![8. a. Evaluate and sketch the output of the system if h[n] G un] x(t) -2-1 0 Find the Fourier series coefficients of the periodic signal shown above. [15 marks b.](http://img.homeworklib.com/questions/dc6a1cb0-6a2c-11eb-9993-05592074f6f6.png?x-oss-process=image/resize,w_560)
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8. a. Evaluate and sketch the output of the system if h[n] G un] x(t) -2-1...
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...
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...
How to find the fourier series and sketch the spectrum x(t) Help me to find the...
How to find the fourier series and sketch the spectrum
x(t)
Help me to find the laplace transform for a and b
Help me to find system response
Question 1 (8 marks) a) Determine the Fourier series coefficients of the periodic signal x(t) shown in Figure 1. Determine the de value of x(t)! b) Sketch the spectrum of x(t). x(t) -352 10 T2 31/2 -A Figure 1 O XU) RUOLO elsewhere exe(t) = el, a > 0 1) Sketch the...
Signal system 8. Consider the periodic signal x(t) = cos(2nt) + cos(2nt) I. a. Find the...
Signal system
8. Consider the periodic signal x(t) = cos(2nt) + cos(2nt) I. a. Find the Fourier series coefficients for this signal. (4 points). b. If this signal passes through a LTI system with the impulse response h(t)=e* u(t), particularly, would the output signal also be a periodic signal ? If so, what would be the Fourier coefficients of the output signal ? (4 points). c. Give the mathematical expression for the output signal y(t). (2 points).
Question 1: The following system gets its input signal g(t) and convolve it with a train...
Question 1: The following system gets its input signal g(t) and convolve it with a train of deltas d(t) g(t) d(t) ſ(t) 1-1 Find the Fourier transform ( Gw) or G(f) ) for the aperiodic signal g(t) 1-2 Find the Fourier series coefficients, Dn for the periodic signal g(t) if d(e) = į 8(t - 4n) N -00 1-3 Plot the frequency spectrum for GW) 1-4 Find the average power of the periodic g(t) Question 1: The following system gets...
5. (12 points) Consider a continuous-time LTI system whose frequency response is sin(w) H(ju) 4w If...
5. (12 points) Consider a continuous-time LTI system whose frequency response is sin(w) H(ju) 4w If the input to this system is a periodic signal 0, -4<t<-1 x(t)=1, -1st<1 0, 1st<4 with period T= 8 (a) (2 points) sketch r(t) for -4ts4 (b) (5 points) determine the Fourier series coefficients at of x(t), (c) (5 points) determine the Fourier series coefficients be of the corresponding system output y(t)
5. (12 points) Consider a continuous-time LTI system whose frequency response is...
3. Let the following periodic signal : x(t) = m+0 8(t -- 3m) + 8(t-1-3m) +...
3. Let the following periodic signal : x(t) = m+0 8(t -- 3m) + 8(t-1-3m) + 8(t – 2 – 3m) be the input to a LTI system with a system function: H(s) = es/4 – e-s/4, Let by represent the Fourier series coefficients of the resulting output signal y(t). Determine bk. (5 points)
Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients as Do = 1, Dn = 2 (1 + j(-1)") Sketch the magnitude and phase spectral-line...
Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients as Do = 1, Dn = 2 (1 + j(-1)") Sketch the magnitude and phase spectral-line up to the a) b) Estimate the signal's power from the 1t four h c) Write the math ematical expression for the complex exponential Fourier series expansion form. 12) Solution:
Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients...
Q1. Consider the system displayed below 8[n] blul y[n] W[n] sin(in/2) where x[n] = sin(itn/4) πη...
Q1. Consider the system displayed below 8[n] blul y[n] W[n] sin(in/2) where x[n] = sin(itn/4) πη w[n] = ejîn, and h[n] πη a) Sketch G(j12), the discrete-time Fourier transform of g[n], for - << +0. b) Find the output signal y[n] of the system. (10 marks) (10 marks)
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)
1. A LTI system has the frequency response function 0, all other o Compute the output y(t) resulting from the in put x(t) given by (a) x(t) -2-5cos(3t)+10sin(6t-jx/3)+4cos(12t-x/4) (b) x(t) = 1 + Σ-...
1. A LTI system has the frequency response function 0, all other o Compute the output y(t) resulting from the in put x(t) given by (a) x(t) -2-5cos(3t)+10sin(6t-jx/3)+4cos(12t-x/4) (b) x(t) = 1 + Σ- cos(2kt ) k-l (c) x(t) is the periodic pulse train signal shown below (repeats beyond the graph) 0.5 0.5 5 t (second) Hint: Refer to lecture 10 note. For (c), find the Fourier series coefficients of x(t) first.
1. A LTI system has the frequency response...
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...
How to find the fourier series and sketch the spectrum
x(t)
Help me to find the laplace transform for a and b
Help me to find system response
Question 1 (8 marks) a) Determine the Fourier series coefficients of the periodic signal x(t) shown in Figure 1. Determine the de value of x(t)! b) Sketch the spectrum of x(t). x(t) -352 10 T2 31/2 -A Figure 1 O XU) RUOLO elsewhere exe(t) = el, a > 0 1) Sketch the...
Signal system
8. Consider the periodic signal x(t) = cos(2nt) + cos(2nt) I. a. Find the Fourier series coefficients for this signal. (4 points). b. If this signal passes through a LTI system with the impulse response h(t)=e* u(t), particularly, would the output signal also be a periodic signal ? If so, what would be the Fourier coefficients of the output signal ? (4 points). c. Give the mathematical expression for the output signal y(t). (2 points).
Question 1: The following system gets its input signal g(t) and convolve it with a train of deltas d(t) g(t) d(t) ſ(t) 1-1 Find the Fourier transform ( Gw) or G(f) ) for the aperiodic signal g(t) 1-2 Find the Fourier series coefficients, Dn for the periodic signal g(t) if d(e) = į 8(t - 4n) N -00 1-3 Plot the frequency spectrum for GW) 1-4 Find the average power of the periodic g(t) Question 1: The following system gets...
5. (12 points) Consider a continuous-time LTI system whose frequency response is sin(w) H(ju) 4w If the input to this system is a periodic signal 0, -4<t<-1 x(t)=1, -1st<1 0, 1st<4 with period T= 8 (a) (2 points) sketch r(t) for -4ts4 (b) (5 points) determine the Fourier series coefficients at of x(t), (c) (5 points) determine the Fourier series coefficients be of the corresponding system output y(t)
5. (12 points) Consider a continuous-time LTI system whose frequency response is...
3. Let the following periodic signal : x(t) = m+0 8(t -- 3m) + 8(t-1-3m) + 8(t – 2 – 3m) be the input to a LTI system with a system function: H(s) = es/4 – e-s/4, Let by represent the Fourier series coefficients of the resulting output signal y(t). Determine bk. (5 points)
Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients as Do = 1, Dn = 2 (1 + j(-1)") Sketch the magnitude and phase spectral-line up to the a) b) Estimate the signal's power from the 1t four h c) Write the math ematical expression for the complex exponential Fourier series expansion form. 12) Solution:
Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients...
Q1. Consider the system displayed below 8[n] blul y[n] W[n] sin(in/2) where x[n] = sin(itn/4) πη w[n] = ejîn, and h[n] πη a) Sketch G(j12), the discrete-time Fourier transform of g[n], for - << +0. b) Find the output signal y[n] of the system. (10 marks) (10 marks)
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)
1. A LTI system has the frequency response function 0, all other o Compute the output y(t) resulting from the in put x(t) given by (a) x(t) -2-5cos(3t)+10sin(6t-jx/3)+4cos(12t-x/4) (b) x(t) = 1 + Σ- cos(2kt ) k-l (c) x(t) is the periodic pulse train signal shown below (repeats beyond the graph) 0.5 0.5 5 t (second) Hint: Refer to lecture 10 note. For (c), find the Fourier series coefficients of x(t) first.
1. A LTI system has the frequency response...
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