Problem 1. (a) and ( c) only.

Problem 1.6

Problem 1.7

Problem 1.8

Problem 1.11

Problem 1.15

Additional Problem: A linear time invariant system given by the differential equation

dy/dt + cy(t) = x(t), for all t

has white noise with autocorrelation Rxx(t) = q δ(t) applied at its input x(t), where δ(t) is the impulse function. The output is denoted by y(t). Determine: (a) the impulse response of the system; (b) the frequency (or Laplace) transfer function for the system; ( c) power spectral densities for the input and output signals, and; (d) the autocorrelation function for the output.