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- The system whose characteristic equation is given as s3 + 2s2 + Ks + 20 = 0 is asymptotically stable for which K valuesStep functions can be used to define a window function. Thusu(t −1)−u(t−4) defines a window 1 unit high and 3 units wide located on the time axis between 1 and 4. A function f(t) is defined as follows: f(t)=0,t≤0;=−20t,0≤t≤1 s= −20,1 s≤t≤2 s=2 cosπ2t,2 s≤t≤4 s;=100−20t,4 s≤t≤5 s=0,5 s≤t<∞. 1. Sketch f(t) over the interval −1 s≤t≤6 s. 2. Use the concept of the window function to write an expression for f(t).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.
- The mathematical models of some continuous time systems are given above. x(t) is the input signal of the system, and y(t) is the output signal of the system. Which of the following systems is linear and which is nonlinear?Suppose an electrical signal generated, y(t) can be modelled as follows where t, is time in second, y(t) is voltage in mv. a) Produce graphs showing the amplitude and phase spectrum of y(t). b) State whether this time-domain signal y(t) is periodical, or non-periodical and justify your answer.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
- When the unit step function is applied to the input of the system whose block diagram is given 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.given that vc=q/C. derive the expression for q in terms of time t.A)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.
- : If F(s) = s 4+ 5s3+20s 2 + 40s + 50 , Investigate the stability of this systemGraph the following functions for the given x[n]= {…,0,2,-2,0,1,3,-2,-3,1,-1,0,…} signal. a) y[n]=x[n](u[n+3]-u[n-2])-2∂[n]+3∂[n-3]x[n b) y[n]=2x[-n]+(x[n])²+x[-n+2]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?. Explain