Previous Year Question
The Nyquist rate for the signal x(t) = [1 + cos(2000πt) + sin(4000πt)] is
Correct answer: A
Explanation
cos(2000πt) has frequency 1000 Hz and sin(4000πt) has frequency 2000 Hz because ω=2πf. The highest frequency is therefore 2000 Hz, so the Nyquist rate is 2fmax=4000 samples/s. Hence option A.
Formula
fmax=4000π/(2π)=2000 Hz; fs,Nyquist=2fmax=4000 samples/s
Step-by-step solution
Correct Answer
A — 4000
Concept and Reasoning
cos(2000πt) has frequency 1000 Hz and sin(4000πt) has frequency 2000 Hz because ω=2πf. The highest frequency is therefore 2000 Hz, so the Nyquist rate is 2fmax=4000 samples/s. Hence option A.
Calculation / Key Relation
fmax=4000π/(2π)=2000 Hz
fs,Nyquist=2fmax=4000 samples/s
Exam Takeaway
Convert angular frequency to hertz before doubling.
Common Mistake
Do not treat the coefficient 4000π as frequency in hertz.
Common mistake
Do not treat the coefficient 4000π as frequency in hertz.
Exam tip
Convert angular frequency to hertz before doubling.
Quick method
Convert angular frequency to hertz before doubling.