Fundamentals of Electric Circuits
6th Edition
ISBN: 9780078028229
Author: Charles K Alexander, Matthew Sadiku
Publisher: McGraw-Hill Education
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Chapter 17, Problem 50P
To determine
Find the exponential Fourier series for the given function.
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2) Periodic signal x(t) which is shown in Figure-1 is applied to a LTI system with
impulse response h:
h(t) = 3 8 (t) + 2 e -4' u(t)
Find the output y(t) using the Fourier Series of x(t) and h(t).
LTI
x(t)
y(t)
h(t)
Find the Fourier transform of the following function.
1
f(t)
2m (3+jt)²
=
a.
O b. F(w)
F(w) =
-we³wu(w)
3w
-2πwе³wu(w)
OC F(w) = 2πwе-3wu(w)
-3wu (w)
O d. F(w)
=we
1 Assume that z(t) and y(t) are both continuous time aperiodic signals, and Fourier transform z(t) is X(w). What is the Fourier transform of
y(t) = r(t) – 2z(t – to)?
Select one:
a. Y(w) = X(w) - 2X(w+ 2un)
b. Y(w) = X(w)
c. Y(w) = X(w) – 2X(w)e juto
O d. Y(w) = X(w) + 2X(w)eiutu
Chapter 17 Solutions
Fundamentals of Electric Circuits
Ch. 17.2 - Find the Fourier series of the square wave in Fig....Ch. 17.2 - Determine the Fourier series of the sawtooth...Ch. 17.3 - Prob. 3PPCh. 17.3 - Find the Fourier series expansion of the function...Ch. 17.3 - Prob. 5PPCh. 17.4 - Prob. 6PPCh. 17.4 - If the input voltage in the circuit of Fig. 17.24...Ch. 17.5 - The voltage and current at the terminals of a...Ch. 17.5 - Find the rms value of the periodic current i(t) =...Ch. 17.6 - Obtain the complex Fourier series of the function...
Ch. 17.6 - Obtain the complex Fourier series expansion of...Ch. 17.7 - Prob. 12PPCh. 17.8 - Rework Example 17.14 if the low-pass filter is...Ch. 17 - Which of the following cannot be a Fourier series?...Ch. 17 - If ft=t,0t,ft+n=ft, the value of 0 is (a) 1 (b) 2...Ch. 17 - Which of the following are even functions? (a) t +...Ch. 17 - Prob. 4RQCh. 17 - Prob. 5RQCh. 17 - If f(t) = 10 + 8 cos t + 4 cos 3t + 2 cos 5t + ,...Ch. 17 - Prob. 7RQCh. 17 - The plot of |cn| versus n0 is called: (a) complex...Ch. 17 - Prob. 9RQCh. 17 - Prob. 10RQCh. 17 - Evaluate each of the following functions and see...Ch. 17 - Using MATLAB, synthesize the periodic waveform for...Ch. 17 - Given that Fourier coefficients a0, an, and bn of...Ch. 17 - Find the Fourier series expansion of the backward...Ch. 17 - Prob. 5PCh. 17 - Find the trigonometric Fourier series for f t =...Ch. 17 - Determine the Fourier series of the periodic...Ch. 17 - Using Fig. 17.51, design a problem to help other...Ch. 17 - Determine the Fourier coefficients an and bn of...Ch. 17 - Find the exponential Fourier series for the...Ch. 17 - Obtain the exponential Fourier series for the...Ch. 17 - Prob. 12PCh. 17 - Prob. 13PCh. 17 - Find the quadrature (cosine and sine) form of the...Ch. 17 - Express the Fourier series...Ch. 17 - The waveform in Fig. 17.55(a) has the following...Ch. 17 - Prob. 17PCh. 17 - Prob. 18PCh. 17 - Obtain the Fourier series for the periodic...Ch. 17 - Prob. 20PCh. 17 - Prob. 21PCh. 17 - Calculate the Fourier coefficients for the...Ch. 17 - Using Fig. 17.61, design a problem to help other...Ch. 17 - Prob. 24PCh. 17 - Determine the Fourier series representation of the...Ch. 17 - Find the Fourier series representation of the...Ch. 17 - For the waveform shown in Fig. 17.65 below, (a)...Ch. 17 - Obtain the trigonometric Fourier series for the...Ch. 17 - Prob. 29PCh. 17 - Prob. 30PCh. 17 - Prob. 31PCh. 17 - Prob. 32PCh. 17 - Prob. 33PCh. 17 - Prob. 34PCh. 17 - Prob. 35PCh. 17 - Prob. 36PCh. 17 - If the periodic current waveform in Fig. 17.73(a)...Ch. 17 - Prob. 38PCh. 17 - Prob. 39PCh. 17 - The full-wave rectified sinusoidal voltage in Fig....Ch. 17 - Prob. 42PCh. 17 - The voltage across the terminals of a circuit is...Ch. 17 - Prob. 44PCh. 17 - A series RLC circuit has R = 10 , L = 2 mH, and C...Ch. 17 - Prob. 46PCh. 17 - Prob. 47PCh. 17 - Prob. 48PCh. 17 - Prob. 49PCh. 17 - Prob. 50PCh. 17 - Prob. 51PCh. 17 - Prob. 52PCh. 17 - Prob. 53PCh. 17 - Find the exponential Fourier series for the...Ch. 17 - Obtain the exponential Fourier series expansion of...Ch. 17 - The Fourier series trigonometric representation of...Ch. 17 - Prob. 57PCh. 17 - Find the exponential Fourier series of a function...Ch. 17 - Prob. 59PCh. 17 - Obtain the complex Fourier coefficients of the...Ch. 17 - The spectra of the Fourier series of a function...Ch. 17 - Prob. 62PCh. 17 - Plot the amplitude spectrum for the signal f2(t)...Ch. 17 - Prob. 64PCh. 17 - Prob. 65PCh. 17 - Prob. 66PCh. 17 - Prob. 67PCh. 17 - Prob. 68PCh. 17 - Prob. 69PCh. 17 - Design a problem to help other students better...Ch. 17 - Prob. 71PCh. 17 - Prob. 72PCh. 17 - Prob. 73PCh. 17 - Prob. 74PCh. 17 - Prob. 75PCh. 17 - Prob. 76PCh. 17 - Prob. 77CPCh. 17 - Prob. 78CPCh. 17 - Consider the full-wave rectified sinusoidal...Ch. 17 - Prob. 82CP
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- The Fourier transform of the signal x(t) =- is, a) ju(@) b) jsgn(@) c) -ju(@) d) -jsgn(@)arrow_forwardYou can do it with any method you want. Write the signal y(t) given in the figure in the form of a Fourier series. (It can be real or complex.) Y(+) A An tarrow_forwardCompute the discrete time Fourier series (DTFS) of the following signal and plot its magnitude response x[n] = 8[n] + 8[n – 1] – 8[n + 1] %3Darrow_forward
- Suppose that X(w) is real but not even. Can we conclude whether X[n]must be or cannot be real ? Can we conclude whether X[n]must be or cannot be even ? Remark: There is one wrong answer that will still give you +1 point. Hint 1: This is based on the logical use of several properties of Fourier transform. Hint 2: If a" = a, what do you conclude ? Hint 3: If a sequence y[n] is Hermitian symmetric, is it true or not that y[n] is real if and only if y[n] is even ? X[n]must be real, and we cannot conclude on its even symmetry. nX[n]cannot be real, and we cannot conclude on its even symmetry. Oxn]must be even, and we cannot conclude whether it is real or not. Oxn]cannot be even, and we cannot conclude whether it is real or not. OXIN]must be real and must be even. xn]must be real and cannot be even. Xn)cannot be real and must be even. x(n]cannot be real and cannot be even. None of the above.arrow_forwardQ1: For the signal f(t), shown in figure beside. i) Find Fourier Transform F(w) ii) Sketch amplitude and phase spectrum of F(w) -1 0 1arrow_forward2. A function f(t) has Fourier transform, F(w) = we-w². What are the Fourier transforms of: (a) f(t-3) (b) f(1/2) (c) f(¹=³)arrow_forward
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- 3) Consider the signal. Xo(-t) -1 Xo(t +1) -1 0 Using only the Fourier Transform of xo(t) and Fourier Transform properties, determine the Fourier Transform of each signal shown in the Figure below. x₁ (t) X₂(t) (a) X3(t) 0 (c) x (t) xo(t) 1 xo(t) 1 = t e 0, t " 0 ≤t≤1 elsewhere -1 -Xo(-t). (b) xo(t) (d) 1 X4(t) txo(t) La 0 1 t (1) tarrow_forwardFind the fourier transform of the following signal. (a) eatu(-t) (b) t"e-atu(t) (c) ejwot (d) sin wot (e) cos wot (f) e-at. sin wot.u(t)arrow_forward6. For each of the following Fourier transform F(@), state whether the corresponding inverse Fourier transform f(t) is periodic or not, and explain why. If periodic, determine its fundamental period. (b) F(@) -3n -2n –n 0 n 2n 3narrow_forward
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