Signals and Systems - Electrical Engineering

104 C H A P T E R 1: Continuous-Time Signals nExample 1.24 One way of transmitting a message over the airwaves is to multiply it ...

1.4 Representation Using Basic Signals 105 FIGURE 1.14 AM signal. − 5 05 − 5 0 5 t z( t) n 1.4.5 Generic Representation of Signa ...

106 C H A P T E R 1: Continuous-Time Signals FIGURE 1.15 Multiplication of a signalf(t)by an impulse signal δ(t−t 0 ). ×= tttt 0 ...

1.5 What Have We Accomplished? Where Do We Go from Here? 107 Table 1.1Basic Signals Signal Definition Complex exponential |A|ert ...

108 C H A P T E R 1: Continuous-Time Signals Problems........................................................................... ...

Problems 109 (a) Determine the periodT 0 ofx(t). (b)Compute the powerPxofx(t). (c)Verify that the powerPxis the sum of the power ...

110 C H A P T E R 1: Continuous-Time Signals (c)Issinh(t)even or odd? (d)Obtain an expression forx(t)=e−tu(t)in terms of the hyp ...

Problems 111 1.10. Ramp in terms of unit-step signals A ramp,r(t)=tu(t), can be expressed as r(t)= ∫∞ 0 u(τ)u(t−τ)dτ (a) Show th ...

112 C H A P T E R 1: Continuous-Time Signals 1.12. Reflection and time shifting Do the reflection and the time-shifting operatio ...

Problems 113 (b)Show that the energy of the signalx(t)can be expressed as the sum of the energies of its even and odd components ...

114 C H A P T E R 1: Continuous-Time Signals (a) Carefully plot the signaly(t)=dx(t)/dt, the derivative ofx(t). (b)Can you compu ...

Problems 115 1.20. Multipath effects, first part—MATLAB In wireless communications, the effects ofmultipathsignificantly affect ...

116 C H A P T E R 1: Continuous-Time Signals sum of these sinusoids. Assume theNPplayers while trying to play the pure tone end ...

CHAPTER 2 Continuous-Time Systems....................................................................... Things should be made a ...

118 C H A P T E R 2: Continuous-Time Systems synthesis short intervals of speech are modeled as the output of linear time-invari ...

2.3 LTI Continuous-Time Systems 119 n Lumped- or distributed-parameter systems—This classification relates as to how the element ...

120 C H A P T E R 2: Continuous-Time Systems When developing a mathematical model for a continuous-time system it is important t ...

2.3 LTI Continuous-Time Systems 121 Solution Lety(t)be the system response corresponding tox(t). Assume then that we scale the i ...

122 C H A P T E R 2: Continuous-Time Systems Solution Superposition is not satisfied for the first system. If the outputs forx 1 ...

2.3 LTI Continuous-Time Systems 123 When the relation is a straight line through the origin with a constant slopeC, using the cu ...