Signals and Systems - Electrical Engineering

4 C H A P T E R 0: From the Ground Up! processing, the trend has been toward digital representation and processing of data, most ...

0.2 Examples of Signal Processing Applications 5 Advances in digital electronics and in computer engineering in the past 60 year ...

6 C H A P T E R 0: From the Ground Up! DAC Laser Sensor Audio amplifier Speaker FIGURE 0.2 When playing a CD, the CD player foll ...

0.2 Examples of Signal Processing Applications 7 different users of the radio spectrum (commercial radio and T V, amateur radio, ...

8 C H A P T E R 0: From the Ground Up! for network services that it can offer to its users. Thus, SDR and CR are bound to change ...

0.3 Analog or Discrete? 9 of a different type than the reference. Such would be the case, for instance, if the plant output is a ...

10 C H A P T E R 0: From the Ground Up! with minimal information loss. Chapters 1, 7, and 8 will provide the necessary informati ...

0.3 Analog or Discrete? 11 FIGURE 0.5 Sampling an analog sinusoid x(t)=2 cos( 2 πt), 0≤t≤ 10 , with two different sampling perio ...

12 C H A P T E R 0: From the Ground Up! signals is given. In Chapter 7, where we consider the problem of sampling, we will use t ...

0.3 Analog or Discrete? 13 which again coincides with the derivative. Finally, we consider a signal that changes faster thanx(t) ...

14 C H A P T E R 0: From the Ground Up! or the sum of the area underx(t)fromt 0 tot. Notice that the upper bound of the integral ...

0.3 Analog or Discrete? 15 FIGURE 0.7 Approximation of area under x(t)=t,t≥ 0 , 0 otherwise, by pulses of width 1 and heightnTs, ...

16 C H A P T E R 0: From the Ground Up! which is a lot better result. In general, we have that the integral can be computed quit ...

0.3 Analog or Discrete? 17 FIGURE 0.8 RC circuit. + − vi(t) 1 Ω 1 F i(t) FIGURE 0.9 Realization of first-order differential equa ...

18 C H A P T E R 0: From the Ground Up! which is represented by the block diagram in Figure 0.9(b). Notice that the integrator a ...

0.3 Analog or Discrete? 19 bevi(t)=1 fort≥0, we have vc(nT)= { 0 n= 0 2 T 2 +T+ 2 −T 2 +Tvc((n−^1 )T) n≥^1 (0.13) The advantage ...

20 C H A P T E R 0: From the Ground Up! 0.4 Complex or Real? Most of the theory of signals and systems is based on functions of ...

0.4 Complex or Real? 21 FIGURE 0.11 (a) Representation of a complex numberzby a vector (b) addition of complex numberszandv; (c) ...

22 C H A P T E R 0: From the Ground Up! so thatj^0 =1,j^1 =j,j^2 =−1,j^3 =−j, and so on. Lettingj= 1 ejπ/^2 , we can see that th ...

0.4 Complex or Real? 23 0.4.2 Functions of a Complex Variable Just like real-valued functions, functions of a complex variable c ...