A digital filter is characterized by the following recursive relation, where x(n) and y(n) are the input and output samples at the nth sampling instant. The sampling frequency is 100 Hz.y(n) = 0.8 y(n-1) – 0.64 y(n-2) + x(n) – x(n-1) + x(n-2) Find the poles and zeros of the discrete time transfer function of the filter. Hencededuce and sketch the magnitude response characteristic of the filter from f =0 to f = infinity. Mark the values at f =0,...
Compute (gof)(2) where the graphs of f and g are shown in Figure. y = f(x) y y= g(x) 'y Find the average rate of change of f(x) = 2x2 - 4 a) from 1 to 2 Done from 4 to 2
discrete random variable has probability mass function, P(X = n) = ?1?n. ? 1, forxeven Let Y = −1, for x odd Find the expected value of Y ; (E[y]). probability function mass A discrete random variable has P ( X = n) = (3) for x Y = { for Find the expected value of Y CE(y)] Let even x odd
Let X N(1,3) and Y~ N(2,4), where X and Y are independent 1. P(X <4)-? P(Y < 1) =? 4、 5, P(Y < 6) =? 7, P(X + Y < 4) =?
Let Uy) = any(n)(x) + an-1 y(n-1)(x) + + ai y'(x) + aoy(x) where ao.a1, .. an are fixed constants. Consider the nth order linear differential equation L(y)=4e9x cos x + 5x20 (*) Suppose that it is known that Llyi(x)]=6xe9x Lb'2(x)] = 6e9x sinx し[y3(x)]-6e9x cos x yi(x)-1 2xe9x y2(x) = 42e9x cosx y3(x) 60e9x cos x + 180e9x sinx when when when Find a particular solution to (*)
Suppose X, Y are independent with X ∼ N (0, 1) and Y ∼ N (0, 1). Show that the distribution of Q = X/Y follows the Cauchy distribution, i.e., f(q) = 1/π(1+q2) . Hint: Let Q = X/Y and V=Y. Find the joint pdf of Q and V and finally find the marginal pdf of Q by integrating the joint pdf of Q and V w.r.t. V: Y π(1+q2) Y V = Y . Find the joint pdf of...
What is the minimum value of the function f(x,y)= x^2+y^2 -y on the region where y greater or equal x^2 and y smaller or equal 1
Let Uy) = any(n)(x) + an-1 y(n-1)(x) + + ai y'(x) + aoy(x) where ao.a1, .. an are fixed constants. Consider the nth order linear differential equation L(y)=4e9x cos x + 5x20 (*) Suppose that it is known that Llyi(x)]=6xe9x Lb'2(x)] = 6e9x sinx し[y3(x)]-6e9x cos x yi(x)-1 2xe9x y2(x) = 42e9x cosx y3(x) 60e9x cos x + 180e9x sinx when when when Find a particular solution to (*) Let Uy) = any(n)(x) + an-1 y(n-1)(x) + + ai y'(x)...
Example: Let x, y ∈ Rn, where n ∈ N. The line segment joining x to y is the subset {(1 − t)x + ty : 0 ≤ t ≤ 1 } of R n . A subset A of Rn, where n ∈ N, is called convex if it contains the line segment joining any two of its points. It is easy to check that any convex set is path-connected. (a) Let f : X → Y be an...
T(n) = T(n-2) + 1 for all n > 2. where T(1) = T(2) = 1. Find the even case and odd case. Recursion relation