Difficulty: Easy
Correct Answer: 300 Hz
Explanation:
Introduction / Context:In sampling theory for signals and systems, the folding frequency (also called the Nyquist frequency) is a crucial limit that separates positive and negative frequency images after sampling. It determines where aliasing reflections occur in the discrete-time spectrum. This question evaluates recognition of the Nyquist frequency when the sampling frequency is specified explicitly.
Given Data / Assumptions:
Concept / Approach:The Nyquist frequency fN is one-half of the sampling frequency: fN = fs / 2. Spectral components above fN will fold (alias) back into the first Nyquist zone upon sampling. The individual analog components have ω1 = 500π rad/s and ω2 = 700π rad/s, corresponding to f1 = ω1 / (2π) = 250 Hz and f2 = ω2 / (2π) = 350 Hz; however, the folding frequency is determined solely by the sampling frequency, not by the signal content.
Step-by-Step Solution:
Compute Nyquist frequency: fN = fs / 2.Substitute fs = 600 Hz → fN = 600 / 2 = 300 Hz.Therefore, the folding frequency is 300 Hz.Verification / Alternative check:
Component at 250 Hz lies below fN, so it will not alias. Component at 350 Hz lies above fN, so it will fold around 300 Hz to 300 − (350 − 300) = 250 Hz in the sampled spectrum, consistent with folding about 300 Hz.Why Other Options Are Wrong:
1400 Hz, 700 Hz, 500 Hz, 200 Hz: These do not equal fs / 2 for fs = 600 Hz. The Nyquist frequency only depends on fs, not on individual sinusoid frequencies.Common Pitfalls:
Confusing a component frequency with the Nyquist frequency; the folding frequency is always fs / 2.Final Answer:
300 Hz
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