- 9.9.1: For each of the following integrals, specify the values of the real...
- 9.9.2: Consider the signal x(t) = e-5tu(t -1), and denote its Laplace tran...
- 9.9.3: Consider the signal x(t) = e- 51 u(t)+e-f31 u(t), and denote its La...
- 9.9.4: For the Laplace transform of x(t) = { et sin 2t, 0, t :::; 0 t>O' i...
- 9.9.5: For each of the following algebraic expressions for the Laplace tra...
- 9.9.6: An absolutely integrable signal x(t) is known to have a pole at s =...
- 9.9.7: How many signals have a Laplace transform that may be expressed as ...
- 9.9.8: Let x(t) be a signal that has a rational Laplace transform with exa...
- 9.9.9: Given that oC 1 e-atu(t) ~ --, s+a ffi-e{ s} > ffi-e{- a}, determin...
- 9.9.11: Use geometric evaluation from the pole-zero plot to determine the m...
- 9.9.12: Suppose we are given the following three facts about the signal x(t...
- 9.9.13: Let g(t) = x(t) +ax( -t), where x(t) = {3 e -t u(t) and the Laplace...
- 9.9.14: Suppose the following facts are given about the signal x(t) with La...
- 9.9.15: Consider two right-sided signals x(t) and y(t) related through the ...
- 9.9.16: A causal LTI systemS with impulse response h(t) has its input x(t) ...
- 9.9.17: A causal LTI system S has the block diagram representation shown in...
- 9.9.18: Consider the causal LTI system represented by the RLC circuit exami...
- 9.9.19: Determine the unilateral Laplace transform of each of the following...
- 9.9.21: Determine the Laplace transform and the associated region of conver...
- 9.9.22: Determine the function of time, x(t), for each of the following Lap...
- 9.9.23: For each of the following statements about x(t), and for each of th...
- 9.9.24: Throughout this problem, we will consider the region of convergence...
- 9.9.25: By considering the geometric determination of the Fourier transform...
- 9.9.26: Consider a signal y(t) which is related to two signals x 1 (t) and ...
- 9.9.27: We are given the following five facts about a real signal x(t) with...
- 9.9.28: Consider an LTI system for which the system function H(s) has the p...
- 9.9.29: Consider an LTI system with input x(t) = e-t u(t) and impulse respo...
- 9.9.31: Consider a continuous-time LTI system for which the input x(t) and ...
- 9.9.32: A causal LTI system with impulse response h(t) has the following pr...
- 9.9.33: The system function of a causal LTI system is s + 1 H(s) = 2 2 2. s...
- 9.9.34: Suppose we are given the following information about a causal and s...
- 9.9.35: The input x(t) and output y(t) of a causal LTI system are related t...
- 9.9.36: In this problem, we consider the construction of various types of b...
- 9.9.37: Draw a direct-form representation for the causal LTI systems with t...
- 9.9.38: Consider a fourth-order causal LTI systemS whose system function is...
- 9.9.39: Let XJ (t) = e-2t u(t) and x2(t) = e- 3(t+I)u(t + 1). (a) Determine...
- 9.9.41: (a) Show that, if x(t) is an even function, so that x(t) = x( -t), ...
- 9.9.42: Determine whether each of the following statements is true or false...
- 9.9.43: Let h(t) be the impulse response of a causal and stable LTI system ...
- 9.9.44: Let x(t) be the sampled signal specified as x(t) = Le-nT 8(t - nT),...
- 9.9.45: Consider the LTI system shown in Figure P9.45(a) for which we are g...
- 9.9.46: Let H(s) represent the system function for a causal, stable system....
- 9.9.47: The signal y(t) = e-2t u(t) is the output of a causal all-pass syst...
- 9.9.48: The inverse of an LTI system H(s) is defined as a system that, when...
- 9.9.49: A class of systems, referred to as minimum-delay or minimum-phase s...
- 9.9.51: Consider a stable and causal system with a real impulse response h(...
- 9.9.52: As indicated in Section 9.5, many of the properties of the Laplace ...
- 9.9.53: As presented in Section 9.5.10, the initial-value theorem states th...
- 9.9.54: Consider a real-valued signal x(t) with Laplace transform X(s). (a)...
- 9.9.55: In Section 9.6, Table 9.2, we listed a number of Laplace transform ...
- 9.9.56: The Laplace transform is said to exist for a specific complex s if ...
- 9.9.57: The Laplace transform X(s) of a signal x(t) has four poles and an u...
- 9.9.58: Let h(t) be the impulse response of a causal and stable LTI system ...
- 9.9.59: IfX(s) denotes the unilateral Laplace transform of x(t), determine,...
- 9.9.61: The autocorrelation function of a signal x(t) is defined as cf>xx(T...
- 9.9.62: In a number of applications in signal design and analysis, the clas...
- 9.9.63: In filter design, it is often possible and convenient to transform ...
- 9.9.64: Consider the RLC circuit shown in Figure 9.27 with input x(t) and o...
- 9.9.65: (a) Determine the differential equation relating vi(t) and v0 (t) f...
- 9.9.66: Consider the RL circuit shown in Figure P9.66. Assume that the curr...

# Solutions for Chapter 9: The Laplace Transform

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Solutions for Chapter 9: The Laplace Transform

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