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signal and system 8) By using Laplace transform determine the transfer function and the impulse response of the system with equation below. y) is the output and u) is the input to the system + 6 d...
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input signal is x[n]...
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input signal is x[n] = 2e-n + sin(nn)- 2, -co <n< 0o. 7. (20 pts.) Determine the response of the system described by the difference equation 1 1 y(n)y(n1)n2)x(n 8 7 for input signal x(n) u(n) under the following initial conditions 1, y(-2) 0.5 y(-1)
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input...
Consider the LTI system with input ??(??) = ?? ?????(??) and the impulse response ?(??) =...
Consider the LTI system with input ??(??) = ?? ?????(??) and the
impulse response ?(??) = ?? ?2????(??). A. (3 points) Determine
??(??) and ??(??) and the ROCs B. (3 points) Using the
convolutional property of the Laplace transform, determine ??(??),
the Laplace transform of the output, ??(??) C. (3 points) From the
answer of part B, find ??(??)
9 points) Consider the LTI system with input x(t)eu(t) and the impulse response h(t)-e-2u(t) A. 3 points) Determine X(s) and H(s)...
1. The signal x(t)- expl-a)u(t) is passed as the input to a system with impulse response...
1. The signal x(t)- expl-a)u(t) is passed as the input to a system with impulse response h(t) -sin(2t)/(7t (a) Find the Fourier transform Y() of the output (b) For what value of α does the energy in the output signal equal one-half the input signal energy? Hint: use the duality property of Fourier Transform to obtain H(a
(a) A system has the impulse response, h[n], and is excited with the input signal, xIn], as shown below. Using either a mathematical or a graphical convolution technique, determine the outp...
(a) A system has the impulse response, h[n], and is excited with the input signal, xIn], as shown below. Using either a mathematical or a graphical convolution technique, determine the output of the system, y[n] (that is, evaluate y[n] h[nl'xIn], where" denotes convolution). 17 marks xIn INPUT FIR filter 0.5 0.25 OUTPUT 0 1 345 6 7 .. 0.5 0123 4567 (b) An IIR filter is shown below: ylnl One sample delay (z) 0.4 i) Derive the difference equation describing...
4. (2 marks) Determine (i) the Laplace transfer function, (ii) the impulse response function, and (ii)...
4. (2 marks) Determine (i) the Laplace transfer function, (ii) the impulse response function, and (ii) the input-output relationship (in the form of a linear constant-coefficient differential equation) for the causal LTI systems with the input-output pairs: a) x(t)-41(t) and y(t)-tu(t) + e-2tu(t). b) x() e2tu(t) andy(t)2u(t-4).
please help. Note: u(t) is unit-step function Consider the system with the differential equation: dyt) +...
please help.
Note: u(t) is unit-step function Consider the system with the differential equation: dyt) + 2 dy(t) + 2y(t) = dr(t) – r(e) dt2 dt where r(t) is input and y(t) is output. 1. Find the transfer function of the system. Note that transfer function is Laplace transform ratio of input and output under the assumption that all initial conditions are zero. 2. Find the impulse response of the system. 3. Find the unit step response of the system...
2. For a system with impulse response h(n) = (,"u(n) (a) determine the output sequence of the sys...
2. For a system with impulse response h(n) = (,"u(n) (a) determine the output sequence of the system when the input signal is (b) determine the spectrum and energy density spectrum of the output signal when the system is excited by the signal x(n) Gu(n) 5
2. For a system with impulse response h(n) = (,"u(n) (a) determine the output sequence of the system when the input signal is (b) determine the spectrum and energy density spectrum of the output...
solve all 22. The input-output relationship for a linear, time-invariant system is described by differential equation...
solve all
22. The input-output relationship for a linear, time-invariant system is described by differential equation y") +5y'()+6y(1)=2x'()+x(1) This system is excited from rest by a unit-strength impulse, i.e., X(t) = 8(t). Find the corresponding response y(t) using Fourier transform methods. 23. A signal x(1) = 2 + cos (215001)+cos (210001)+cos (2.15001). a) Sketch the Fourier transform X b) Signal x() is input to a filter with impulse response (1) given below. In each case, sketch the associated frequency response...
- A causal system has input x[n] and output y[n]. Use the transfer function to determine...
- A causal system has input x[n] and output y[n]. Use the transfer function to determine the impulse response of this system. (a) x[n] = [[n]+} \n - 1]- 38[n – 20, x[n] = [[n] - [n – 1] (b) x[n] = (-3)" u[n], y[n] = 4(2)"u[n] – (7)" u[n]
Problem 3. The input and the output of a stable and causal LTI system are related...
Problem 3. The input and the output of a stable and causal LTI system are related by the differential equation dy ) + 64x2 + 8y(t) = 2x(t) dt2 dt i) Find the frequency response of the system H(jw) [2 marks] ii) Using your result in (i) find the impulse response of the system h(t). [3 marks] iii) Find the transfer function of the system H(s), i.e. the Laplace transform of the impulse response [2 marks] iv) Sketch the pole-zero...
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input signal is x[n] = 2e-n + sin(nn)- 2, -co <n< 0o. 7. (20 pts.) Determine the response of the system described by the difference equation 1 1 y(n)y(n1)n2)x(n 8 7 for input signal x(n) u(n) under the following initial conditions 1, y(-2) 0.5 y(-1)
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input...
Consider the LTI system with input ??(??) = ?? ?????(??) and the
impulse response ?(??) = ?? ?2????(??). A. (3 points) Determine
??(??) and ??(??) and the ROCs B. (3 points) Using the
convolutional property of the Laplace transform, determine ??(??),
the Laplace transform of the output, ??(??) C. (3 points) From the
answer of part B, find ??(??)
9 points) Consider the LTI system with input x(t)eu(t) and the impulse response h(t)-e-2u(t) A. 3 points) Determine X(s) and H(s)...
1. The signal x(t)- expl-a)u(t) is passed as the input to a system with impulse response h(t) -sin(2t)/(7t (a) Find the Fourier transform Y() of the output (b) For what value of α does the energy in the output signal equal one-half the input signal energy? Hint: use the duality property of Fourier Transform to obtain H(a
(a) A system has the impulse response, h[n], and is excited with the input signal, xIn], as shown below. Using either a mathematical or a graphical convolution technique, determine the output of the system, y[n] (that is, evaluate y[n] h[nl'xIn], where" denotes convolution). 17 marks xIn INPUT FIR filter 0.5 0.25 OUTPUT 0 1 345 6 7 .. 0.5 0123 4567 (b) An IIR filter is shown below: ylnl One sample delay (z) 0.4 i) Derive the difference equation describing...
4. (2 marks) Determine (i) the Laplace transfer function, (ii) the impulse response function, and (ii) the input-output relationship (in the form of a linear constant-coefficient differential equation) for the causal LTI systems with the input-output pairs: a) x(t)-41(t) and y(t)-tu(t) + e-2tu(t). b) x() e2tu(t) andy(t)2u(t-4).
please help.
Note: u(t) is unit-step function Consider the system with the differential equation: dyt) + 2 dy(t) + 2y(t) = dr(t) – r(e) dt2 dt where r(t) is input and y(t) is output. 1. Find the transfer function of the system. Note that transfer function is Laplace transform ratio of input and output under the assumption that all initial conditions are zero. 2. Find the impulse response of the system. 3. Find the unit step response of the system...
2. For a system with impulse response h(n) = (,"u(n) (a) determine the output sequence of the system when the input signal is (b) determine the spectrum and energy density spectrum of the output signal when the system is excited by the signal x(n) Gu(n) 5
2. For a system with impulse response h(n) = (,"u(n) (a) determine the output sequence of the system when the input signal is (b) determine the spectrum and energy density spectrum of the output...
solve all
22. The input-output relationship for a linear, time-invariant system is described by differential equation y") +5y'()+6y(1)=2x'()+x(1) This system is excited from rest by a unit-strength impulse, i.e., X(t) = 8(t). Find the corresponding response y(t) using Fourier transform methods. 23. A signal x(1) = 2 + cos (215001)+cos (210001)+cos (2.15001). a) Sketch the Fourier transform X b) Signal x() is input to a filter with impulse response (1) given below. In each case, sketch the associated frequency response...
- A causal system has input x[n] and output y[n]. Use the transfer function to determine the impulse response of this system. (a) x[n] = [[n]+} \n - 1]- 38[n – 20, x[n] = [[n] - [n – 1] (b) x[n] = (-3)" u[n], y[n] = 4(2)"u[n] – (7)" u[n]
Problem 3. The input and the output of a stable and causal LTI system are related by the differential equation dy ) + 64x2 + 8y(t) = 2x(t) dt2 dt i) Find the frequency response of the system H(jw) [2 marks] ii) Using your result in (i) find the impulse response of the system h(t). [3 marks] iii) Find the transfer function of the system H(s), i.e. the Laplace transform of the impulse response [2 marks] iv) Sketch the pole-zero...
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