MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems--Fall 2003 PROBLEM SET 3 Issued: September 18, 2003 Due: September 26. 2003 Reading Assignments Lectures #5-6& PS#2: Chapter 3 of Oppenheim and Willsky(O& w) Lectures #3-4 &z PS#3: Chapters 3&4 of Oppenheim and Willsky(O&w) Exercise for home study (not to be turned in, although we will provide solutions) O&W3.46(a),(c) Problems to be turned in: Problem 1 O&W 3.22(a)-only the signal in Figure p3. 22(c) Problem 2 O&W 3.23(a) Problem 3 Determine the Fourier series coefficients for the periodic signal a[n] depicted below. Plot the magnitude and phase of these coefficient Problem 4 O&W 3.29(a)
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems—Fall 2003 Problem Set 3 Issued: September 18, 2003 Due: September 26, 2003 Reading Assignments: Lectures #5-6 & PS#2: Chapter 3 of Oppenheim and Willsky (O&W) Lectures #3-4 & PS#3: Chapters 3&4 of Oppenheim and Willsky (O&W) Exercise for home study (not to be turned in, although we will provide solutions): O&W 3.46 (a),(c) Problems to be turned in: Problem 1 O&W 3.22 (a) - only the signal in Figure p3.22 (c) Problem 2 O&W 3.23 (a) Problem 3 Determine the Fourier series coefficients for the periodic signal x[n] depicted below. Plot the magnitude and phase of these coefficients. x[n] 2 −12 −6 0 6 12 · · · · · · n 1 −1 Problem 4 O&W 3.29 (a) 1
Problem 5 Consider the following CT periodic signals, a(t), y(t), and z(t) y(t) AAVv z(t) (a) Determine the fundamental frequency, period, and Fourier series coefficients, ak, for (t) (b) Determine the fundamental frequency, period, and Fourier series coefficients, bk, for (c) Determine the fundamental frequency and period for z(t). Also, using the results of parts(a) and(b), determine the Fourier series coefficients, ck for z(t) Problem 6 Let r(t)be a periodic signal with fundamental period T and Fourier series coefficients ak. Derive the Fourier series coefficients of each of the following signals in terms (a)Od{x(t-T/2)} (b)x(T/4-t)
Problem 5 Consider the following CT periodic signals, x(t), y(t), and z(t). x(t) 1 − t 6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 y(t) −6 −4 −2 2 4 6 1 −1 t z(t) −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 1 −1 t (a) Determine the fundamental frequency, period, and Fourier series coefficients, ak, for x(t). (b) Determine the fundamental frequency,period, and Fourier series coefficients, bk, for y(t). (c) Determine the fundamental frequency and period for z(t). Also, using the results of parts (a) and (b), determine the Fourier series coefficients, ck for z(t). Problem 6 Let x(t) be a periodic signal with fundamental period T and Fourier series coefficients ak. Derive the Fourier series coefficients of each of the following signals in terms of ak: (a) Od{x(t − T/2)} (b) x(T/4 − t) 2
Problem 7 O&W3.31 (also determine ao Problem 8 O&W3.51 Reminder: The first 20 problems in each chapter of O&w have answers included at the end of the text. Consider using these for additional practice, either now or as you study for tests
Problem 7 O&W 3.31 (also determine a0) Problem 8 O&W 3.51 Reminder: The first 20 problems in each chapter of O&W have answers included at the end of the text. Consider using these for additional practice, either now or as you study for tests. 3
