Sxx0 where sxxco is the fourier transform of rxxtau -

Question

Question 1: Verify Stoke's for F^→ = (2x - y)i^→ - yz²j^→ - y²zk^→

(1) over the surface of the box bounded by the planes

x = 0,x = a, y = 0, y = b, z = 0 and z = c.

where S is the upper half of the sphere x² + y² + z² = 1 and C is the boundary in the xoy plane.

Question 2: X(t) is the input voltage to a circuit system and Y(t) is the output voltage.

{X(t)} is a stationary random process with the autocorrelation function R_xx(τ) = e^-α|| IT'. Find

(i) S_xx((0), where S_xx(co) is the Fourier transform of Rxx(τ).

(ii) R_yy(τ),if the power transfer function is H(ω) = R/R+jLω, where R_yy(τ) denotes the inverse Fourier transform of S_xx(ω)|H(ω)²

Question 3: Find the inverse Z -transform of

F(z) = 1/ (1 - z^-1)(1 - 0.5z^-1)(1 - 0.75z^-1).

Also compute f(n) for the first 25 integer values and plot a bar diagram using excel spreadsheet (attach a copy of the graph).

For detailed study of pedagogical things concerning this part of coursework, refer to the following Ebrary resources.