b) The Z transfom of a LTI discrete time system is represented as: H(z) = 4z-1 1- 11z-1+30z¬2 Determine the followings: i. the difference equation of the discrete tìme system. ii. the output signal y(n) if the input signal is given as 8(n – 3).
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- 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.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.Then considering the given input, what are the energies of the input and the resulting output of the system?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.
- 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 appliedGiven an RC circuit in Figure 1 is modelled by the differential equation written as, ????+1???(?)=1???(?).If the input, ?(?)=0.8?−??(?) with initial condition ?(0−)=3?, by using the Laplace transform approach determine,a) overall output response, ?(?)b) zero input responsec) zero state responsethe following statements given, write if each statement is true or false. a. If the complex frequency domain function, F(s), is derived using a “One-sided” Laplace Transform, the inverse of that function, f(t), is only valid for t ≥ 0. b. When using an ideal transformer, if voltage increases from primary side to secondary side, current also increases from primary side to the secondary side. c. Initial value theorem states that the initial value of a time function f(t) can be obtained from its Laplace Transform F(s) by multiplying the transform by s and letting s approach zero. ..
- Find the Z transform of the given function along with its RoC: x[n]=(2/3)nu(n) where u(n) is the unit step function.sequence x(n) = {-3,-2,1,0,-5,6,7,-4}; where x(n=0) = 0 arrow point under 0Find the Discrete Time Fourier Transform, Laplace Transform (LT), Z Transform (ZT) and ROC.Explain the concept of transfer function in system modeling and its relationship to the Laplace transform.
- Homework Q1: Solve the following difference equation by using Z transform 3 1 mk Y0 ~3y(k=1)+5y(k—2) = 2sin (T) YD =2,y(-2)=4 112 w 96 g5 Sin (Ek) e Ems(— Q2: The signal f(k) has Z transform as the following: Fy o 22437 127 D=2+ +2405 Compute f(3). Ans: f(3)=8 Q3: The signal f(t) = 2 — 2cos(2mt) is sampled every T second. What is the Z transform for the sampled signal f(k) atT = 0.1 sec. Q4: Find Z transform for the following sampled signal: (-1 k=4,56,.. fk) = 0 elsewhere Q5: Write the Difference Equation for the following sampled system, and solve it:Find z transform for the given Discrete time signals below: a. x[n]=2sin(100n)u[n] b. x[n]=2+0.65^n cos(200n)u[n] Note: Use z transform pairsI need help with the question below Consider a causal linear-time invariant system described by the differential equation 2y′(t) + 6y(t) = x′(t) − 4x(t)1. Using Laplace transform technique, determine the zero-input response yz (t) if y(0−) = -3. Assume x(0−) and its higher order derivative in the vicinity of t = 0 to be zero.2. Using the Laplace transform technique, determine the zero-state response if x(t) = δ(t − π)