An analog signal m(t) = 3 sin(500π t) + 2 sin(700π t) is sampled at 600 samples per second. What is the folding (Nyquist) frequency of this sampled system?

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:

• m(t) = 3 sin(500π t) + 2 sin(700π t).
• Sampling frequency fs = 600 samples per second (600 Hz).
• Standard radian–frequency to hertz conversion: ω = 2π f.

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.

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