1 Signal and System B. Energy(Discrete-time) Instantaneous power: p(n=xin Energy over n1n≤n2:E=∑x2n Total Energy E2=∑x2[n Average Power lim2N+
1 Signal and System B. Energy (Discrete-time) Instantaneous power: ( ) [ ] 2 p n = x n Energy over n1 n n2 : = = 2 1 [ ] 2 n n n E x n Total Energy : =− = n E x [n] 2 Average Power: → =− + = N N n N x n N P [ ] 2 1 1 2 lim
1 Signal and System C. Finite Energy and Finite Power Signal Finite Energy Signal: (P>0) -+OO E x2()dt<+∞ E x-n<+ Finite Power Signal:(E→>∞) P=limiT ∫r x(tdt <+oo P=lim2N+1 x-n|<+
1 Signal and System C. Finite Energy and Finite Power Signal Finite Energy Signal : = + + − E x (t)dt 2 = + + n=− E x [n] 2 Finite Power Signal : + + = → =− N N n N x n N P [ ] 2 1 1 2 lim − → = + T T T x t dt T P ( ) 2 1 2 lim ( P → 0 ) ( E → )
1 Signal and System 2 Transformations of the Independent variable 1.2. 1 Examples of Transformations A. Time Shift Right shift x(t-to Xn-noI Delay) Left shift X(t+to) x[n+nol (Advance)
1 Signal and System 1.2 Transformations of the Independent Variable 1.2.1 Examples of Transformations A. Time Shift Right shift : x(t-t0 ) x[n-n0 ] (Delay) Left shift : x(t+t0 ) x[n+n0 ] (Advance)
1 Signal and System Examples 0 xIn-nol no
1 Signal and System Examples
1 Signal and System B. Time Reversa x(t)or x[-n]: Reflection of x(t or x[n] x() x[-n x(-t) sItll
1 Signal and System B. Time Reversal x(-t) or x[-n] : Reflection of x(t) or x[n]