1.2 Discrete-time signals ◆ Rectangle sequence R、(mn) ∫10≤n≤N-1 0 Others R(n)=u(n)-u(n-N D3了 0.5 0 5 Time index n
◆ Rectangle sequence 1.2 Discrete-time signals 0 1 2 3 4 5 6 7 8 9 10 0 0.5 1 Time index n Amplitude ( ) 1 0 1 0 N n N R n Others − = R n u n u n N N ( ) = − − ( ) ( )
1.2 Discrete-time signals Rectangle sequence An application of the above sequence is in extracting all samples in the range n<=n<=N, of an infinite-length or very long length sequence x[n] and setting all other samples outside the above range to zero values by multiplying x[n] with Rn)
◆ Rectangle sequence 1.2 Discrete-time signals An application of the above sequence is in extracting all samples in the range N1<=n<=N2 of an infinite-length or very long length sequence x[n] and setting all other samples outside the above range to zero values by multiplying x[n] with RN(n)
1.2 Discrete-time signals Real exponential sequence Where a is a rea 15 Time index n
◆ Real exponential sequence 1.2 Discrete-time signals ( ) ( ) n x n a u n = 0 5 10 15 20 25 30 35 0 20 40 60 80 100 120 Time index n Amplitude where a is a real
1.2 Discrete-time signals ◆ Sinusoidal sequence xa((=sin( @2t) x(n)=sin(Q2nT) sin(t 0.4 Where QT 0.6 -0.8 -20 -5 Time index n
1.2 Discrete-time signals ◆ Sinusoidal sequence ( ) ( ) ( ) ( ) ( ) sin sin sin a x t t x n nT T = = = s T F = = -20 -15 -10 -5 0 5 10 15 20 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Time index n Amplitude where
1.2 Discrete-time signals ◆ periodic sequence A commonly encountered sequence is the real sinusoidal sequence with constant amplitude of the form x[n]=Acos(oono) 0<n<0
1.2 Discrete-time signals ◆ periodic sequence A commonly encountered sequence is the real sinusoidal sequence with constant amplitude of the form x n A n n = + − cos , ( 0 )