c) d) d'y(1),dy(1) 3 +2 dt¹ dt y(t+2)-t²y(t+1) Property linear causal fixed (time invarient) dynamic system order + = c***"x(+3) y(t) +0.9y(t) = x(1) a b
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- Signal and system The mathematical model of a system is y" (t) + ay'(t) + by(t) = a (t) + ca (t) where a=1, b=2 and c=1. 1) Find zeros and poles of the system. 2) Show them onto the S-Plane (the complex plane) 3) Discuss the BIBO stability of the system.The response of a system, h(t) is given as in Figure 1 below where the amplitudeof this signal is 7. Then,this system is excited by an input of x(t) = (u(t) × (u(-t)+u(t))) /1. 1)Illustrate the input signal, x(t). 2)Calculate the convolution output of the system y(t) = x(t) ∗ h(t). Nextdetermine y(t) when t is 1 sec 2)Prove the solution in Q2 is comparable when solving in frequency domain(Laplace). Next, sketch the signal for convolution output.When the unit step function is applied to the system input given the block diagram below, the output response takes the value c (0.2) = 0.11 fort = 0.2 s and c (infinity) = 0.333 for t = infinity. What is the steady-state error of the system? calculate
- : If F(s) = s 4+ 5s3+20s 2 + 40s + 50 , Investigate the stability of this systemA)Perform the N=5 point circular convolution of x and h using DFT. B)Perform the N=5 point circular convolution of x and h in time-domain.15 - When the unit step function is applied to the system input given the block diagram below, the output response takes the value c (0.2) = 0.11 for t = 0.2 s and c (infinity) = 0.333 for t = infinity. What is the steady-state error of the system? calculate.A) 0.33B) 0C) 0.25D) 0.5E) 0.67
- Consider a system whose input x (t) and output y (t) satisfy the differential equation of the first order dy(t)/dt + 2y(t) = x(t) The system also satisfies the initial rest condition. Determine the output of the system y (t) when the input is x (t) = e ^3t u(t)The block diagram of a time-invariant, linear, continuous-time system is given below. X1(s) and X2(s) are the state variables of the system. U(s) is the input signal of the system, Y(s) is the output signal of the system. What is the value of parameter E?Q: In the network of Fig. (1), the switch is closed at t=0 and there is no initial charge on either of the capacitors. Find the resulting current ( i ). (Using Laplace Transform). 100 Fig. 1
- I need help with the question below Consider a causal LTI continuous system described by the differential equation y′′(t) + 3y′(t) + 2y(t) = x(t) where y(t) is the system output and x(t) is the input.1. Find the transfer function H(s) of the system.2. Find its poles and zeros. From its poles and zeros, determine if the system is BIBO stable or not.3. If x(t) = u(t) and initial conditions are zero, determine the steady-state response yss(t)4. If the initial conditions were not zero, would you get the same steady state?. Explaina) Y(ω) = 1/(5+jω) The expression above defines the frequency domain signal Y(ω) from a time domain signal y(t) i) Determine the imaginary & real parts of Y(ω). ii.Determine the signal y(t) that produced the signal Y(ω). b)What are the 3 areas of application of i.Signals ii.Systems c) Briefly summarise with explanation the difference between discrete & continuous time signal and also write an expression that describes each signal type.GIven the difference equation:y(n)=0.0899x(n)+0.0257x(n−1)−0.0257x(n−2)−0.0899x(n−3)+1.6148y(n−1)−1.9395y(n−2)+1.2807y(n−3)−0.5852y(n−4)Solve the following:1.) The system function, H(z)2.) Poles and zeros