$4.(15$ points$)$ Consider the following BPSK passband transmissions:

Station $1$: Carrier frequency of $1$ MHz and a data rate of $100$ kbps $.$

Station $2$: Carrier frequency of $1\mathrm{.}5$ MHz and a data rate of $300$ kbps

Assume noise free transmission and assume the corresponding baseband digital NRZ$-$L transmission shows a simple SINC profile, up to $3$R on each side, in the frequency domain. Note, $\backslash ($ R $\backslash )$ is the baseband data rate of the station, which as seen above is different for the two stations.

For Station $2$ reception, if the receiver first mixes $($multiplies$)$ the incoming signal with the carrier frequency and then filters the mixed signal using an ideal LPF of cutoff frequency $\backslash (2\mathrm{.}5$ R $\backslash ),$ where is $\backslash ($ R $\backslash )$ is the data rate of station $2.$ Sketch:

a$.$ The two$-$sided magnitude spectrum measured at the antenna before the mixer stage. Assume only the above $2$ stations exist in the world for now!!

b$.$ The two$-$sided magnitude spectrum measured at the output of the mixer stage.

c$.$ The two$-$sided magnitude spectrum measured at the output of the filter stage.

Note: For all sketches, show all the SINC profile overlaps exclusively and clearly. You may use different colors to show the overlap. A small example is shown below for referenc

Assume all SINC profiles are normalized to peak magnitude of $1$ in the frequency domain.

NOTE: All NULL frequency values of the assumed $($See above$)$ SINC profile must be clearly mentioned!