Consider a DSSS$-$BPSK spread spectrum transmitter. Let bk be a binary sequence $1101$ arriving at a rate of $100$ bps$,$ where left most bit is the earliest bit. Let ck be the pseudorandom binary sequence $100110111000$ with a clock rate of $300$ Hz$.$ Assuming a bipolar signaling scheme with a binary $0$ and binary $1$ represented by a signal levels $-1$ and $+1,$ respectively. Calculate:

$($a$)$ DSSS modulated signal, m$($t$),$ and the corresponding the binary sequence.

$($b$)$ The PSD of the DSSS modulated signal.

$($c$)$ The processing gain in dB$.$