Find. The QPSK-modulated waveform for the given bit sequence, i.e. the sequence of carrier phases and the resulting sketch.
Approach. QPSK sends 2 bits per symbol, so first split the 14-bit stream into 7 consecutive dibits, look each up in the given phase table, then sketch one constant-amplitude carrier segment per symbol period at the assigned phase — the waveform is continuous in amplitude but its PHASE jumps discontinuously at every symbol boundary.
Split the sequence into dibits. Grouping the 14 bits two at a time in the order given:
$$\underbrace{00}_{1}\ \underbrace{10}_{2}\ \underbrace{01}_{3}\ \underbrace{11}_{4}\ \underbrace{10}_{5}\ \underbrace{00}_{6}\ \underbrace{01}_{7}$$
which is exactly 7 symbols (14 bits ÷ 2 bits/symbol), consistent with QPSK's 2-bits-per-symbol rate.
Map each dibit to its carrier phase using the table given in the question:
Symbol
1
2
3
4
5
6
7
Dibit
00
10
01
11
10
00
01
Phase
$5\pi/4$
$3\pi/4$
$7\pi/4$
$\pi/4$
$3\pi/4$
$5\pi/4$
$7\pi/4$
Draw the waveform. Each symbol interval carries $s(t)=\cos(2\pi f_c t+\theta_k)$ at its own phase $\theta_k$ for the symbol's duration, with the SAME constant amplitude and carrier frequency $f_c$ throughout (only the phase changes symbol-to-symbol) — visible below as a phase "kink" at every dashed symbol boundary rather than any change in amplitude or envelope.
Explain the sketch. Five of the six symbol boundaries (1→2, 3→4, 4→5, 5→6, 6→7) are quarter-turn ($\pm\pi/2$) phase steps, the smallest jump this constellation allows; boundary 2→3 (dibit 10→01, $3\pi/4\to7\pi/4$) is a full $\pi$ (180°) reversal, the largest possible jump, since $10$ and $01$ sit at diametrically opposite phases in the constellation. No two consecutive symbols repeat the same dibit in this particular sequence, so every one of the six boundaries shows a visible phase discontinuity in the sketch — there is no "flat" (same-phase) stretch anywhere in this example.
Fig. Q7 — QPSK waveform for the 7-symbol sequence; each vertical divider is a symbol boundary where only the carrier's PHASE changes (amplitude and frequency stay constant).
