GATE 2014 EC (EC3) – Question 61
A PCM system samples $m(t)=\sin(100\pi t)+\cos(100\pi t)$ V at the Nyquist rate and uniformly quantizes with step 0.75 V. Find minimum data rate (bits/s).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 199 to 201
Explanation
The message sin(100πt)+cos(100πt) has highest frequency50Hz and peak amplitude√2V. Nyquist sampling needs100samples/s. Its full range2√2V divided by0.75V requires ceil(2√2/0.75)=4levels, or2bits/sample. Therefore the minimum rate is **100×2=200bits/s**.