- 1.1.1: Express each of the following complex numbers in Cartesian form (x ...
- 1.1.2: Express each of the following complex numbers in polar form (re.i8,...
- 1.1.3: Determine the values of P x and Ex for each of the following signal...
- 1.1.4: Let x[n] be a signal with x[n] = 0 for n < -2 and n > 4. For each s...
- 1.1.5: Let x(t) be a signal with x(t) = 0 fort < 3. For each signal given ...
- 1.1.6: Determine whether or not each of the following signals is periodic:...
- 1.1.7: For each signal given below, determine all the values of the indepe...
- 1.1.8: Express the real part of each of the following signals in the form ...
- 1.1.9: Determine whether or not each of the following signals is periodic....
- 1.1.11: Determine the fundamental period of the signal x[n] = 1 + ej4mzn - ...
- 1.1.12: Consider the discrete-time signal x[n] = 1 - .L o[n - 1 - k]. k=3 D...
- 1.1.13: Consider the continuous-time signal x(t) = o(t + 2) - o(t - 2). Cal...
- 1.1.14: Consider a periodic signal y(t) = tx X(T)dT. 0 ~ t ~ 1 l
- 1.1.15: Consider a systemS with input x[ n] and output y[ n]. This system i...
- 1.1.16: Consider a discrete-time system with input x[n] and output y[n]. Th...
- 1.1.17: Consider a continuous-time system with input x(t) and output y(t) r...
- 1.1.18: Consider a discrete-time system with input x[n] and output y[n] rel...
- 1.1.19: For each of the following input-output relationships, determine whe...
- 1.1.21: A continuous-time signal x(t) is shown in Figure P1.21. Sketch and ...
- 1.1.22: A discrete-time signal is shown in Figure P1.22. Sketch and label c...
- 1.1.23: Determine and sketch the even and odd parts of the signals depicted...
- 1.1.24: Determine and sketch the even and odd parts of the signals depicted...
- 1.1.25: Determine whether or not each of the following continuous-time sign...
- 1.1.26: Determine whether or not each of the following discrete-time signal...
- 1.1.27: In this chapter, we introduced a number of general properties of sy...
- 1.1.28: Determine which of the properties listed in 1.27 hold and which do ...
- 1.1.29: (a) Show that the discrete-time system whose input x[n] and output ...
- 1.1.31: In this problem, we illustrate one of the most important consequenc...
- 1.1.32: Let x(t) be a continuous-time signal, and let Yt (t) = x(2t) and Y2...
- 1.1.33: Let x[ n] be a discrete-time signal, and let { x[n/2] y 1 [n] = x[2...
- 1.1.34: In this problem, we explore several of the properties of even and o...
- 1.1.35: Consider the periodic discrete-time exponential time signal x[n] = ...
- 1.1.36: Let x(t) be the continuous-time complex exponential signal x(t) = e...
- 1.1.37: An important concept in many communications applications is the cor...
- 1.1.38: In this problem, we examine a few of the properties of the unit imp...
- 1.1.39: The role played by u(t), o(t), and other singularity functions in t...
- 1.1.41: Consider a systemS with input x[n] and output y[n] related by y[n] ...
- 1.1.42: (a) Is the following statement true or false? The series interconne...
- 1.1.43: (a) Consider a time-invariant system with input x(t) and output y(t...
- 1.1.44: (a) Show that causality for a continuous-time linear system is equi...
- 1.1.45: In 1.37, we introduced the concept of correlation functions. It is ...
- 1.1.46: Consider the feedback system of Figure P1.46. Assume that y[n] = 0 ...
- 1.1.47: (a) LetS denote an incrementally linear system, and let x 1 [n] be ...
- 1.1.48: Let zo be a complex number with polar coordinates (r0, 00 ) and Car...
- 1.1.49: Express each of the following complex numbers in polar form, and pl...
- 1.1.51: Using Euler's relation, derive the following relationships: (a) cos...
- 1.1.52: Let z denote a complex variable; that is, z = x + jy = re.i 8 . The...
- 1.1.53: Derive the following relations, where z, z1, and z2 are arbitrary c...
- 1.1.54: The relations considered in this problem are used on many occasions...
- 1.1.55: Using the results from 1.54, evaluate each of the following sums an...
- 1.1.56: Evaluate each of the following integrals, and express your answer i...

# Solutions for Chapter 1: Basic System Properties

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ISBN: 9780138147570

Solutions for Chapter 1: Basic System Properties

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