By Hwei Hsu
Converted to comply to the present curriculum, Schaums define of signs and platforms enhances those classes in scope and series that can assist you comprehend its easy options. The ebook bargains perform on subject matters similar to rework ideas for the research of LTI structures, the LaPlace rework and its software to continuous-time and discrete-time LTI platforms, Fourier research of indications and structures, and the kingdom house or country variable inspiration and research for either discrete-time and continuous-time structures. applicable for the subsequent classes: simple Circuit research, electric Circuits, electric Engineering and Circuit research, creation to Circuit research, AC and DC Circuits.
Features:
- 571 solved problems
- extra fabric on matrix idea and intricate numbers
- aid for all of the significant textbooks for electric engineering classes family electrical circuits
Topics contain: signs and structures, Linear Time-Invariant structures, LaPlace rework and Continuous-Time LTI structures, The z-Transform and Discrete-Time LTI structures, Fourier research of Continuous-Time indications and structures, Fourier research of Discrete-Time, kingdom area research, evaluation of Matrix conception, homes of Linear Time-Invariant platforms and numerous Transforms, evaluation of advanced Numbers, priceless Mathematical formulation
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Additional resources for Schaum's Outline of Signals and Systems, Second Edition
Example text
Examples of the above convolution integral operation are given in Probs. 6. F. 11) CHAPTER 2 Linear Time-Invariant Systems In many applications, the step response s(t) is also a useful characterization of the system. The step response s(t) can be easily determined by Eq. 12) Thus, the step response s(t) can be obtained by integrating the impulse response h(t). Differentiating Eq. 13) Thus, the impulse response h(t) can be determined by differentiating the step response s(t). 3 A. 14) y(t) = Kx(t) where K is a (gain) constant.
Determine whether the system is linear. y, [n] 2 2 -2 - 1 0 1 2 3 4 n -2- 1 0 1 2 3 4 ---+0--+ -2 - 1 0 2 3 4 n n 2 -2- 1 0 1 2 3 4 n Y3[n] x3(nj 3 ---+0--+ 2 -2 - 1 0 1 2 3 4 -2- 1 0 1 2 3 4 n Fig. 1-39 n -- CHAPTER 1 Signals and Systems From Fig. 1-39 it is seen that Thus, if Tis linear, then which is shown in Fig. 1-40. From Figs. 1-39 and 1-40 we see that Hence , the system is not linear. 2 2 2 + -2- 1 0 1 2 3 4 n n - 2- 1 0 1 2 3 4 -2- 1 0 1 2 3 4 n Fig. 42. 67). 116) where x*[n] is the complex conjugate of x[n] .
47. Express the sequences shown in Fig. 1-42 in terms of unit step sequences. x[n] x[n] >- - 4 - 3- 2 - 1 -2- 1 0 1 2 - n N 01 • 4• I I 1 ~ 2 3 - 1 (b) (a) x[n] - 4 - 3- 2 - 1 O 1 2 3 4 5 n (c) Fig. 48. 49. (t), respectively. 50. Let x[n] be an arbitrary sequence with even and odd parts denoted by x,[n] and xJn], respectively. 51. Determine whether or not each of the following signals is periodic. If a signal is periodic , determine its fundamental period. 52. 53. (a) }: (b) }: x[k] = }: x[k] k=O k=no What is lJ(2t)?