Signals and Systems - Electrical Engineering

464 C H A P T E R 8: Discrete-Time Signals and Systems Obtain an expression forx[n−k] for− 2 ≤n≤2 and determine in which directi ...

8.2 Discrete-Time Signals 465 Solution The even component ofx[n] is given by xe[n]=0.5 ( x[n]+x[−n] ) Whenn=0 thenxe[0]=0.5× 2 x ...

466 C H A P T E R 8: Discrete-Time Signals and Systems Discrete-Time Complex Exponential Given complex numbersA=|A|ejθandα=|α|ej ...

8.2 Discrete-Time Signals 467 − 6 − 4 − 2 0 2 4 6 0 1 2 3 4 n x^1 [n ]= (0.8) n x^2 [n ]= 1.25 n − 6 − 4 − 2 0246 n 0 1 2 3 4 − ...

468 C H A P T E R 8: Discrete-Time Signals and Systems Assuming the maximum frequency ismax=N 0 forN≥2 (since the signal is no ...

8.2 Discrete-Time Signals 469 nExample 8.13 Show how to obtain the discrete-time exponentialx[n]=(− 1 )nforn≥0 and zero otherwis ...

470 C H A P T E R 8: Discrete-Time Signals and Systems FIGURE 8.5 Discrete frequenciesω. ω=π/2, 5π/2, 9π/2 · · · =π/2 ω= 3 π/2, ...

8.2 Discrete-Time Signals 471 01020 (a) (b) (c) (d) 30 40 − 1 −0.5 0 0.5 1 − 1 −0.5 0 0.5 1 − 1 −0.5 0.5 0 1 − 1 −0.5 0 0.5 1 n ...

472 C H A P T E R 8: Discrete-Time Signals and Systems Discrete-Time Unit-Step and Unit-Sample Signals The unit-stepu[n]and the ...

8.2 Discrete-Time Signals 473 The representation of any signalx[n] in terms ofδ[n] results from thesifting propertyof the unit-s ...

474 C H A P T E R 8: Discrete-Time Signals and Systems Solution Using the unit-sample signal generic representation, we have r[n ...

8.2 Discrete-Time Signals 475 nExample 8.17 Consider how to generate a train of triangular, discrete-time pulsest[n], which is p ...

476 C H A P T E R 8: Discrete-Time Signals and Systems obtained by sampling a continuous-time signal formed by ramp and unit-ste ...

8.2 Discrete-Time Signals 477 N = length(t); y = zeros(1, N); for i = 1:N, if t(i)>=−ad, y(i) = m∗(t(i) + ad); end end Likewi ...

478 C H A P T E R 8: Discrete-Time Signals and Systems − 30 − 20 − 10 0 (a) (c) (b) 10 20 30 − 1 0 1 2 3 4 5 6 7 y[ n] n − 30 − ...

8.3 Discrete-Time Systems 479 nExample 8.19 A square-root computation system.The input–output relation characterizing a discrete ...

480 C H A P T E R 8: Discrete-Time Signals and Systems FIGURE 8.8 Nonlinear system: (a) square root of 2, (b) square root of 4 c ...

8.3 Discrete-Time Systems 481 the signals in the above two cases and compare the resulting signal with the one we obtain when fi ...

482 C H A P T E R 8: Discrete-Time Signals and Systems Solution This is a nonrecursive system that uses a present sample,x[n], a ...

8.3 Discrete-Time Systems 483 y[n−2]=ay[n−3]+bx[n−2], and so on, we obtain y[n]=a(ay[n−2]+bx[n−1])+bx[n] =a(a(ay[n−3]+bx[n−2]))+ ...