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신호및시스템 solution(2nd edition) Pages 1-50 – Flip PDF Download | FlipHTML5

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신호및시스템 solution(2nd edition) Pages 1-50 - Flip PDF Download | FlipHTML5
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(PDF) 신호및 시스템 솔루션[1] | 승환 김 – Academia.edu

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  • Summary of article content: Articles about (PDF) 신호및 시스템 솔루션[1] | 승환 김 – Academia.edu [10] (a) Linear, time-varying, causal, BIBO stable system; (b) modulated signal is periodic of pe- riod 28; (c) x(t) = u(t) → y(t) = u(t)−u(t−2) and … …
  • Most searched keywords: Whether you are looking for (PDF) 신호및 시스템 솔루션[1] | 승환 김 – Academia.edu [10] (a) Linear, time-varying, causal, BIBO stable system; (b) modulated signal is periodic of pe- riod 28; (c) x(t) = u(t) → y(t) = u(t)−u(t−2) and … 신호및 시스템 솔루션[1]
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Partial Answers to End-of-Chapter Problems

Chapter 2

(PDF) 신호및 시스템 솔루션[1] | 승환 김 - Academia.edu
(PDF) 신호및 시스템 솔루션[1] | 승환 김 – Academia.edu

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파일첨부(#1) : 신호및시스템 2판 솔루션 (signal systems , Alan V.Oppenheim , Prentice Hall) 신호및시스템 (파일첨부1).zip | hsit63zaab

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파일첨부(#1) : 신호및시스템 2판 솔루션   (signal systems , Alan V.Oppenheim , Prentice Hall) 신호및시스템 (파일첨부1).zip | hsit63zaab
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애플레포트✔신호 및 시스템 2판 솔루션 (저자 Alan V Oppenjeim 2nd ed Discrete Time Signal Processing) 디지털신호처리전기전자솔루션

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애플레포트✔신호 및 시스템 2판 솔루션   (저자 Alan V. Oppenjeim , 2nd ed Discrete Time Signal Processing) 디지털신호처리전기전자솔루션 – Apple Report
애플레포트✔신호 및 시스템 2판 솔루션 (저자 Alan V. Oppenjeim , 2nd ed Discrete Time Signal Processing) 디지털신호처리전기전자솔루션 – Apple Report

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[솔루션] 신호와 시스템 2판 Signals and Systems 2Ed – Haykin – Solutions Manual 솔루션 | 멋쟁이응님의 스페이스

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    [솔루션] 신호와 시스템 2판 Signals and Systems 2Ed – Haykin – Solutions Manual 솔루션 | 멋쟁이응님의 스페이스 [솔루션] 신호와 시스템 2판 Signals and Systems 2Ed – Haykin – Solutions Manual 솔루션 Signals and Systems 2Ed – Haykin.pdf 분량 : 634 페이지 /pdf 파일 설명 … …
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[솔루션] 신호와 시스템 2판 Signals and Systems 2Ed – Haykin – Solutions Manual 솔루션 | 멋쟁이응님의 스페이스
[솔루션] 신호와 시스템 2판 Signals and Systems 2Ed – Haykin – Solutions Manual 솔루션 | 멋쟁이응님의 스페이스

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신호및 시스템 솔루션[1]

Partial Answers to End-of-Chapter Problems

Chapter 0

[1] A 75 min. recording gives 7.938×10 8 bytes for maximum frequency of 22.05 KHz, 8 bits/sample, two channels (stereo); vocoder reduces number of bits transmitted; (c) texting is cheaper;

(d) DVD audio 192 KHz sampling rate, and 24 bits/sample; (e) 352 × 240 × 60 pixels/sec.

[2] Analog and discrete signals for T s = 0.1 are very similar, not for T s = 1.

[3] y(t) = −8π sin(2πt), finite difference for T s = 0.01 looks like derivative, not so for T s = 0.1.

[4] (a) ∆ 1 [x[n + 1]] = ∆ ]; average gives better approximation to derivative.

[5] (a) di L (t)/dt + i L (t) = i s (t) dual of the difference equation in the chapter.

[6] (a) Σ k ca k = cΣ k a k , Σ k [a k + b k ] = Σ k a k + Σ k b k , a 0 + a 1 + a 2 + a 3 = a 0 + a 2 + a 3 + a 1 (i.e., in any order); (b) S = 0.5(N (N + 1)); (c) S 1 = (α + βN/2)(N + 1).

[7] The definite integral is 0.5, then [(N − 1)(N − 2) + 2(N − 1)]/(2N 2 ) ≤ 0.5 ≤ [(N − 1)(N − 2) + 2(N − 1)]/(2N 2 ) + 1/N .

[8] S 1 = S + 50, S 2 = S. [10] (c) α = e a ; (d) v c (1) = 0.79.

[11] (a) |z| = √ 2, ∠z = π/4; (b) |u| = √ 2, ∠u = −π/4; (c) z/w = w/v = u/z = −j; (d) y = 10 −6 z, negligible magnitude, same phase as z.

[12] (a) log(w) = z; (c) w + w * = 2e cos(1); (e) | log(w)| 2 = 2.

[13] Compare e jα e jβ (use Euler’s) to e j(α+β) .

[14] Use sin(α) = cos(α − π/2) and sin(β) = cos(β − π/2).

[15] (a) zz * = x 2 +y 2 , 1/z = z * /(zz * ), using polar representation is easier; (z+w) * = z * +w * , (zw) * = z * w * ; (d) zw = rρe j(θ+φ) .

[16] (a) z = x + jy = |z|e jθ , |x| = |z|| cos(θ)| ≤ |z| since | cos(θ)| ≤ 1; add two vectors graphically.

[17] (a) x(t) = (1 − t 2 ) + j2t, y(t) = −2t + 2j; (c) 1 0 x(t)dt = (2/3) + j; (d) [18] e jπn = (−1) n ; (b)(c) use Euler’s identity T0 0 sin(πt) cos(πt)dt = 0. 1 0 sin 2 (2πt)dt = 0.5.

[20] z 2 = 1 has roots −1 and 1; z 2 = −1 has roots −j and j; z 3 = 1 has roots 1 and e ±j2π/3 ; z 3 = −1 has roots −1 and e ±j2π/3 .

[21] log(−2) = log(2) ± jπ, log(2e jπ/4 ) = log(2) + jπ/4.

[22] cosh(θ) = cos(jθ) is even; sinh(θ) = −j sin(jθ) is odd.

[23] (a) sin(Ω 0 t) = cos(Ω 0 t − π/2); phasor Ae −jπ/2 generates sine; (c) phasor Ae jπ/2 .

Chapter 1

[2] (a) P a = 0; (b) P a = 0.25; (c) P a = 0.5; (d) the real part of the complex power, P = 0.5V s I * for phasors V s and I, in given cases gives same results.

[

[5] (a) x(t + 1) is x(t) advanced by 1, i.e., shifted to the left by 1;

shifted to the right by 1; (c) y(t) equals Λ(t) except y(0) = 2 while Λ(0) = 1.

[7] (a) Triangular pulse has width 2∆ and height 1/∆ thus unit area, as ∆ → 0 it gives δ(t); (b) S ∆ (t) = sin(πt/∆)/(πt), S ∆ (0) = 1/∆, and ∞ −∞ S ∆ (t)dt = 1, so that as ∆ → 0 it gives δ(t).

[

[9] (a) Steady state: voltage across capacitor equals voltage of source, so no current through resistor; (b) v c (t) = 1 in steady state; (c) (d) capacitor discharges through resistor.

[10] (a)

[11] ss T (t) = Σ ∞ k=0 u(t − kT ), a stairway to the stars; (b) digitized ramp and cosine, using ss T (t) approximate signal.

[12] (a) y(t) = z(t), operations do not commute.

[13] (a) x(2t) = 2t[u(t) − u(t − 0.5)], i.e., x(t) has been compressed;

i.e., x(t) has been expanded; (c) play it faster (contraction) or slower (expansion) than the speed at which it was recorded.

[14] (a) Even-odd decomposition

[16] (a) x(t/2) is periodic of period 4; x(2t) is periodic of period 1.

[20] F s = 8192 samples/sec, N N = 4096 samples.

[21] (a) 1 + 0.7e jφt = (1 + 0.7 cos(φt)) + j0.7 sin(φt) = A(t)e jθ(t) , A(t) = 1.49 + 1.4 cos(φt), θ(t) = tan −1 (0.7 sin(φt)/(1 + 0.7 cos(φ(t)).

Chapter 2

[1] (a) v 0 (t) = −(1 + 0.5 cos(20πt))u(t);

[2] (a) Nonlinear system.

[4] (a) Convolution integral, h(t) = e −t u(t); causal; (c) s(t) = (1 − e −t )u(t); (d) use superposition and TI.

[5] (a) Nonlinear; large q/kT gives large current for positive voltages; (c) nonlinear.

, v c (0) = −1, v c2 = 2v c1 , i.e., nonlinear; nonlinear.

[7] i 1 (t) = −2π sin(2πt)[1 + 2 cos(2πt)]; (c) time varying system.

[8] Not LTI, LTI, not LTI, LTI respectively.

[9] x 1 (t) = u(t) → y 1 (t) = cos(πt)u(t), x 2 (t) = u(t − 1) → y 2 (t) = cos(πt)u(t − 1) = y 1 (t − 1),

[10] (a) Linear, time-varying, causal, BIBO stable system; (b) modulated signal is periodic of pe-

[11] (a) Nonlinear if y(0) = 0; (b) dy(t)/dt + 2y(t) = 2x(t); (c) y ss (t) = 1, independent of IC; (d) convolution gives y(t) = (1 − e −t )u(t); (e) BIBO stable.

[12] Nonlinear, time invariant system.

[13] (a) TV; (b) s(t) = √ 2m(t) cos(Ω c t − π/4), one modulator with a phase, linear.

[14] (a) LTI system

[16] (a) Non-causal; (b) BIBO stable.

also not bounded.

[2] (a) X(s) = cos(s), (c) X(s) = cos(Ω) cosh(σ)+j sin(Ω) sinh(σ) from which you find magnitude and phase.

[

) with ROC the whole plane except for the origin; (c) 0.5[(1/s) + (s/(s 2 + 4)].

[4] No Laplace transform, empty ROC.

[5] X(s) = (e s−1 s + e s−1 − 2)/(s 2 − 1), ROC σ > −1.

[6] (a) d 2 y(t)/dt 2 + 4y(t) = x(t), (b) y(0) = 0 and y (0) = −1.

[7] H(s) = (s + 2)/(s(s + 1) 2 ) with ROC σ > 0.

[8] (a) First two terms: −4δ(t) and dδ(t)/dt;

[9] (a) 0.1;

smoother than x(t) as output of an averager; (c) 3M.

[12] (a)

[16] (a) X(s) has infinite number of zeros on jΩ axis;

with residues 0.087 and −0.044 ± 0.083j.

[18] (a) Y (s) = X(s)/(s 2 + 0.5s + 0.15); (b) the system is not LTI; (c) Y 1 (s) = (s 2 + 1.5s + 2)/(s 3 + 0.5s 2 + 0.15s).

[19] (a) Ignoring IC,

[20] (a) The zero-state response is y

[21] (a) System is unstable;

[24] (a) y(t) = 1

[25] (a) System is not BIBO stable; x(t) = 2 cos(2t)u(t); (c) No.

[26] (a) y(t) = 1

[27] (a) d 2 y1(t)

Chapter 4 No, the eigenfunction property is not valid for non-linear systems as in (a) or time-varying systems as in .

[2] y ss (t) = 2|H(j2π)| cos(2πt + ∠H(j2π)

and y ss (t) = A = Y (s)s | s=0 = 2.

[7] (a) X k = j/(2πk);

, k = 0,

[11] X k = 1 2 sin(πk/2) πk/2 e −jπk/2 , Y k = 1 2 sin(πk/2) πk/2 2 (−1) k using 1 − cos(πk) = 2 sin 2 (πk/2). |Y k | = 2|X k | 2 and X 0 = 1 2 = Y 0 .

[12] Periods:

πk e −jπk/2 for kΩ 0 = πk and Y k = X k for kΩ 1 = 2πk.

[13] (a) Derivative of period of x(t) in −0.5 ≤ t ≤ 0.5 gives

and

Ts e jkΩst ; (b) line spectrum of δ Ts (t) is periodic of period Ω s and magnitude T s .

[15] (a) x(t) periodic of period T 0 , x(t+T 0 ) = k A k cos(Ω k (t+T 0 )+θ k ) = x(t) then Ω k T 0 = 2πk or Ω k = 2π T0 k multiples of Ω 0 , the fundamental frequency; (b) x(t) = 2 cos(0Ω 0 + 0) + 1 cos(1Ω 0 t + 0) − 3 cos(3Ω 0 t + π/4) then A 0 = 2, θ 0 = 0; A 1 = 1, θ 1 = 0 and A 3 = −3 and θ 3 = π/4; (c) not periodic.

[16] (a) X k = 2(−1) k (1−4k 2 )π , X 0 = 2/π; (b) y(t) = X 0 H(j0) + ∞ k=−∞,k =0 X k H(j2πk)e j2πkt , if y(t) = X(0) = 2/π then H(j0) = 1 and H(j2πk) = 0 for k = 0.

is periodic of period T 0 and Z k = X k (1 + e −2jΩ0k ); w(t) is periodic of period T 0 /2 and

[20] N = 5.

[21] (a) Z n = k X k Y n−k ; (b) Z n = k X k Y (n−k)/2

[22] (a) s(t) = [23] X 0 = 1/2, X 2 = X −2 = −1/4; (b) Y k = 2/(π(1 − 4k 2 )); (c) x(t) = y(t); (d) low-pass filter of magnitude 2 and cutoff frequency 0 < Ω x < 4π gives a steady state z(t) = 1. [24] (a) W k = 2e −jkπ (cos(πk) − cos(πk/2))/(−Ω 2 0 k 2 ) Ω 0 = 352π; (b) s(t) has harmonics of w(t) shifted to central frequency 2πf A . [25] π = 4 ∞ k=1 sin(πk/2)/k sin(πk/T0) kπk/T0 ; (c) spectrum gets smaller and denser as T 0 increases (so multiply X k by T 0 ) [2] (b)X 1 (Ω) = sin(Ω/2)/(Ω/2), X 2 (Ω) = 4πe −j(Ω/4) cos(Ω/4)/(4π 2 −Ω 2 ), X 3 (Ω) = 2(1−cos(Ω))/Ω 2 [4] (a) x(t) absolutely integrable and finite energy, X(Ω) = X(s) | s=jΩ = 2 jΩ + 2 (jΩ + 2) 2 + 4π 2 [5] (a)(c) X 1 (Ω) = 1 2+jΩ and X 3 (Ω) = 1 (2+jΩ) 2 from their Laplace transforms, x 2 (t) = r(t) ↔ X 1 (s) = 1/s 2 , σ > 0 so we can’t find its FT (jΩ-axis not included)

[8] (a) T 0 = 1, X(Ω) = sin(Ω/2) Ω/2 e −jΩ/2 and |X(2πk)| = 0. For T 0 = 10, X(Ω) = sin(5Ω) 5Ω e −j5Ω and |X(kπ/5)| = 0, i.e., expansion in time corresponds to contraction in frequency

[10] (a) x(t) = r(t+1)−2r(t)+r(t−1), triangular pulse, y(t) = dx(t)/dt = u(t+1)−2u(t)+u(t−1), (d) y(t) is smoother.

[12] (a) X(Ω) = 2 cos(Ω);

[13] (a) X(Ω) = 2 cos(ΩT 1 ); (b) Y (Ω) = 1 + 2 ∞ k=1 cos(kT 0 Ω), both y(t) and Y (Ω) are periodic of period 2π/T 0

Ts e jkΩst , Ω s = 2π Ts with FT ∆(Ω) = 2π

Ts k δ(Ω − kΩ s ); (c) δ Ts (t) and ∆ Ts (Ω) periodic, of periods T s and 2π/T s δ(Ω − (k + 1)Ω 0 ) + δ(Ω − (k − 1)Ω 0 ) + δ(Ω + (k − 1)Ω 0 ) + δ(Ω + (k + 1)Ω 0 ) (c) Same message available at different carrier frequencies

[20] (a) Fourier coefficients: X k = cos(πk/2)e −jπk/2 /(π(1 − k 2 )), X 0 = 1/π, |X 1 | = 1/4 and |X 2 | = 1/(3π); (b) Low-pass filter: amplitude π and cut-off frequency 0 < Ω c < π [23] (a) h(t) = sin(πt)/(πt), non-causal; (b) g(t) = h(t)2 cos(5πt) with magnitude response G(jΩ) = H(j(Ω − 5π)) + H(j(Ω + 5π)) [24] H 1 (s) = (s − 1)((s − 1) 2 + π 2 )/((s + 1)((s + 1) 2 + π 2 )), all-pass filter. low-pass filter [3] −(R 2 /R 1 )V i (s) = V 0 (s) + (V 0 (s)/A)(1 + R 2 /R 1 ) can be written as negative feedback. As [4] (a) RC circuit transfer function V 0 (s)/V i (s) = (1/RC)/(s + 1/RC) from which to obtain the feedback system; (b) steady-state error e(t) = v i (t) − v 0 (t) = 0 [5] Differential equation corresponding to transfer function is can be implemented using two integrators and an adder; [1] (a) f s ≥ 10 KHz, bits/hour = 288 × 10 6 ; (b) f s ≥ 44KHz [2] (a) X(Ω) = π[u(Ω + 1) − u(Ω − 1)]; (b) T s ≤ π sec/sample; (c) T s ≤ π/2; (d) T s = π [3] (a) Y (Ω) = e −jΩ (sin(Ω/2)/(Ω/2)) 2 ; (b)(c) y(t) smoother than x(t), since Ω x = 5.6 > Ω y = 2.6 rad/sec, T sy > T sx , aliasing if x(t) is sampled using T sy ; (d) T sx appropriate for sampling and y(t)

[4] (a)(b) Ω max ≈ 22 rad/sec; computing ∆(t) and ∆(Ω) the uncertainty bound is satisfied.

[5] (a) X(Ω) = 2π[u(Ω+0.5)−u(Ω−0.5)]; (b)(c) bandlimited, T s ≤ 2π; (d) X s (Ω) = (1/(2π)) k X(Ω0k) = 1, passing x(t) through a low-pass filter with amplitude 2π and cutoff frequency 1/2 we obtain the original signal No.

[9] (a) T s = 1, Ω s = 2π ≥ 2Ω max , low-pass filter of magnitude 1 and cutoff frequency Ω max < Ω c < 2π − Ω max ; (b) maximum frequency should be less than π [10] CD player is reproducing a signal that has been processed by an antialiasing filter before being sampled, quantized and coded. High frequencies might have been filtered out and also quantization error is present possibly making the reproduced signal of less quality than the After denominator coefficients are found, replace them in the following equation to get the {b k }: [22] Use the convolution property, so that if D(z) has d coefficients, then D 2 (z) has coefficients d * d, i.e., the convolution sum of the coefficients d with itself. [23] (a) h 1 [n] = h[n/2] for n = 0, 2, 4, · · · and zero otherwise, H 1 (z) = H(z 2 ) [24] (a) Cascade H(z) = H 1 (z)H 2 (z) = 2(1 − z 1 ) 1 + 0.5z −1 1 + √ 2z −1 + z −2 1 − 0.9z −1 + 0.81z −2 (b) Parallel H(z) = −4.94 + 2.16 1 + 0.5z −1 + 4.78 − 1.6z −1 1 − 0.9z −1 + 0.81z −2

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