Bilingual Course Network Communications 网络通信 For Master Students in the Department of Electronic Engineering) Chapter 3 Data Transmission Instructor: Dr. Tianshuang Qiu School of the Electronic and Information Engineering Fall of 2004
1 Bilingual Course Network Communications 网络通信 (For Master Students in the Department of Electronic Engineering) Chapter 3 Data Transmission Instructor: Dr. Tianshuang Qiu School of the Electronic and Information Engineering Fall of 2004
83-1 Concepts and Terminologies Expressions of signals In time domain Continuous time signal x(1) Discrete time signal x(n) Periodic signal x((=x(t+r) x(n)=x(n+) Aperiodic signal In frequency domain Fourier series x(t)e Joo'dt Fourier transform X(o)=x(t)e o dt Discrete fourier series a=x2xinje Discrete Fourier transform r(k)=>xne mt Discrete time fourier transform x(e)=∑xnlm n=-00 Fast Fourier transform 2
2 §3-1 Concepts and Terminologies ◼ Expressions of signals ◼ In time domain ◼ Continuous time signal ◼ Discrete time signal ◼ Periodic signal ◼ Aperiodic signal ◼ In frequency domain ◼ Fourier series ◼ Fourier transform ◼ Discrete Fourier series ◼ Discrete time Fourier transform ◼ Discrete Fourier transform ◼ Fast Fourier transform x(t) x(n) x(t) = x(t + T) x(n) = x(n + N) x t t T a T jk t k ( )e d 1 0 − = − − X j = x t t j t ( ) ( )e d = − = n N jk n k x n e N a 0 [ ] 1 =− − = m j j t X e x n e ( ) [ ] − = − = 1 0 2 ( ) [ ] N n N nk j X k x n e
Relations ■连续←→非周期 离散→周期 x(1)←→>x{m] k k Y(jo)<-→)X(e1) X(s)<→X(z)
3 Relations ◼ 连续→非周期 ◼ 离散→周期 ( ) ( ) ( ) ( ) ( ) [ ] X s X z X j X e a a x t x n j k k → → → →
Examples of Signals and spectra(Figure 3.3, E.6) (a)A=1,f=1,9=0 b)A=0.5,f=1,中=0 sin) c)A=1,f=2,@=0 (d)A=1,f=1中=74 Figure 3.3 s(0)= A sin(2ft o)
4 Examples of Signals and spectra (Figure 3.3, E.6)
Figure 3.4 0.0T 0.5T 0.5T 1.0T 2.0T 0.0T (c)(4/r)lsin(2xf+(1/3)sin(2n(30) Figure 3.4 Addition of Frequency Components(T=1/n
5 Figure 3.4