2.4.1. Suppose (t is as shown 3-2 1 3 4 (a) Determine the fundamental period To,...
Let a periodic signal x(t) with a fundamental frequency ??e2? have a period 4.6 (a) Plot x(t), and indicate its fundamental period To (b) Compute the Fourier series coefficients of x(t) using their integral (c) (d) Answers: x(t) is periodic of fundamental period definition. Use the Laplace transform to compute the Fourier series coefficients Xk. Indicate how to compute the dc term. Suppose that y(t) = dx(t)/dt, find the Fourier transform of x(t) by means of the Fourier series coefficients...
(b) Let X(ju) denote the Fourier transform of the signal r(t) shown in the figure x(t) 2 -2 1 2 Using the properties of the Fourier transform (and without explicitly evaluating X(jw)), ii. (5 pts) Find2X(jw)dw. Hint: Apply the definition of the inverse Fourier transform formula, and you can also recall the time shift property for Fourier Transform. (c) (5 pts) Fourier Series. Consider the periodic signal r(t) below: 1 x(t) 1 -2 ·1/4 Transform r(t) into its Fourier Series...
Question 3 (30 points) Consider the signals defined below: *:(t) = cos(2) xz(t) = cos(4+) a) Determine the fundamental period for each signal. b) Determine the fundamental period and fundamental frequency of the signal: y(t) = x;(C)x(0) (t) and x2(c) when the fundamental frequency is c) Determine the Fourier Series coefficients of defined as determined in part (b). d) Using Parseval's relation, determine the power of xy(t) and xy(t) e) Determine and plot the Fourier Series Coefficients of y(t). Show...
Signals and systems Problem 2 (20 points) Let -S2t+1, Osts1 x(t) = -t +4, 1sts 3 be a periodic signal with fundamental period T=3 and Fourier coefficients ar a. Determine the value of ao. b. Determine ak, k = 0, by: 1. first finding the Fourier coefficients of ii.then using the appropriate property of the continuous-time Fourier series. c. Use the result of part (b) to express the Fourier transform of x().
l, f) is a periodic signal with period f(t)-n(t)-u(t-t/2 ) for 0 2π a.) Find the exponential Fourier series of f() and sketchf). What is the fundamental radian frequency. b.) Evaluate and sketch |Dml, the magnitude of the Fourier series coefficients vs.o in the range of -4s n S4 c.) Evaluate and sketch the phase angle of D, vs. co in the same range (-4S n S4) d.) Find the signal average power e) Find the approximate average power of...
Problem 1 (20 pts) Suppose that x(t) = e 2 for 0 st <3 and is periodic with period 3. a) Determine the fundamental frequency of this signal. (2 pts) b) Determine the Fourier series representation for this signal. (7 pts) c) Suppose that this signal is the input to an LTI system with impulse response h(t) = 5sinc(0.5t). Determine the Fourier series representation for the output signal y(t). Be sure to specify the fundamental period and all Fourier series...
1. Using the Fourier series analysis Equation 3 for the periodic function r(t) shown in Figure 2.1, determine both the DC coefficient ao and a general expression for the other Fourier series coefficients ak. Do this by hand, not in Matlab. Show all your work in your lab report. You can add these pages as hand-written pages, rather than typing them in to your lab report, if you prefer Hint 1: It will be easiest to integrate this function from...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fundamental frequency. 3. Calculate the Trigonometric Fourier Series and sketch the amplitude spectrum and phase spectrum of the signal x(t) for the first 5 harmonics. b) Find the Continuous Time Fourier Series (CTFS) and Continuous Time Fourier Transform (CTFT) of the following periodic signals...
Problem 2 (20 points) Let (2t +1, Ostsi x() +4 st 3 be a periodic signal with fundamental period T=3 and Fourier coefficients ar. a. Determine the value of an b. Determine ax, k 0, by: 1.first finding the Fourier coefficients of CID II.then using the appropriate property of the continuous-time Fourier series. c. Use the result of part(b) to express the Fourier transform of (t).
Consider the periodic signal x(t) shown in the Figure below: x(t) . 3 2 0 1 2 3 4 5 6 t A. Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.