for LTI discrete time system described by: y(n)= 0.5 y(n-1) + 0.2 x(n) yl-1) = 0 x(n) = (0.6)" u(n) find 1. The output response y(n) using Z-transform 2. Impulse resporse h(n) 3 Boc of X(z). H(z) and Y(z) کی
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- a) The dynamics of a discrete-time system are determined by the difference equation;8yk+2 –6y+1 +yk=9Determine the response of the system given thaty0=1 and y1=1.5 b) Find the state transition matrix for the digital system given byX (k+1) = [ -1 0] x (k) [ 1 3] c) Obtain Z-transform of (1-e-Ts )/s(1/s+1) d) The z-transform X (z) of a function X (k), is given by;X (z) =z(0.1065z +0.09021)/(z-1)(z2-1.5z+0.6967) Determine an expression for X (k), by finding the inverse z-transform function of X(z)For the discrete time signal x(n)= [0,2,-1,0,-3,4, 0], find x(3n-4) and show its graphical and sequence representation.Let x(n) be a causal sequence with z-transform X(z) whose pole-zero plot is shown below. Sketch the pole-zero plots and the ROC of the following sequence:
- a) 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 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 responseExamine the stability of the system given by the characteristic polynomial Δ(s)=2s^3+4s^2+ s+1 using the Routh-Hurwitz criterion.
- Q1. Solve the sequence x[n]={3, 4, 1, 1, 1} into a sum of weighted impulse δ[n], and unit step u[n] sequences.Find the steady state output (?) for the input ? (?) = ? (?) of a system with the transfer function ? (?) = (? + 2) ?2 + 10? + 20. The original of the problem is attached. This is a control systems question.f(x,y,z,w)= Σ m(0, 1, 5, 7, 8, 10, 14, 15)+ Σ x( 2, 12) all prime products of the function K-Map and Quine-Find it with the help of McCluskey. Simplify the function with the options table. Cost criterion: 2 units for each variable and 1 unit for the integration event.
- the 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. ..17.3) Using K – map, simplify the following Boolean expression. Y = ∑ m ( 0, 1, 2, 4, 5, 6, 8, 10, 11, 13, 15)For a particular digital processing system, inputting the finite sequence x[n]= (1,-1) results in the finite output sequence of (1, 2, - 1, - 2 ) . Determine the z-transforms for the two signals and give the transfer function for the processing system