Chapter 4 The Continuous-Time Fourier Transform
1 The Continuous-Time Fourier Transform Chapter 4
Chapter 4 Fourier transform 94.1 Representation of Aperiodic Signals: The Continuous-Time fourier Transform T-T/2T0 T T/2 T t a, Tysinckko,r) Tar=2T sinc(oT)
2 Chapter 4 Fourier Transform §4.1 Representation of Aperiodic Signals : The Continuous-Time Fourier Transform 1 x(t) -T -T/2 –T1 0 T1 T/2 T t ( ) 0 1 1 sin 2 c k T T T ak = ( ) 0 1 1 2 sin k Tak T c T = =
Chapter 4 Fourier transform Figure 4.2 200 (b)T=87 (l)T=16T 7个→an=2/T↓□谱线变密
3 Chapter 4 Fourier Transform T 0 = 2 /T 谱线变密 ( ) 4 1 a T = T ( ) 8 1 b T = T ( ) 1 c T = 16T Figure 4.2
Chapter 4 Fourier transform Consider an aperiodic signals x y(t)=0 > T 0 ●● T T 0 T 4
4 Chapter 4 Fourier Transform –T1 0 T1 t x(t) ( ) 1 x t = 0 , t T -T –T1 0 T1 T t x(t) ~ Consider an aperiodic Signals
Chapter 4 Fourier transform Fourier transform pair factor x() J X(o)elon do Synthesis equation 2丌J-∞ X(o)=丁 x(te Ja t dt Analysis equation 1. A linear combination of complex exponentials 2.x(o)- Spectrum(频谱)ofx() x()<"→X(io) 5
5 Chapter 4 Fourier Transform ( ) ( ) j t X j x t e dt + − − = ( ) ( ) 1 2 j t x t X j e d + − = Synthesis equation Analysis equation Fourier Transform Pair 1. A linear combination of complex exponentials. factor 2. X(j) ——Spectrum（频谱） of x(t) x(t)⎯→X(j) F