Signals and Systems Using MATLAB 3rd. Edition by Luis F. Chaparro, Aydin Akan | 9780128142042 | 0128142049 | Holooly

Analog and Digital Signals and Systems

Signals and Systems Using MATLAB

271 SOLVED PROBLEMS

Question: 9.14

Consider the following four sinusoids: x1[n] = sin(0.1πn), x2[n] = sin(0.2πn), x3[n] = sin(0.6πn), x4[n] = sin(0.7πn) −∞ <n< ∞. Find if they are periodic and if so find their fundamental periods. Are these signals harmonically related? Use MATLAB to plot these signals from n = 0,··· , 40. Comment ...

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To find if they are periodic, we rewrite the given...

Question: 9.12

Given the analog signal x(t) = e^−at cos(Ω0t)u(t), determine the values of a > 0, Ω0, and Ts that permit us to obtain a discrete-time signal y[n] = α^n cos(ω0n) n ≥ 0 and zero otherwise. Consider the case when α = 0.9 and ω0 = π/2, find a, Ω0, and Ts that will permit us to obtain y[n] from x(t) by ...

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Comparing the sampled continuous-time signal [late...

Question: 9.11

Find the even and odd components of the following discrete-time signal: x[n] = { 4 − n 0 ≤ n ≤ 4, 0 otherwise. ...

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The even component of x[n] is given by

x_e[...

Question: 9.10

We will see that in the convolution sum we need to figure out how a signal x[n − k] behaves as a function of k for different values of n. Consider the signal x[k] = { k 0 ≤ k ≤ 3, 0 otherwise. Obtain an expression for x[n − k] for −2 ≤ n ≤ 2 and determine in which direction it shifts as n increases ...

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Although x[n − k], as a function of k, is reflecte...

Question: 9.9

A triangular discrete pulse is defined as x[n] = { n 0 ≤ n ≤ 10, 0 otherwise. Find an expression for y[n] = x[n + 3] + x[n − 3] and z[n] = x[−n] + x[n] in terms of n and carefully plot them. ...

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Replacing n by n + 3 and by n − 3 in the definitio...

Question: 9.8

Determine if a discrete-time exponential x[n] = 2 (0.5)^n, n ≥ 0, and zero otherwise, has finite energy, finite power or both. ...

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The energy is given by

\varepsilon_{x}=\sum...

Question: 9.6

Determine if the signal x[n] = ∑m=0 ^∞ Xm cos(mω0n), ω0 = 2π/N0 is periodic, and if so determine its fundamental period. ...

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The signal x[n] consists of the sum of a constant ...

Question: 9.5

The signal z[n] = v[n] + w[n] + y[n] is the sum of three periodic signals v[n], w[n] and y[n] of fundamental periods N1 = 2, N2 = 3 and N3 = 4, respectively. Determine if z[n] is periodic, and if so give its fundamental period. ...

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Let x[n] = v[n] + w[n], so that z[n] = x[n] + y[n]...

Question: 9.4

What is true for analog sinusoids—that they are always periodic—is not true for discrete sinusoids. Discrete sinusoids can be non-periodic even if they result from uniformly sampling a periodic continuous-time sinusoid. Consider the discrete-time signal x[n] = cos(n + π/4), −∞ <n< ∞, which is ...

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The sampled signal x[n] =

x(t)|_{t=nT_s}[/l...

Question: 8.3

Consider the two sinusoids x1(t) = cos(Ω0t), x2(t) = cos((Ω0 + Ω1)t) −∞ ≤ t ≤ ∞ where Ω1 > 2Ω0. Show that if we sample these signals using Ts = 2π/Ω1, we cannot differentiate the sampled signals, i.e. x1(nTs) = x2(nTs). Let Ω0 = 1 and Ω1 = 7 rad/s, use MATLAB to show the above graphically. Explain ...

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