The ROC of a system is the. I all of them range of frequency for which the signal gets transmitted range of frequency for which the z transform exists range in which the signal is free of noise J none of all The region of convergence of z/ (1+2z+z^2) is.
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- 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 responseA continuous time signal, x(t) = sin(20πt) + cos(40πt), is sampled uniformly at intervals of T to obtaina discrete time signal,x(n) = sin(πn/5) + cos(2πn/5).a) What is the value of T assuming no aliasing has occurred?b) Assume both frequency components have been aliased. In this case, is your choice of T unique? If not,specify some choices of T consistent with the information given
- 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 appliedThe 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.For a DA converter, the LRC circuit chosen has inductance L= 10 H , resistance R= 10 ohms and inductance C= 0.2 F . The input digital signal is a power surge (impulse) of magnitude 100 V lasting an instant at t = a . Use your notes to model the second order differential equation in terms of the charge q suited to this application. Simplify the equation with the coefficient of q'' as 1. Use the Laplace transform and calculate the (general) output voltage vo if vo = 1/C q . Your solution will be in terms of a . Use the initial conditions q(0)=0 and q'(0)=0 . Do not use Matlab as its solution will not be identifiable in the solution entry. You must indicate in your solution:1. The simplified differential equation in terms of the charge q you will be solving2. The simplified Laplace transform of this equation where you have made L{q} subject of the equation3. The partial fractions process if required4. The completing the square process if required5. Express the solution q as a piecewise…
- Problem 4. Which gives the Laplace transforms of the given time-domain function? 1.5 ln [(s^2 + 142129)/s^2] 1.5 ln [(s^2 - 142129)/s^2] -1.5 ln [(s^2 - 142129)/s^2] -1.5 ln [(s^2 + 142129)/s^2]An electromotive force ?(?)={? volts,0≤?<10 volts,?≥1 is applied to an RC-series circuit in which the resistance is 10 ohms and the capacitance is 0.1 farad. If the initial charge ?(0)=0,(a) Specify the differential equation as an IVP for the RC-series circuit.(b) Write ?(?) in terms of unit step function.(c) Apply the second translation theorem of Laplace Transform to solve the IVP and find the charge ?(?) at any time t.In the following circuit, R=1 [ohm], C=1[F], and all initial values are 0. 1. Using Laplace Transform, find the ratio H(s)=Vo(s)/Vi(s).2. Find the roots of the characteristic equation.3. Find the conditions for K which will make the circuit over-damped and under-damped, respectively.4. When K=2, vi(t)=sqrt(10)cost, find vo(t) after a long time has passed.
- 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)Given the following ordinary differential equation describing the dynamics of a system y'''+17y''+80y'+100y=3(u''+5u'+4u) Here, y(t) is the output and u(t) is the input. Laplace table is given below. Find the transfer function G(s) [=Y(s)/U(s)] by applying Laplace transform (all initial valus are zero) Find the poles and zeros of the system. Is the system stable or unstable? Which pole(s) is/are slow and which ones is/are fast? Find Y(s) if input is unit step function. Find initial and final values of the system by applying the theorems.Determine the simplified expression for the given function using K-Map: W(P,Q,R,S,T)=Σ m(0,2,5,7,31,27,24,23,21,16,10,8) + d(13,15)