Homework Answers
Answer:- The Fourier transform of 10*sinc(5t) is-
The Fourier transform of 6*sinc2(2t) is-
at f = 1 Hz-
Convolution in time domain is equivalent to multiplication in frequency domain. Hence the result is-
So the option b is the correct answer.
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h(t) = 6 sinc? (2t) y(t) X2. Consider this system: «(t) = 10 sine(5t) Evaluate Y...
Question 1 (10 points) Determine Fourier Transform of f(t) = u(t – 2) + 6(t –...
Question 1 (10 points) Determine Fourier Transform of f(t) = u(t – 2) + 6(t – 6)? e-12w + e-jow (ies + 70(w))er2we=you Giv - 70()e=12W +e=you Gius + 78(w))e=124 +e-sou Question 2 (10 points) Using the convolution property of Fourier Transform to find the following convolution: sinc(t) * sinc (4t) [Hint: sinc(t) én rect(w/2)] π sinc (2t) 2 TT 8 sinc(t)sinc(2t) TT sinc(4t) TT sinc(t)
3. Consider the signal h(t) -2u(t) +4u(t-2) 6u(t-6) (a) Sketch h(t). (b) Find H(f) in terms of si...
3. Consider the signal h(t) -2u(t) +4u(t-2) 6u(t-6) (a) Sketch h(t). (b) Find H(f) in terms of sinc functions in three different ways to get three different expressions. (c) Evaluate the gain and phase (in degrees) of H(f) at 0.2 Hz from each expression.
3. Consider the signal h(t) -2u(t) +4u(t-2) 6u(t-6) (a) Sketch h(t). (b) Find H(f) in terms of sinc functions in three different ways to get three different expressions.
(c) Evaluate the gain and phase (in degrees)...
4. Evaluate (F•dr for F(x, y, z)=(3xz)i +(2z - y)j+(22)k and с C:r(t)= (2t+1)i+(3).j+(5t)k, Ostsi
4. Evaluate (F•dr for F(x, y, z)=(3xz)i +(2z - y)j+(22)k and с C:r(t)= (2t+1)i+(3).j+(5t)k, Ostsi
In each step to follow, the signals h(t), a(t), and y(t) denote respectively the impulse response...
In each step to follow, the signals h(t), a(t), and y(t) denote respectively the impulse response, input, and output of a continuous-time LTI system. Accordingly, H(w), 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. (b) (25 points) On the axes below, provide a clearly labeled sketch of y(t) for all t given Σ H(w)-( ) sine? (w/8) j2Tt r(t)-e δ(t-n/2) and with sinc(t) = sin(t)/t...
Use Taylor's second order method to approximate the solution. y'=-5y+5t^(2)+2t, 0 ≤ t ≤ 1, y(0) =...
Use Taylor's second order method to approximate the solution. y'=-5y+5t^(2)+2t, 0 ≤ t ≤ 1, y(0) = 1/3,with h = 0.1 Also, compare relative errors if the actual solution is: y=t^(2) + 1/3 * e^(-5t)
3-(10 points) Consider a C-T. LTI system given below X(t) - h(t) y(t) The impulse response...
3-(10 points) Consider a C-T. LTI system given below X(t) - h(t) y(t) The impulse response is h(t)=sinc(200t). We apply an input signal x(t)=sinc(100t) to produce the output y(t). Find and plot Y(m). Find y(t).
1. Consider the system shown in Figure 1 below. Ideal Ideal y(t) Sample period T Sample period T ...
please help as soon as possible
1. Consider the system shown in Figure 1 below. Ideal Ideal y(t) Sample period T Sample period T Figure 1. System for Problem 1. The input to the above system is x(), the output is y), and the sampling period for both the ideal A/D and ideal D/A is T>0. For your answers to the various parts below, be sure to include appropriate units, where applicable. a) Suppose that x(t)-5. Determine all numerical values...
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. Consider the system shown in Figure 1 below. Ideal Ideal r(t) Sample period Sample period...
1. Consider the system shown in Figure 1 below. Ideal Ideal r(t) Sample period Sample period T Figure 1. System for Problem 1. The input to the above system is x(), the output is y(), and the sampling period for both the ideal A/D and ideal D/A is T>0. For your answers to the various pa be sure to include appropriate units, where applicable. rts below., Suppose that x(1) Justify your answer. a) 5. Determine all numerical values of T...
Question 1 (10 points) Determine Fourier Transform of f(t) = u(t – 2) + 6(t – 6)? e-12w + e-jow (ies + 70(w))er2we=you Giv - 70()e=12W +e=you Gius + 78(w))e=124 +e-sou Question 2 (10 points) Using the convolution property of Fourier Transform to find the following convolution: sinc(t) * sinc (4t) [Hint: sinc(t) én rect(w/2)] π sinc (2t) 2 TT 8 sinc(t)sinc(2t) TT sinc(4t) TT sinc(t)
3. Consider the signal h(t) -2u(t) +4u(t-2) 6u(t-6) (a) Sketch h(t). (b) Find H(f) in terms of sinc functions in three different ways to get three different expressions. (c) Evaluate the gain and phase (in degrees) of H(f) at 0.2 Hz from each expression.
3. Consider the signal h(t) -2u(t) +4u(t-2) 6u(t-6) (a) Sketch h(t). (b) Find H(f) in terms of sinc functions in three different ways to get three different expressions.
(c) Evaluate the gain and phase (in degrees)...
4. Evaluate (F•dr for F(x, y, z)=(3xz)i +(2z - y)j+(22)k and с C:r(t)= (2t+1)i+(3).j+(5t)k, Ostsi
In each step to follow, the signals h(t), a(t), and y(t) denote respectively the impulse response, input, and output of a continuous-time LTI system. Accordingly, H(w), 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. (b) (25 points) On the axes below, provide a clearly labeled sketch of y(t) for all t given Σ H(w)-( ) sine? (w/8) j2Tt r(t)-e δ(t-n/2) and with sinc(t) = sin(t)/t...
3-(10 points) Consider a C-T. LTI system given below X(t) - h(t) y(t) The impulse response is h(t)=sinc(200t). We apply an input signal x(t)=sinc(100t) to produce the output y(t). Find and plot Y(m). Find y(t).
please help as soon as possible
1. Consider the system shown in Figure 1 below. Ideal Ideal y(t) Sample period T Sample period T Figure 1. System for Problem 1. The input to the above system is x(), the output is y), and the sampling period for both the ideal A/D and ideal D/A is T>0. For your answers to the various parts below, be sure to include appropriate units, where applicable. a) Suppose that x(t)-5. Determine all numerical values...
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. Consider the system shown in Figure 1 below. Ideal Ideal r(t) Sample period Sample period T Figure 1. System for Problem 1. The input to the above system is x(), the output is y(), and the sampling period for both the ideal A/D and ideal D/A is T>0. For your answers to the various pa be sure to include appropriate units, where applicable. rts below., Suppose that x(1) Justify your answer. a) 5. Determine all numerical values of T...
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