TIME SIGNALS DESCRIPTION 11. Energy E=x() 12. Instantaneous Power P(t) watts R 13. Average Power ∫P()t M Note: For periodic signal, TM is generally taken as T Exercise: Calculate the average power of x(=Acos(at
TIME SIGNALS DESCRIPTION 11. Energy ( ) − E = x t dt 2 Exercise: Calculate the average power of x(t)=Acos(wt) 12. Instantaneous Power ( ) ( ) watts R x t P t 2 = 13. Average Power ( ) + = t T M M t av P t dt T P 1 1 1 Note: For periodic signal, TM is generally taken as To
TIME SIGNALS DESCRIPTION 14. Power Ratio PR=10logsYy unit is decibel(db) In Electronic Engineering and Telecommunication power is usually resulted from applying voltage v to a resistive load R, as P R Alternative expression for power ratio(same resistive load): V/R P=logo P2 P=1010g10 V2/R 2010g10 v2
TIME SIGNALS DESCRIPTION 14. Power Ratio 2 1 10 10 P P P log R = In Electronic Engineering and Telecommunication power is usually resulted from applying voltage V to a resistive load R, as The unit is decibel (db) R V P 2 = Alternative expression for power ratio (same resistive load): V / R V / R log P P PR log 2 2 2 1 10 2 1 =10 10 =10 2 1 10 20 V V = log
TIME SIGNALS DESCRIPTION 5. Orthogonality Two signals are orthogonal over the interval L,4+mI if t1+M r=3x,(B( dt=0 Exercise: Prove that sin(ot) and cos(at are orthogonal for 2丌
TIME SIGNALS DESCRIPTION 15. Orthogonality Exercise: Prove that sin(wt) and cos(wt) are orthogonal for Two signals are orthogonal over the interval if ( ) ( ) 0 1 2 1 1 = = + r x t x t dt t T M t TM t 1 ,t 1 + w 2 TM =
TIME SIGNALS DESCRIPTION 5. Orthogonality: graphical illustration x, (t) x,(t)and x(t)are x,(t)and x,(t)are correlated orthogonal When one is large, So is Their values are totall the other and vice versa unrelated
TIME SIGNALS DESCRIPTION 15. Orthogonality: Graphical illustration x1 (t) x2 (t) x1 (t) and x2 (t) are correlated. When one is large, so is the other and vice versa x1 (t) x2 (t) x1 (t) and x2 (t) are orthogonal. Their values are totally unrelated
TIME SIGNALS DESCRIPTION 16. Convolution between two signals ()=x(0+x(0)=jx(-xr=jx(=xr Convolution is the resultant corresponding to the interaction between two signals
TIME SIGNALS DESCRIPTION 16. Convolution between two signals y(t) = x (t) x (t) = x ( )x (t − )d = x ( )x (t − )d − − 1 2 1 2 2 1 Convolution is the resultant corresponding to the interaction between two signals