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1、Fourier series representation of periodic signalsResponses of basic signalsResponses of signalsCh. 3g H (j w), H (e j w )Periodic signalsCh. 4Aperiodic signalsFourier transform Fourier analysis连续离散连续Ch.5The discrete-time Fourier transform5.1 非周期信号的表示： 离散时间傅立叶变换(FT)5.1.1 离散时间傅立叶变换的导出 Comparison with
2、continuous-time:5.1.2 Sample Ex. 5.1 频谱特点w=-7:0.01:7;fm=sqrt(1+4-4*cos(w);y=1./fm;plot(w,y)Ex.5.3 Consider signal,Solutionx=-(2*pi+0.01):0.02:(3*pi+0.01);a=sin(2.5*x);b=sin(0.5*x);y=a./b;plot(x,y)5.1.3 收敛问题The convergence conditions is: convergence of impulse5.2 FT for periodic signals 考虑基本信号 考虑任意信号
3、： Ex. 5.5解 Ex. 5.6Solution5.3 离散时间 FT的性质5.3.1 Periodicity5.3.3 时移与频域性质 Ex. 5.7SolutionProof Ex. 5.8Solution5.3.4 共轭与共轭对称性If the system is an accumulator,5.3.5 Differencing & accumulation5.3.6 Time Reversal5.3.7 Time expansionProof DefiningInserting zeroes of (k-1) number. 尺度变换特性：时域展宽，频域压缩。Ex. 5.9xny
4、ny(2)n2y(2)n-1SolutionStart from:解题思路：利用FT特性与已知的变换对5.3.8 频域微分特性5.3.9 Parsevals relationDiscuss:1. xn is Periodic?2. xn is real?PO3. xn is real & even ?O4. xn has finite energy ?PProofProofEx. 5.10: The FT of xn are shown in the right. Discussing properties of the xn.周期g离散谱5.4 The Convolution Propert
5、y5.4.1 Examples Ex. 5.11SolutionSolution it againProof Ex. 5.13Solutiona ba = b频域微分特性时移特性, n0=1 Ex. 5.14,Analyzing the frequency response of following system. Solution5.5 The Multiplication Propertyin which Ex. 5.15SolutionProof5.6 Tables The FT of unit step sequence Proof of the FT of summationReal
6、 & odd g imaginary & odd SupposeThe FT of sign function5.7 DualityIt is also periodic. 5.7.1 The duality of DFS The duality of some properties of the DFSEx. 5.16Solution, 5.7.2 Duality between the DFT & CFSEx. 5.18TABLE 5.3 Summary of Fourier Series & Transform Expressions对偶关系实例阿贝成像物像光场的频谱面空间滤波：5.8 Systems Characterized by LCCDE Ex. 5.19Find the h n of y n, ifSolution Ex. 5.20 Find the y n of the system in the last Ex., if the input isSolution 小节1. 建立了离散时间周期信号与非周期信号的频域描述方法。2.通过讨论傅立叶变换性质，研究了信号时域特性与频域特性 的关系。3. 对离散时间LTI系统建立了频域分析的方法。（部分分式展开法）
