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Problem 11: Discretization of a Continuous-Time Filter Consider the continuous-time system with transfer function Hc(s) A...
Convert the following continuous time transfer function to discrete time transfer functions with sampling rates of 0.01 and 0.1. Write with an equation editor the two discrete transfer functions. Next...
Convert the following continuous time transfer function to discrete time transfer functions with sampling rates of 0.01 and 0.1. Write with an equation editor the two discrete transfer functions. Next apply a unity feedback to the continuous transfer function and the two discrete transfer functions. Based on the poles of the closed-loop continuous transfer function, is the system stable? Why? Plot the poles of the discrete transfer functions on the z-plane. Are the two systems stable and why?
Using MATLAB 4) Consider the stable second-order continuous transfer function (in s domain): H = S...
Using MATLAB
4) Consider the stable second-order continuous transfer function (in s domain): H = S +1 S2 + 3s + 2 Using the command Hd = c2d (H, Ts) with Ts = 0.1, convert H to the z domain. On the same Figure, plot the continuous impulse response of the system against the discrete one. Considering your work in problem 4, 5) Vary Ts (Ts = 0.7, 0.5, 0.3, 0.1) and observe the plot of the continuous impulse response...
1. Evaluate stability of the following systems: a) A continuous time system described by the following...
1. Evaluate stability of the following systems: a) A continuous time system described by the following transfer function: 4 2s2 +4s 5 b) A continuous time system described by the following transfer function (s-6)(5s3 +3s +7s + 1) c) A discrete time system described by the following transfer function: 0.3 (z-0.4) (z +0.7) d) A second order discrete time system with the following poles: z1 0.8+0.75i, z2 0.8-0.75i
a continuous time causal LTI system has a transfer function: H(s)=(s+3)/(s^2 +3s +2) a) find the...
a continuous time causal LTI system has a transfer function: H(s)=(s+3)/(s^2 +3s +2) a) find the poles and zeros b) indicate the poles and the zeros on the s-plane indicate the region of convergence (ROC) c) write the differential equation of the system. d) determine the gain of the system at dc (ie the transfer function at w=0) e) is the system described by H(s) stable? explain f) for the system described by H(s), does the Fourier transform H(jw) exist?...
O 0.5 Question 10 1 pts Consider a continuous-time linear system with transfer function (). To...
O 0.5 Question 10 1 pts Consider a continuous-time linear system with transfer function (). To design an equivalent digital filter with sampling period T and transfer function H(z) using the "frequency domain approach" from our class, we replace all values of s with: Oz OKT
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 +...
5. Consider a CT system with transfer function This system is called an integrutor because t by h...
the subject is in digital signal processing
5. Consider a CT system with transfer function This system is called an integrutor because t by he d to the ingent t y)-x(r)dr. Discretize the above system using the bilinear transform. (a) What is the transfer function H'(:) of the resulting DT system b) If xin] is the input and yin] is the output of the resulting DT system, write the (c) Obtain an expression for the frequency response H'(o) of the...
1. Consider the block diagram continuous-time, linear, time-invariant system shown be- low. A Ali (a) Find...
1. Consider the block diagram continuous-time, linear, time-invariant system shown be- low. A Ali (a) Find the transfer function of the system. Show your work. (5 points) (b) Draw the canonical direct form realization of this system using multipliers, in- tegrators and adders. Show your work. If you do not know how to do part (a), you can state so, and draw the canonical realization of the system with transfer function 3s - 11 52 + 7s +12 Note: This...
you can use matlab to solve 1. Given the plant model differential equation: y" + 6y'+ 12y 12u(t) Find: a) G(s) continuous transfer function he step response of the unity feedback system c) The...
you can use matlab to solve
1. Given the plant model differential equation: y" + 6y'+ 12y 12u(t) Find: a) G(s) continuous transfer function he step response of the unity feedback system c) The appropriate sampling time d) G(z) pulse transfer function e) Continuous State Space, A, B, C, D f) Discrete State Space, A, B, C, D
1. Given the plant model differential equation: y" + 6y'+ 12y 12u(t) Find: a) G(s) continuous transfer function he step response of...
= 2s +1 Consider the continuous-time LTI causal system with Transfer function H(s) $? + 5s...
= 2s +1 Consider the continuous-time LTI causal system with Transfer function H(s) $? + 5s +6' a) Compute the ROC for H(s). (3 pts) b) Discuss the BIBO stability of the system. (2pts) c) Compute the system output when the input is x(t) = 8(t) (Dirac's delta). (5 pts)
Using MATLAB
4) Consider the stable second-order continuous transfer function (in s domain): H = S +1 S2 + 3s + 2 Using the command Hd = c2d (H, Ts) with Ts = 0.1, convert H to the z domain. On the same Figure, plot the continuous impulse response of the system against the discrete one. Considering your work in problem 4, 5) Vary Ts (Ts = 0.7, 0.5, 0.3, 0.1) and observe the plot of the continuous impulse response...
1. Evaluate stability of the following systems: a) A continuous time system described by the following transfer function: 4 2s2 +4s 5 b) A continuous time system described by the following transfer function (s-6)(5s3 +3s +7s + 1) c) A discrete time system described by the following transfer function: 0.3 (z-0.4) (z +0.7) d) A second order discrete time system with the following poles: z1 0.8+0.75i, z2 0.8-0.75i
O 0.5 Question 10 1 pts Consider a continuous-time linear system with transfer function (). To design an equivalent digital filter with sampling period T and transfer function H(z) using the "frequency domain approach" from our class, we replace all values of s with: Oz OKT
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 +...
the subject is in digital signal processing
5. Consider a CT system with transfer function This system is called an integrutor because t by he d to the ingent t y)-x(r)dr. Discretize the above system using the bilinear transform. (a) What is the transfer function H'(:) of the resulting DT system b) If xin] is the input and yin] is the output of the resulting DT system, write the (c) Obtain an expression for the frequency response H'(o) of the...
1. Consider the block diagram continuous-time, linear, time-invariant system shown be- low. A Ali (a) Find the transfer function of the system. Show your work. (5 points) (b) Draw the canonical direct form realization of this system using multipliers, in- tegrators and adders. Show your work. If you do not know how to do part (a), you can state so, and draw the canonical realization of the system with transfer function 3s - 11 52 + 7s +12 Note: This...
you can use matlab to solve
1. Given the plant model differential equation: y" + 6y'+ 12y 12u(t) Find: a) G(s) continuous transfer function he step response of the unity feedback system c) The appropriate sampling time d) G(z) pulse transfer function e) Continuous State Space, A, B, C, D f) Discrete State Space, A, B, C, D
1. Given the plant model differential equation: y" + 6y'+ 12y 12u(t) Find: a) G(s) continuous transfer function he step response of...
= 2s +1 Consider the continuous-time LTI causal system with Transfer function H(s) $? + 5s +6' a) Compute the ROC for H(s). (3 pts) b) Discuss the BIBO stability of the system. (2pts) c) Compute the system output when the input is x(t) = 8(t) (Dirac's delta). (5 pts)
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