Signals and Systems - Electrical Engineering

444 CHAPTER 7: Sampling Theory 7.4.3 Sampling, Quantizing, and Coding with MATLAB The conversion of an analog signal into a digi ...

7.4 Practical Aspects of Sampling 445 %%%%%%%%%%%%%%%%%%%%%%%%%%% % Sampling, quantization and coding %%%%%%%%%%%%%%%%%%%%%%%%%% ...

446 CHAPTER 7: Sampling Theory The binary signal corresponding to the quantized signal is computed using the functioncoderwhich ...

Problems 447 is an important problem that is left for texts in digital signal processing. We will, however, develop the theory o ...

448 CHAPTER 7: Sampling Theory where 1(t)=     ∞∫ −∞ t^2 |x(t)|^2 dt Ex     0.5 measures the duration of the signal fo ...

Problems 449 7.8. Sampling output of nonlinear system The input–output relation of a nonlinear system is y(t)=x^2 (t) wherex(t)i ...

This page intentionally left blank ...

CHAPTER 8 Discrete-Time Signals and Systems......................................................... It’s like dej ́a-vu,` all o ...

452 C H A P T E R 8: Discrete-Time Signals and Systems just like those for continuous-time signals. However, some of these basic ...

8.2 Discrete-Time Signals 453 Determine an appropriate sampling periodTsaccording to the Nyquist sampling rate condition, and ob ...

454 C H A P T E R 8: Discrete-Time Signals and Systems 8.2.1 Periodic and Aperiodic Signals A discrete-time signalx[n]isperiodic ...

8.2 Discrete-Time Signals 455 From their frequencies determine if these signals are periodic, and if so, determine their corresp ...

456 C H A P T E R 8: Discrete-Time Signals and Systems wish to have a sinusoid with periodN=10, thenTs=0.2kπforkchosen so the Ny ...

8.2 Discrete-Time Signals 457 which says that a period(m= 1 )or several periods(m> 1 )should be divided intoN>0 segments o ...

458 C H A P T E R 8: Discrete-Time Signals and Systems nExample 8.6 Determine if the signal x[n]= ∑∞ m= 0 Xmcos(mω 0 n) ω 0 = 2 ...

8.2 Discrete-Time Signals 459 nExample 8.7 A “causal” sinusoid, obtained from a signal generator after it is switched on, is x(t ...

460 C H A P T E R 8: Discrete-Time Signals and Systems To find the power we use the trigonometric identity (or Euler’s equation) ...

8.2 Discrete-Time Signals 461 FIGURE 8.1 (a) Signalx 2 [n] (nonperiodic forn≥ 0 ) and (b) signalx 1 [n] (periodic forn≥ 0 ). The ...

462 C H A P T E R 8: Discrete-Time Signals and Systems Likewise, forx[n+M] thex[0] appears advanced byMsamples, or shifted to th ...

8.2 Discrete-Time Signals 463 − 5 0 5 10 15 0 5 10 15 n y[ n] = x[ n+ 3] +x [n −3] − 5 051015 n x[ n +3] 0 2 4 6 8 10 12 x[ n− 3 ...