Modulation

The symbol sequence $b=\{-1,1,1,-1,1,1,-1,-1\}$ is to be transmitted at a rate of one symbol per $T$ seconds. For each of the following modulation formats sketch in the space provided below

• the magnitude,
• the phase, and
• the modulated signal assuming a carrier frequency of $1/T$.

1. Binary Phase Shift Keying (BPSK) with rectangular pulses.

2. Quaternary Phase Shift Keying (QPSK) with triangular pulses.
   

3. Full-response Continuous Phase Modulation (CPM) with modulation index and rectangular pulses.
   

4. Partial-response ($L=2$) Continuous Phase Modulation (CPM) with modulation index and rectangular pulses.
   

5. Comment on the bandwidth requirements for each of these modulation formats. Which modulation format has the narrowest (widest) main-lobe? Which modulation format provides the fastest (slowest) side-lobe decay?