A 16-ary phase-shift keying (16-PSK) system modulates a 9600 bit/s digital…
2012
A 16-ary phase-shift keying (16-PSK) system modulates a 9600 bit/s digital data stream. What is the symbol rate (modulation rate)?
Answer: A. 2400 baud — ConceptIn an M-ary digital modulation scheme, one symbol represents log2(M) bits. The symbol rate, measured in baud, is the bit rate divided by the number of…
- A.
2400 baud
- B.
1200 baud
- C.
4800 baud
- D.
9600 baud
Attempted by 4 students.
Show answer & explanation
Correct answer: A
Concept
In an M-ary digital modulation scheme, one symbol represents log2(M) bits. The symbol rate, measured in baud, is the bit rate divided by the number of bits carried by each symbol.
Equivalently, bits per symbol = log2(M), and symbol rate = bit rate ÷ log2(M).
Application
For 16-PSK, M = 16, so bits per symbol = log2(16) = 4.
Substitute the bit rate: symbol rate = 9600 bit/s ÷ 4 bit/symbol.
Thus, the symbol rate = 2400 symbols/s = 2400 baud.
Cross-check
At 2400 symbols/s and 4 bits/symbol, the recovered bit rate is 2400 × 4 = 9600 bit/s, matching the given data rate. Therefore, the modulation rate is 2400 baud.