TIME SIGNALS DESCRIPTION 1. Mathematical expression x(=Asin(at+o) 2. Continuous(Analogue) 2 75 3. Discrete Digital)
TIME SIGNALS DESCRIPTION 1. Mathematical expression: x(t)=Asin(wt+f) 2. Continuous (Analogue) -15 -10 -5 0 5 10 15 0 5 10 15 20 3. Discrete (Digital) x[n] n
TIME SIGNALS DESCRIPTION 4. Periodic x()=x(计T0 Period= t 70 5. Aperiodic
TIME SIGNALS DESCRIPTION 4. Periodic -15 -10 -5 0 5 10 15 x 0 10 20 30 40 (t)= x(t+To ) To Period = To 5. Aperiodic -2 0 2 4 6 8 10 12 0 10 20 30 40
TIME SIGNALS DESCRIPTION 6. Even signal x(t)=x(t) 7. Odd signal x(()=-x(t) Exercise: Calculate the integral v= cos ct sin tdt
TIME SIGNALS DESCRIPTION 6. Even signal x(t) = x(−t) Exercise: Calculate the integral 7. Odd signal x(t) = −x(−t) -15 -10 -5 0 5 10 15 -10 -5 0 5 10 -15 -10 -5 0 5 10 15 -10 -5 0 5 10 − = T T v coswtsin wtdt
TIME SIGNALS DESCRIPTION 8. Causalit Analogue signals: x(t)=0 fort<0 Digital signals: xIn=0 forn <0
TIME SIGNALS DESCRIPTION 8. Causality Analogue signals: x(t) = 0 for t < 0 Digital signals: x[n] = 0 for n < 0
TIME SIGNALS DESCRIPTION 9. Average/Mean/DC value 10. AC value xc(0)=x()-x DC Direct Component DC AC: Alternating Component Exercise: 2丌 Calculate the aC& DC values of x(t=Asin(ar with TM O
TIME SIGNALS DESCRIPTION 9. Average/Mean/DC value ( ) + = t T M M t DC x t dt T x 1 1 1 Exercise: Calculate the AC & DC values of x(t)=Asin(wt) with w 2 TM = TM -15 -10 -5 0 5 10 15 0 10 20 30 40 10. AC value ( ) ( ) AC DC x t = x t − x DC: Direct Component AC: Alternating Component