t is the signal x(n) whose z-transform X(z)=log(1+az'); |z|>|a )".. u(n – 1) a" -)". . u(n + 1) n )n-1, " . u(n – 1) . u(n + 1) 2-1 a"
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- Show that the derivative of a 1-D signal, I=I(x), amplifies the higher frequency components of the signal. Then, prove that even a slight amount of noise n=n(x), can be responsible for a large difference between the derivative I and I+n (Hint: Assume that n can be written as εsin(ωx) for some very small ε and very large ω).A discrete time signal x[n]= {4,4,0,2} is applied to a 4-bit microprocessor to compute the frequency domain sequence which is periodic and discrete in nature. Assume the microprocessor computes the frequency coefficients in a fast and efficient manner than the conventional method.A 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
- 1. Finding the closed loop transfer function of the system2.What is the steady state error of the system when a unit ramp signal is applied to its input?3. Given Km=5 and Kb=0.01, what should be the K value for a steady-state error to occur at the unit ramp input of the system?3. The __________ is, in essence, a switch which closes for a brief period oftime and then open, closing and opening many times a second. 4. The ___________ is a way to tell how many frequency components are neededto make up a signal.Given the linear mechanical system below:Determine the transfer function ?3(?)/?(?). Express your answer as a single fraction andarrange the degree of variables in descending order.
- Calculate the range of values K will take for the steady-state error to be ??? ≤ 0.04 when the input of the system is ?(?) = ?. Calculate the range of values K will take for the damping ratio to be 1>ξ ≥(1/2√6). Calculate the damping rate ξ and the undamped natural frequency ?? so that ? = 0.5What is Fourier Transform? How is it used for transformation of signals and systems? What is Laplace Transform? How is it used for transformation of signals and systems? .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 response
- Two parter- Using this form how would I derive Lasas, Lasbs, Larbr, Lasbr, Larar, when g is constant I know Lasar is W_as and W_ar into the first equation, I am also thinking Lasas is W_x=W_as and W_y =W_as in the first equation. Part B where does the theta come from.a) Calculate the range of values K will take for the steady-state error to be “??? ≤ 0.04” when the input of the system is ?(?) = ?. b) Calculate the value range that K will take so that the damping ratio can be “1 > ξ ≥ 1 2√6”. c) Calculate the damping ratio “ξ” and the undamped natural frequency ?? value so that “? = 0.5”.1. The CT signal x(t)=3cos (600πt) + 6cos2 (mπt) is critically sampled (Nyquist rate)by fs=4000 Hz. Find:i. The value of m.ii. The frequency components of the signal.iii. The frequency resolution (Δf) of the output spectrum if the sampled signal isprocessed by 64 point-DFT.iv. Define frequency resolution.