xln) yla) (a) Find the impulse response of the causal system given above (b) When the input sequence is unit-step, i.e. x(n) = u(n) = 1, for n20 -0, for n<0, find and plot the output sequence y(n) (c) Is this system stable in the sense of bounded-input/ bounded-output?
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- A system is said to be completely observable if there exists an unconstrained control u(t) that can transfer any initial state x(to) to any other desired location x(t) in a finite time to T. b. Investigate the observability of the system below. (X1 X2, -2 (X1 y = [1 2] Knowing that X = Ax + Bu and y= Cx.A discrete-time system can be (Static or dynamic, Linear or nonlinear, Time invariant or time varying, Causal or noncausal and/or Stable or unstable). Examin the following systems with respect to the properties above: (a) y(n) = x(n) cos(won). (b)y(n) = x(n)]. (c) y(n) = x(n) (d)y(n) (e) y(n) = sign[x(n)]. +nx(n + 1). (x(n), if x(n) 20 (0, if x(n) <0' ‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒Sample Questions on Fuzzy control: 1. Answer the following questions about the RBF(Radial basis Function) neural network: a) State two differences of MLP and RBF neural networks. b) State two advantages of adding the variance parameter to the neurons' Gaussian functions. of the following network using the steepest descent ij 2. We want to estimate the parameters w method based on the partial error I = (y - y)². Obtain the derivative, I / Ow
- Write a short computer program to calculate CV for an Einstein solid and show these resultsas a graph of Cv/Nk vs. kT/epsilon. Include three scenarios: The q << N and q >> N limits and also the more general case which is applicable for "any" q10. Let W be a wff. If no free occurrence of the variable x in W (x) is in the scope of a quantifier that binds a variable in t, then we say the term t is... (A) out of bounds (C) bound to x (B) free to replace x in W (x) (D) a solitary termB. Suppose we wish to animate a bouncing ball. We are given keyframes for the ball's motion. The key frames are at times T = {0, 3, 9, 15} with associated height values of H = {1, 6, 8, 3}. 1. Plot the graph of height versus time using linear interpolation between key frames. 2. Since the ball's speed changes as it falls and as it bounces, linear interpolation will not give a realistic result. Which method would create the most realistic bounce? And how would the graph look like? H 16- 14- 12- 10- 8- 6- 4- 2- 0- →T 4 6 8. 10 12 14 16
- It is known that a natural law obeys the quadratic relationship y = ax“. What is the best line of the form y = px + q that can be used to model data and minimize Mean-Squared-Error if all of the data points are drawn uniformly at random from the domain [0,1]? r* ur, a,An input signal of unit amplitude is applied repeatedly to a synaptic connection whoseinitial value is also unity. Calculate the variation in the synaptic weight with time usingthe following two rules: (a) The simple form of Hebb's rule described in Eq. (2.9) assuming the learning-rateparameter n = 0.1.b) The covariance rule described in Eq. (2.10), assuming that the presynaptic activityr = 0 and the postsynaptic activity y = 1.0.4. Given a random variable w with den sity F(w) and a random variable p as the umiform im the interval (-71, +71) where wlP (two w and p are independent) R.V.S Suppose the stochastic process, xt) =a Cos (wt+P). meam a) show that xlt) is wss with zero and auto correlation equal R(E) = E (Coswr) j(wt+P) b) show that zt)=aé is also a Wss.
- Computer Science Suppose A ≈PPT B and let f be a function computable in probabilistic polynomial time on the (shared) domain of A, B. Show that f(A) ≈PPT f(B), where f(X ) denotes the distribution which arises from applying f to samples of X . Does the statement from the previous exercise hold even if f is not efficiently computable? Prove or give a counterexampleGenerate the Simulink models for the constitutive equations of stress and strain for Kelvin-Voigt and Maxwell viscoelastic models with the following constraints: Your source should always be a step function with a step of 10 - regardless of whether it's stress or strain For all models, use the following values: E-3 n-5 You should have a total of 4 models: 1. Kelvin Voigt– input is strain, output (scope) is stress 2. Kelvin Voigt – input is stress, output (scope) is strain 3. Maxwell – input is strain, output (scope) is stress 4. Maxwell – input is stress, output (scope) is strain3. Consider the formula A=Vx (p(x) V q(x)) → (Vxp(x) Vrq(x)). (a) Show that A is valid. (b) Show that the converse of A is not valid.