Don't use z/laplace/fourier transforms.
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Don't use z/laplace/fourier transforms. 3. Find x[n] * v[n] when (a) x[n] = ()" u[n] v[n]...
(24%) Find the Fourier transform of the signals given below: 1) x() 4e U() x(t) = e-3,Cos(12m)U(t) 2) x(t) = 36(1 + 4) + 26(1) + 43(1-5) 3) x[n]=(0.7)"U(n) 4)
(24%) Find the Fourier transform of the signals given below: 1) x() 4e U() x(t) = e-3,Cos(12m)U(t) 2) x(t) = 36(1 + 4) + 26(1) + 43(1-5) 3) x[n]=(0.7)"U(n) 4)
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...
8. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the Fourier transform of sgn(t 1)e4t-1| (b) Hence, find the Fourier transform of 5i sgn(t 1) eit-4e-1| (Simplify your answer.
8. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the Fourier transform of sgn(t 1)e4t-1| (b) Hence, find the Fourier transform of 5i sgn(t 1) eit-4e-1| (Simplify your answer.
3) Compute the Z-Transforms of the following time series: (a) x(n)k2"u(n) (b) + 1) x(n) = u(-n (c) x(n) -k2"u-1) (d) x(n) 0.5%1(n) + 3"11(-n) (e) x(n) = 4-nu(n) + 5-nu(n + 1) In the above, u(n) stand for the unit step signal in the discrete time domain. Also, if you can in each case determine the region of convergence of the Z-Transform you obtain.
1. Determine the Laplace/Z transforms of the following signals, including the regions of vergence Con (a) (t)e-u(t 2) 2e u(t)ut)3e'u-t) 2" u 3(2)"u 4-1)"un2(-3)u[-n 1 (b) (t) (c) n (d) n 2 2l-
5) Use the method of Laplace transforms to the solve the following boundary value problem IC: u(x, 0) 2 in the following way: a) Apply the Laplace transform in the variable of t to obtain the initial value problem b) Show that U =-+ cie'sz +cge-Vsz s the general solution to the above equation and solve for the constants c and c2 to obtain that c) By taking a power series about the origin and using the identities, sinh iz-...
9. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of 4 9+w2 9w2 (b) The function f(t) satisfies the integral equation -4u f(t u) H(u) du 6sgn(t)e-3¢|. f(t) 4 Find the Fourier transform of the function f(t) and hence find the solution f(t)
9. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of 4 9+w2 9w2 (b) The function f(t)...
3. Use Fourier Transforms to solve u(0, )sin(ar) -o0 o0, t > 0,
3. Use Fourier Transforms to solve u(0, )sin(ar) -o0 o0, t > 0,
Fourier transform from Laplace transform-The Fourier transform of finite support signals, which are absolutely integrable or finite energy, can be obtained from their Laplace transform rather than doing the integral. Consider the following signals 5.30 x3(t) - r(t + 1) - 2r(t) + r(t - 1) (a) Plot each of the above signals. (b) Find the Fourier transforms (X,(S2)) for1, 2, and 3 using the Laplace transform (c) Use MATLAB's symbolic integration function int to compute the Fourier transform of...
3. Let the Laplace transforms of signals (t) and y(t) be X(s) and Y(s) with appropriate regions of convergence, respectively (a) Show that the Laplace transform of x(t) * y(t) is X(s)Y (s). What is the region of convergence? (b) Show that the Laplace transform of tx(t) is -dX(s)/ds with the same region of x(t) convergence as tn-1 1 for Re{sa} > 0. -at e (c) Show that the Laplace transform of 'u(t) is n 1)! (sa)" 1 for Refsa}...