trigonometric series 三角级数252 Undamped natural frequency 无阻尼自然频率253 Undamped system 无阻尼系统254 Underdamped system 欠阻尼系统255 Unilateral Laplace transform 单边拉普拉斯变换256 Unilateral z transform 单边Ｚ变换257 Unit circle 单位圆258 Unit delay 单位延时259 Unit doublet 单位冲激偶260 Unit impulse 单位冲激261 Unit impulse response 单位冲激响应262 Upsampling 升率抽样263 Variable 变量264 Vestigial sideband modulation 残留边带调制265 Voltage 电压266 Wideband 宽带267 Window function 窗函数268 Windowing 加窗269 Wireless 无线的270 Weighted average 加权平均271 Wavelength 波长272 Zero-input response 零输入响应273 Zero-state response 零状态响应274 Zero location 零点位置275 Zero-order hold 零阶保持器整理提供。

专业名词--专业英语-信号处理导论专业名词总结部分1.A/D conversion [eɪ] [diː][kən'vɜːʃ(ə)n]模数转换指为把数字信号转换为信息基本相同的模拟信号而设计的处理过程。

2.adder ['ædə]加法器加法器是产生数的和的装置。

加数和被加数为输入，和数与进位为输出的装置为半加器。

若加数、被加数与低位的进位数为输入，而和数与进位为输出则为全加器。

3.additive gauss white noise ['ædɪtɪv][gaʊs] [waɪt] [nɒɪz]加性高斯白噪声加性高斯白噪声指的是一种各频谱分量服从均匀分布（即白噪声），且幅度服从高斯分布的噪声信号。

因其可加性、幅度服从高斯分布且为白噪声的一种而得名。

4.aliasing ['eliəsɪŋ]混叠频混现象又称为频谱混叠效应，它是指由于采样信号频谱发生变化，而出现高、低频成分发生混淆的一种现象。

5.all-pass function ['ɔl,pæs] ['fʌŋ(k)ʃ(ə)n] 全通函数全通函数是凡极点位于左半开平面，零点位于右半开平面，并且所有零点与极点对于虚轴为一一镜像对称的系统函数。

6.amplifier ['æmplɪfaɪə] 放大器是指能够使用较小的能量来控制较大能量的任何器件。

7.amplitude ['æmplɪtjuːd]振幅指振动物体离开平衡位置的最大距离。

8.analog signal ['ænəlɒɡ] ['sɪgn(ə)l]模拟信号指信息参数在给定范围内表现为连续的信号。

或在一段连续的时间间隔内，其代表信息的特征量可以在任意瞬间呈现为任意数值的信号。

9.antialiasing profiler [,ænti'eliəsɪŋ] ['prəufailə] 抗混叠预滤波器指一种用以在输出电平中把混叠频率分量降低到微不足道的程度的低通滤波器。