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() Describe analog and digital signals in terms of Noise and interference...
What are the absolute bandwidths of the signals shown in Problem 2(a) above? Note: Absolute BW-hi...
What are the absolute bandwidths of the signals shown in Problem 2(a) above? Note: Absolute BW-highest frequency component present in a signal). What is the null-null bandwidth of the waveform in Problem 2 part (iv)? What is the 3 dB bandwidth of x(t) 0.5eu(t)? Abo, write down an equation to find the 3 dB bandwidth of a ilter with transfar finction, H(4). 605+1) a) Find the Fourier transforms of the following signals and sketch their magnitude spectrums i) x(t) 12e...
Problem 2 In each step to follow the signals h(t) r (t) and y(t) denote respectively the impulse ...
Problem 2 In each step to follow the signals h(t) r (t) and y(t) denote respectively the impulse response. input, and output of a continuous-time LTI system. Accordingly, H(), X (w) and Y (w) denote their Fourier transforms. Hint. Carefully consider for each step whether to work in the time-domain or frequency domain c) Provide a clearly labeled sketch of y(t) for a given x(t)-: cos(mt) δ(t-n) and H(w)-sine(w/2)e-jw Answer: y(t) Σ (-1)"rect(t-1-n)
Problem 2 In each step to follow...
1. Using appropriate properties and the table of Fourier transforms, obtain and sketch the sin(at) Fourier...
1. Using appropriate properties and the table of Fourier transforms, obtain and sketch the sin(at) Fourier transform of the signal x()cn(31-4 marks) 2fX(a), determine the Fourier transform of the signal y(t)dx( F.T. dx(2t) dt (3 marks) 3. Find the Fourier transform of x(t)-cos(2t/4). (3 marks) 4. Let x(t) be the input to a linear time-invariant system. The observed output is y(t) 4x(t 2). Find the transfer function H() of the system. Hence, obtain and sketch the unit-impulse response h(t) of...
What are the absolute bandwidths of the signals shown in Problem 4(a) above? (Note: Absolute BW=...
What are the absolute bandwidths of the signals shown in Problem 4(a) above? (Note: Absolute BW= highest frequency component present in a signal). What is the null-null bandwidth of the waveform in Problem 4(a) - (iii)? What is the 3 dB bandwidth of x(t) = -2e-4tu(t)? Write down an equation to find the 3 dB bandwidth of a filter with transfer function and then solve it to find its 3-dB bandwidth: H(s) = (+2)(+3). -4. Please use a Table of...
A cascaded system that consists of an LTI system and a delay system is shown in...
A cascaded system that consists of an LTI system and a delay system is shown in Figure Q4(b). The input signal X(t) and impulse response of the LTI system, h(t) are given as the following: x(t) = 6-2&u(t) h(t) = e-fu(t) Determine: The Fourier transform of y(t). (3 marks) The Fourier transform of z(t). (3 marks) A basic modulator circuit is shown in Figure Q4(c). Modulation is a multiplication between input signal, m(t), and a carrier signal, c(t). The process...
Question given an LTI system, characterized by the differential equation d’y() + 3 dy + 2y(t)...
Question given an LTI system, characterized by the differential equation d’y() + 3 dy + 2y(t) = dr where x(t) is the input, and y(t) is the output of the system. a. Using the Fourier transform properties find the Frequency response of the system Hw). [3 Marks] b. Using the Fourier transform and assuming initial rest conditions, find the output y(t) for the input x(t) = e-u(t). [4 Marks] Bonus Question 3 Marks A given linear time invariant system turns...
Find the fourier transform of the following function
1. Find the Fourier transforms of the following functions:
(1) f(x) = rect * (x) * r * e * c * t * (x - 1)
(2) g(x) = 2sin c * (2x) * sin(x)
(3) p(x) = rect(x - 2)/2x
(4) u(x) = 3sin c * (3x) - sin c * (x)
(5) v(x) = sinc(x) * sinc (x) * sinc (x)
2. Find and sketch the functions and the corresponding Fourier transforms:
(1) f(x) = 1/5 *...
Home-Work 5 All questions carry equal points. Don't forget to highlight your final answers 25 ues...
Home-Work 5 All questions carry equal points. Don't forget to highlight your final answers 25 uestion # 1 Use table to find Fourier transform. Sketch the magnitude response and phase response (i) x(t) Cos(1000t) (ii) x(t) 13Cos(100t)- 7Sin(500t) (iv) x(t) rect To (v) xo)-rect ()Cos(10001) (v) x(o) -ret)Cos(000t) Question # 2 Let h(t) be a linear time invariant system, with the following transfer function s + 1 000m (a) Find H(w) (b) Sketch the magnitude and phase response of H(w)...
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...
Question B2 Figure 8 shows a DC electric circuit with a 2-way switch. The capacitor is...
Question B2 Figure 8 shows a DC electric circuit with a 2-way switch. The capacitor is initially not charged. At t= Os, switch is at position and the capacitor is then charged up 1000 Position1 RT Position2 (20V R 500 0.02F (NV Figure 8 (a) Whent > sec, the capacitor is charged through R, to steady state, 0 Find the complete response of y(t) fort > 0s. (5 marks) (m) Sketch the response of (t) for t> Os. (3 marks)...
What are the absolute bandwidths of the signals shown in Problem 2(a) above? Note: Absolute BW-highest frequency component present in a signal). What is the null-null bandwidth of the waveform in Problem 2 part (iv)? What is the 3 dB bandwidth of x(t) 0.5eu(t)? Abo, write down an equation to find the 3 dB bandwidth of a ilter with transfar finction, H(4). 605+1) a) Find the Fourier transforms of the following signals and sketch their magnitude spectrums i) x(t) 12e...
Problem 2 In each step to follow the signals h(t) r (t) and y(t) denote respectively the impulse response. input, and output of a continuous-time LTI system. Accordingly, H(), X (w) and Y (w) denote their Fourier transforms. Hint. Carefully consider for each step whether to work in the time-domain or frequency domain c) Provide a clearly labeled sketch of y(t) for a given x(t)-: cos(mt) δ(t-n) and H(w)-sine(w/2)e-jw Answer: y(t) Σ (-1)"rect(t-1-n)
Problem 2 In each step to follow...
1. Using appropriate properties and the table of Fourier transforms, obtain and sketch the sin(at) Fourier transform of the signal x()cn(31-4 marks) 2fX(a), determine the Fourier transform of the signal y(t)dx( F.T. dx(2t) dt (3 marks) 3. Find the Fourier transform of x(t)-cos(2t/4). (3 marks) 4. Let x(t) be the input to a linear time-invariant system. The observed output is y(t) 4x(t 2). Find the transfer function H() of the system. Hence, obtain and sketch the unit-impulse response h(t) of...
What are the absolute bandwidths of the signals shown in Problem 4(a) above? (Note: Absolute BW= highest frequency component present in a signal). What is the null-null bandwidth of the waveform in Problem 4(a) - (iii)? What is the 3 dB bandwidth of x(t) = -2e-4tu(t)? Write down an equation to find the 3 dB bandwidth of a filter with transfer function and then solve it to find its 3-dB bandwidth: H(s) = (+2)(+3). -4. Please use a Table of...
A cascaded system that consists of an LTI system and a delay system is shown in Figure Q4(b). The input signal X(t) and impulse response of the LTI system, h(t) are given as the following: x(t) = 6-2&u(t) h(t) = e-fu(t) Determine: The Fourier transform of y(t). (3 marks) The Fourier transform of z(t). (3 marks) A basic modulator circuit is shown in Figure Q4(c). Modulation is a multiplication between input signal, m(t), and a carrier signal, c(t). The process...
Question given an LTI system, characterized by the differential equation d’y() + 3 dy + 2y(t) = dr where x(t) is the input, and y(t) is the output of the system. a. Using the Fourier transform properties find the Frequency response of the system Hw). [3 Marks] b. Using the Fourier transform and assuming initial rest conditions, find the output y(t) for the input x(t) = e-u(t). [4 Marks] Bonus Question 3 Marks A given linear time invariant system turns...
Home-Work 5 All questions carry equal points. Don't forget to highlight your final answers 25 uestion # 1 Use table to find Fourier transform. Sketch the magnitude response and phase response (i) x(t) Cos(1000t) (ii) x(t) 13Cos(100t)- 7Sin(500t) (iv) x(t) rect To (v) xo)-rect ()Cos(10001) (v) x(o) -ret)Cos(000t) Question # 2 Let h(t) be a linear time invariant system, with the following transfer function s + 1 000m (a) Find H(w) (b) Sketch the magnitude and phase response of H(w)...
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...
Question B2 Figure 8 shows a DC electric circuit with a 2-way switch. The capacitor is initially not charged. At t= Os, switch is at position and the capacitor is then charged up 1000 Position1 RT Position2 (20V R 500 0.02F (NV Figure 8 (a) Whent > sec, the capacitor is charged through R, to steady state, 0 Find the complete response of y(t) fort > 0s. (5 marks) (m) Sketch the response of (t) for t> Os. (3 marks)...
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