信号与系统 奥本海姆-答案.doc【DOC精选】.doc

Signals and System Chap1 1.6 Determine whether or not each of the following signals is periodic: (a): (b): (c): Solution: (a).No【周期信号无始无终，单边肯定不周期】 Because when t0, =0. (b).No【注意n＝0】 Because (c).Yes【画图、归纳】 Because N=4. 1.9 Determine whether or not each of the following signals is periodic, if a signal is periodic, specify its fundamental period: (a): (b): (c): (d): (e): Solution: (a). T=/5 Because =10, T=2/10=/5. (b). Aperiodic. Because , while is not periodic, is not periodic. (c). N=2 Because =7, N=(2/)*m, and m=7. (d). N=10 Because , that is =3/5, N=(2/)*m, and m=3. (e). Aperiodic. Because =3/5, N=(2/)*m=10m/3 , it’s not a rational number. 1.14 consider a periodic signal with period T=2. The derivative of this signal is related to the “impulse train”, with period T=2. It can be shown that. Determine the values of , , , . Solution: A1=3, t1=0, A2=-3, t2=1 or -1 Because , 1.15. Consider a system S with input x[n] and output y[n].This system is obtained through a series interconnection of a system S1 followed by a system S2. The input-output relationships for S1 and S2 are S1: S2: Where and denote input signals. (a) Determine the input-output relationship for system S. (b)Does the input-output relationship of system S change if the order in which S1 and S2 are connected in series is reversed(ie., if S2 follows S1)? Solution: (a) Then, 【可以考虑先求取单位脉冲响应，再做卷积】 (b).No. because it’s linear, S1 and S2 do not diverge. 1.16. Consider a discrete-time system with input x[n] and output y[n].The input-output relationship for this system is (a) Is the system memory less? (b) Determine the system output when the input is, where A is any real or complex number. (c) Is the system invertible? Solution: (a). No. For example, when n=0, y[0]=x[0]x[-2]. So the system is memory. (b). y[n]=0. When the input is,, so y[n]=0. (c). No. For example, when x[n]=0, y[n]=0; when x[n]=, y[n]=0. So the system is not invertible. 1.17.Consider a co