ONLY NUMBER 2 1. Find the CTFS coefficients of the periodic signal 1 1-4 」E [0, 1] 0 otherwise 2. In this problem you will practice using properties to derive the CTFS coefficients of 0 otherwise...
3. Consider the periodic signal x(t) = 0 otherwise (a) Plot r(t). (b) What is the period T of x(t)? (c) Find the CTFS coefficients ak for (t). 3. Consider the periodic signal x(t) = 0 otherwise (a) Plot r(t). (b) What is the period T of x(t)? (c) Find the CTFS coefficients ak for (t).
Practice problem All parts of this problem involve the infinite-duration periodic signal r(t) shown below. ) (periodic 7-5 -1 7 0 (a) (15 points) On the axes below, provide a clearly labeled sketch of the spectrum X(w). Hint: Employ the infinite impulse train b) (10 points) Suppose r(t) is the input to a continuous-time LTI system with impulse response 3 2TT πί. h(t)-2-sine(9) . Determine the output y(t) for -oo<t<oo
Let x(t) = t, 0<t 1 and Fourier series coefficients a , be a periodic signal with fundamental period of T 2 -t,-1t0 dz(t) a) Sketch the waveform of r(t)d3 marks) b) Calculate ao (3 marks) c) Determine the Fourier series representation of gt)(4 rks) d) Using the results from Part (c) and the property of continuous-time Fourier series to dr(t) determine the Fourier series coefficients of r(t) (4 marks)
Consider the signal 2, defined for allt e Ras sin(at) 1<t<4 (t) 0 otherwise. Define the signal y as y(t) = x(4 – t) for allt ER For which value of t does (x+y)(t) assume its maximum value? 3 2 6 none of the other answers 4 0
filtering of periodic signals: damental frequency 120 = 1/4 is the Answers: Gk = 0.J, Consider the following problems related to filtering of (a) A periodic signal x(t) of fundamental frequen input of an ideal band-pass filter with the following response the following frequency 11312 3 3/2 1 -37% -21 322 5 3/2 ZH(N2) = 2 -3/2 223 - 0 otherwise ero Fourier series coefficients of x(t) are (92)/ = o otherwise The non-zero Fourie X = X-1 = ),...
Suppose, we let g(t) of problem 1 be periodic (i.e., g(t) is 9T (t) according to the notation using). To be precise let A 4Volts, let the pulse width T-0.1 seconds and let the 0.2 seconds. Find its continuous Fourier transform. Hint: gr. (t) is now that we are fundamental period To periodic and hence you can first find the Fourier series coefficients (C,) and relate those coefficients to the continuous Fourier transform of a periodic signal. Accurately sketch the...
(a) Given the following periodic signal a(t) a(t) -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 i. [2%) Determine the fundamental period T ii. [5%] Derive the Fourier series coefficients of x(t). iii. [396] Calculate the total average power of z(t). iv. [5%] If z(t) is passed through a low-pass filter and the power loss of the output signal should be optimized to be less than 5%, what should be the requirement of cutoff frequency of the low-pass filter?...
For all parts of this problem, let z(t) be the signal shown below. (Note that x(t) is defined by: x(t) = 3 - t for 0 <t <3; (t) = 0, otherwise.) 3 x(t) to i à (a) (6 points) Find the values of: (i) ſo r(t)8(t – 1)dt (ii) x(t)(t – 1)dt. (b) (6 points) Plot the signal y(t) defined by y(t) = x(r – 2)8(t – r)dr. (c) (6 points) Find the energy in x(t). (d) (7 points)...
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).
Problem 2 125 Marks Given the following periodic signal: 5-3-2 e) a- Find the trigonometric Fourier series, sketch the amplitude, and phase spectra. [15 Marks] Student b- Does the signal has a de component? Exp Explain. [5 Marks] If you are given the signal x(t) = tu (t). Can we write the Fourier series of the signal in the period 0 t < 1? Explain. [5 Marks] c-