For three sequences X[n],y[n],z[n], assume that Y(w)= X(-w) and (w)= X(w + TT) in the Fourier...
Problem 3: Let x(n) be an arbitrary signal, not necessarily real valued, with Fourier transform X (w). Express the Fourier transforms of the following signals in terms of X() (C) y(n) = x(n)-x(n-1) (d) v(n) -00x(k) (e) y(n)=x(2n) (f) y n even n odd , x(n/2), (n) 0 Problem 4: etermine the signal x(n) if its Fourier transform is as given in Fig. P4.12. X(a) 0 10 10 10 X(o) 0 X(a) Figure P4.12
Problem 3: Let x(n) be an...
3. For each reagent Q, R, W, X, Y, and Z in the list below, provide one correct function and the two correct reasons for your choice. .. Na O: S: Na Ho KI Na : Q RW > The options are: FUNCTIONS 1 - strong nucleophile + strong base; (choose one) 2 - strong nucleophile + weak base; 3 - weak nucleophile + strong base; 4 - weak nucleophile + weak base REASONS (choose two) A - conjugate acid...
(a) Let the correlation be defined as r (t) x(T) y (tT) dT T Express R jw= F{r (t)} in terms of X (jw) and Y (jw), the Fourier transform of x (t) and y (t) respectively. (b) Suppose (t) = y (t) = e-H. Find R (jw) using frequency domain properties and the relationship derived in (a) extra Find R (jw) by evaluating the convolution integral in the time domain to get r (t) and then doing the FT.
Consider these three moment generating functions, for X, Y and Z: (5 points each) m (t)=W-3 m, (t)=e + m,(t)=eW-7 a. What is the mean of X? b. What is the mean of Y? c. What is the mean of Z? d. What is the variance of X? e. What is the variance of Y? f. What is the variance of Z? Consider independent random variables X and Y with the following pmfs: y=1 (0.5 x=1 S(x)= {0.5 x =...
The discrete Fourier transform of an mxn matrix X = (Xj.k) is an m x n matrix X = (ĉik) m,n ypj yqk pqSm Sn, p.q=1 where Šm = e270i/m The corresponding inverse Fourier transform is m.n Xj,k = (mn)-1 » počinje-k. p, Sm Sn . peq=1 Let X and Y be mxn matrices with the discrete Fourier transforms X and Y respectively. Define two dimensional circular convolution Z = X * Y to be min Za,b = XXj,kYa–j,b-k j,k=1...
Let F(x, y, z) be the gradient vector field of f(x, y, z) = exyz , let C be the curve of the intersection of the plane y + z = 2 and the cylinder x2 + y2 = 1, oriented counterclockwise, evaluate Sc F. dr. OT O -TT O None of the above. 00
Find the trigonometric Fourier series (FS) and the exponential FS of the following: x(t) TT Ana -3т -2n -TT 2TT d) x(t) πι -no -TT 0 TE 2TT exponential FS f(t) = En=-- Cnejnwot Where (n = +S40+" f(t)e-inwot dt trigonometric 30 f(t)=a, + a, cos(no),t)+b, sin(no,t n-1 ao 1 T. 2 to a. So f(t)dt -5° f(t)cos(no),1)dt Sº f(t)sin(no,t)dt oy b 2 T
Given the function f : {w, x, y, z} 5 with ordering w < x < y < z and f = (4, 3, 5, 4). i. Identify each of the following: domain, codomain or range, image ii. Is f one-to-one? Explain. 1 iii. Is f onto? Explain.
QUESTION 17 The sequence x[n]=cos os(n)i -n is input into the difference equation y[n] + y[n – 1]+2y[n - 2]= – 2x[n]+V3x[n – 1] – x[n-2]. What is y[n]? CA VIND=v3 cos(n) va coscien B.V[n]= n+ T 12 TT TT y[n]=v2 cosi 2 n+ C. 12 TT D.V[n]= Te coschino 12) 12 E. None of the above
Consider the function y = x2 for x E (-7,7) . a) Show that the Fourier series of this function is n cos(nz) . b) (i) Sketch the first three partial sums on (-π, π) (ii) Sketch the function to which the series converges to on R . c) Use your Fourier series to prove that 2and1)"+1T2 12 2 2 Tu . d) Find the complex form of the Fourier series of r2. . e) Use Parseval's theorem to prove...