A noise process has a power spectral density given by

This noise is passed through an ideal band pass filter with a bandwidth of 2 MHz centered at 50 MHz.

1. Find the power content of the output process.

2. Write the output process in terms of the in-phase and quadrature components, and find the power in each component. Assume f₀ = 50 MHz.

3. Find the power spectral density of the in-phase and quadrature components.

4. Now assume that the filter is not an ideal filter and is described by

Repeat parts 1, 2, and 3 with this assumption.