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5 . A) A causal Continuous-time system has the following pole-zero diagram: jw S-plane Re -1...
Q6 A second CT system has the following pole-zero diagram: jw X S-plane Re х let...
Q6
A second CT system has the following pole-zero diagram: jw X S-plane Re х let assume that the input signal is as follows {1; cos(t) > 0; otherwise. Let ak and by represent the Fourier series coefficients of the input and output signals, respectively, where the fundamental (lowest frequency component) of each signal has a period of 27. It is known that he . Determine , justify your answers mathematically.
B A second CT system has the following pole-zero diagram: jw X S-plane Re х let...
B
A second CT system has the following pole-zero diagram: jw X S-plane Re х let assume that the input signal is as follows {1; cos(t) > 0; otherwise. Let ak and by represent the Fourier series coefficients of the input and output signals, respectively, where the fundamental (lowest frequency component) of each signal has a period of 27. It is known that he . Determine , justify your answers mathematically.
Please write very clear B) A second CT system has the following pole-zero diagram: jw x...
Please write very clear
B) A second CT system has the following pole-zero diagram: jw x 1 S-plane Re X let assume that the input signal is as follows (1; cos(t) > z(t) 0; otherwise. Let at and be represent the Fourier series coefficients of the input and output signals, respectively, where the fundamental (lowest frequency component) of each signal has a period of 2n. It is known that bo. Determine bo, justify your answers mathematically.
2.6.1 Consider a causal continuous-time LTI system described by the differential equation u"(t) +...
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
P5.6-3 displays the pole-zero plot of a system that has re 5.6-5 Figure second-order real, causal...
P5.6-3 displays the pole-zero plot of a system that has re 5.6-5 Figure second-order real, causal LTID s Figure P5.6-5 (a) Determine the five constants k, bi, b2, aj, and a2 that specify the transfer function (b) Using the techniques of Sec. 5.6, accurately hand-sketch the system magnitude response lH[eill over the range (-π π) (c) A signal x(t) = cos(2πft) is sampled at a rate Fs 1 kHz and then input into the above LTID system to produce DT...
A) Given: H(S) = 32 - 48 +3 52 +8s +12 1. Construct the pole-zero diagram...
A) Given: H(S) = 32 - 48 +3 52 +8s +12 1. Construct the pole-zero diagram and clearly indicate all poles and zeros II . Write the equivalent differential equation for the system III. Find h(t) IV . Is the system Causal? Stable? Justify your answers mathematically
part c) Figure 1 5 ma Pag c) The zero-pole diagram of the Laplace transform of y(t), Y(s), is shown in fig. 2 jw Figure 2 [Please turn over] Page 2 of 9 Determine and justify the region of converg...
part c)
Figure 1 5 ma Pag c) The zero-pole diagram of the Laplace transform of y(t), Y(s), is shown in fig. 2 jw Figure 2 [Please turn over] Page 2 of 9 Determine and justify the region of convergence (ROC) ifit is known that Y(Go), that is the Fourier transform of y(t), exists. 5 marks/
Figure 1 5 ma Pag c) The zero-pole diagram of the Laplace transform of y(t), Y(s), is shown in fig. 2 jw Figure 2...
The pole -zero diagram in figure 1 corresponds to the Z-transform [X(z)] of a causal sequence...
The pole -zero diagram in figure 1 corresponds to the Z-transform [X(z)] of a causal sequence (xIn]). Sketch the pole-zero diagram of Y(z), where y[n]-x-n5]. Also, determine the region of convergence for Y (z). 2. a. (15 Marks) rm z-plane Figure 1 b. Discuss any six applications of Multirate Digital Signal processing or explain the need of Multirate Signal Processing with suitable Example. (10 Marks)
2. Let y(t)(e')u(t) represent the output of a causal, linear and time-invariant continuous-time system with unit...
2. Let y(t)(e')u(t) represent the output of a causal, linear and time-invariant continuous-time system with unit impulse response h[nu(t) for some input signal z(t). Find r(t) Hint: Use the Laplace transform of y(t) and h(t) to first find the Laplace transform of r(t), and then find r(t) using inverse Laplace transform. 25 points
Question# 2 Given a continuous-time control system Y (s) R(s) (s 16 2)(s + 8) ntt pole-zero mappi...
Question# 2 Given a continuous-time control system Y (s) R(s) (s 16 2)(s + 8) ntt pole-zero mapping equivalent discrete-time system YeaR) ofth above system in the following form: Y(z) R(z) (z+ b)(z +c) b) Find a,b and c c Using transfer function in part (a).Find the response y(k) in terms of a,b and c due to a unit step input sequence with zro initial conditions
Question# 2 Given a continuous-time control system Y (s) R(s) (s 16 2)(s +...
Q6
A second CT system has the following pole-zero diagram: jw X S-plane Re х let assume that the input signal is as follows {1; cos(t) > 0; otherwise. Let ak and by represent the Fourier series coefficients of the input and output signals, respectively, where the fundamental (lowest frequency component) of each signal has a period of 27. It is known that he . Determine , justify your answers mathematically.
B
A second CT system has the following pole-zero diagram: jw X S-plane Re х let assume that the input signal is as follows {1; cos(t) > 0; otherwise. Let ak and by represent the Fourier series coefficients of the input and output signals, respectively, where the fundamental (lowest frequency component) of each signal has a period of 27. It is known that he . Determine , justify your answers mathematically.
Please write very clear
B) A second CT system has the following pole-zero diagram: jw x 1 S-plane Re X let assume that the input signal is as follows (1; cos(t) > z(t) 0; otherwise. Let at and be represent the Fourier series coefficients of the input and output signals, respectively, where the fundamental (lowest frequency component) of each signal has a period of 2n. It is known that bo. Determine bo, justify your answers mathematically.
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
P5.6-3 displays the pole-zero plot of a system that has re 5.6-5 Figure second-order real, causal LTID s Figure P5.6-5 (a) Determine the five constants k, bi, b2, aj, and a2 that specify the transfer function (b) Using the techniques of Sec. 5.6, accurately hand-sketch the system magnitude response lH[eill over the range (-π π) (c) A signal x(t) = cos(2πft) is sampled at a rate Fs 1 kHz and then input into the above LTID system to produce DT...
A) Given: H(S) = 32 - 48 +3 52 +8s +12 1. Construct the pole-zero diagram and clearly indicate all poles and zeros II . Write the equivalent differential equation for the system III. Find h(t) IV . Is the system Causal? Stable? Justify your answers mathematically
part c)
Figure 1 5 ma Pag c) The zero-pole diagram of the Laplace transform of y(t), Y(s), is shown in fig. 2 jw Figure 2 [Please turn over] Page 2 of 9 Determine and justify the region of convergence (ROC) ifit is known that Y(Go), that is the Fourier transform of y(t), exists. 5 marks/
Figure 1 5 ma Pag c) The zero-pole diagram of the Laplace transform of y(t), Y(s), is shown in fig. 2 jw Figure 2...
The pole -zero diagram in figure 1 corresponds to the Z-transform [X(z)] of a causal sequence (xIn]). Sketch the pole-zero diagram of Y(z), where y[n]-x-n5]. Also, determine the region of convergence for Y (z). 2. a. (15 Marks) rm z-plane Figure 1 b. Discuss any six applications of Multirate Digital Signal processing or explain the need of Multirate Signal Processing with suitable Example. (10 Marks)
2. Let y(t)(e')u(t) represent the output of a causal, linear and time-invariant continuous-time system with unit impulse response h[nu(t) for some input signal z(t). Find r(t) Hint: Use the Laplace transform of y(t) and h(t) to first find the Laplace transform of r(t), and then find r(t) using inverse Laplace transform. 25 points
Question# 2 Given a continuous-time control system Y (s) R(s) (s 16 2)(s + 8) ntt pole-zero mapping equivalent discrete-time system YeaR) ofth above system in the following form: Y(z) R(z) (z+ b)(z +c) b) Find a,b and c c Using transfer function in part (a).Find the response y(k) in terms of a,b and c due to a unit step input sequence with zro initial conditions
Question# 2 Given a continuous-time control system Y (s) R(s) (s 16 2)(s +...
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