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Question 1 (20pts]: Let x(0) = 1-1.2 st <3 Question 1 120ntsl: Let (t) 1,0 Stsi...
Problem 1 (20 pts) Suppose that x(t) = e 2 for 0 st <3 and is...
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...
Let x(t) = t, 0<t 1 and Fourier series coefficients a , be a periodic signal...
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)
Problem 2 (20 points) Let (2t +1, Ostsi x() +4 st 3 be a periodic signal...
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...
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.
3. (20pts.) Find the Fourier series of the function given 0- <x<0 x. 0<x<
3. (20pts.) Find the Fourier series of the function given 0- <x<0 x. 0<x<
Signals and systems Problem 2 (20 points) Let -S2t+1, Osts1 x(t) = -t +4, 1sts 3...
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().
3. For the equation 24 = r, in 0 <<1,0<t<1, (1,0) = sin(x), on 0 SEST...
3. For the equation 24 = r, in 0 <<1,0<t<1, (1,0) = sin(x), on 0 SEST (0,1)=0, u(1. t) = 0, on 0 <t<1, (1) Using the separation of variables, find its solution.
Let a periodic signal x(t) with a fundamental frequency ??e2? have a period 4.6 (a) Plot...
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...
20 points) Consider the periodic signal z(t) shown in the Figure below: X(t) 3 2 N....
20 points) Consider the periodic signal z(t) shown in the Figure below: X(t) 3 2 N. 0 1 2 3 4 5 6 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.
4. (20 points) Consider the periodic signal r(t) shown in the Figure below: x(t) 3 2...
4. (20 points) Consider the periodic signal r(t) shown in the Figure below: x(t) 3 2 N VAA 0 1 2 3 4 5 6 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.
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...
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)
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.
3. (20pts.) Find the Fourier series of the function given 0- <x<0 x. 0<x<
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().
3. For the equation 24 = r, in 0 <<1,0<t<1, (1,0) = sin(x), on 0 SEST (0,1)=0, u(1. t) = 0, on 0 <t<1, (1) Using the separation of variables, find its solution.
20 points) Consider the periodic signal z(t) shown in the Figure below: X(t) 3 2 N. 0 1 2 3 4 5 6 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.
4. (20 points) Consider the periodic signal r(t) shown in the Figure below: x(t) 3 2 N VAA 0 1 2 3 4 5 6 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.
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