5. Find the z-transform of the following finite duration signals and indicate their ROC a. x(n) = u(n - k) n b. x(n) = (2) n(n) c. x(n) = 2 [u(n) + 8(n)]
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- From the first order system in the picture kv = 0.5 kp = 1.5 and ka = 4 using laplace transforms derive an expression to show how the output (angular displacement) will vary with time when a step input of 10v is appliedQ.1 Find the z-transform f(z) and sketch the pole-zero plot with the ROC for each of the following sequences?Problem 1. Which gives the Laplace transforms of the given time-domain function? Let a = 2 pi - 2arctan (s/6) pi - 2arctan (2s/3) pi - 2arctan (s/3) (1/2)pi - 2arctan (s/3)
- Determine the Total Response when x(n)=4(0.5)nu(n)+3(0.75)nu(n) using the Z-transform, given the system described below and its initial conditions.z- transform (signal and system) (1+0.8z^-1+0.5z^-2)Y = (1+z^-1)X how can I do z transform for this equation for impulse response H(w), h[n]?Assume X[z] is the z-transform of the signal x[n]. What is the z-transform of X*[n]?
- Z transform is very important in frequency domain signal processing. With this in mind, find out the Z transform of nu(n) where u(n) is the unit step function.T(s)= 15.2/ s^3 +8s^2+16s+15.2 From T(s) in Question # 2, use Routh Hurwitz method to make Routh table and find whether the system is stable or not. K = 15.2. Is the system stable? Why? Find poles of T(s) to find the stability of system. Is the system stable? Why? From transfer function, how we can find stability in time domain? Find inverse Laplace transform if T(s), and show that the system is stable in time domain.Determine the Zero-state Response when x(n) = 0.25nu(n)+0.75nu(n-3) using the Z-transform, given the system described below and its initial conditions.
- For the following time signal, determine the Z-transform and Region of Convergence (ROC). If the ROC and poles exist, draw them in the z-plane.Problem 1. Which gives the inverse transforms of the given s-domain function? [(e^-5t)/72](24te^6t - 20e^6t + 27e^8t - 7) [(e^5t)/72](-24te^6t - 20e^6t + 27e^8t - 7) [(e^-5t)/72](-24te^6t + 20e^6t - 27e^8t - 7) [(e^-5t)/72](-24te^6t - 20e^6t + 27e^8t - 7)y'' + 4y' + 5y = δ(t-1), y(0) = 0, y'(0) = 3 Given the IVP, use Laplace transforms to determine the transfer function Q(s) by setting the initial conditions to zero and making the delta function fire at t = 0 with unit magnitude.