Introduction / Context:
In digital signal processing, the folding frequency (also called the Nyquist frequency) defines the highest frequency that can be represented without aliasing when a continuous-time signal is uniformly sampled. This question checks whether you can identify the Nyquist frequency from a given sampling rate and interpret sinusoidal components written in radians per second form.
Given Data / Assumptions:
- Sampling rate fs = 1200 samples per second.
- Signal components are sinusoids with angular frequencies 120π, 240π, 360π, 480π, 600π and 720π rad/s.
- Folding (Nyquist) frequency fN = fs / 2 for real, uniform sampling.
Concept / Approach:
The Nyquist (folding) frequency equals half the sampling rate. Any spectral content above this frequency will mirror (fold) into lower frequencies, causing aliasing. We convert the given angular frequencies to hertz using f = ω / (2π) to understand the placement of components relative to fN.
Step-by-Step Solution:
Compute fN: fN = fs / 2 = 1200 / 2 = 600 Hz.Convert one term to check: for ω = 120π rad/s, f = (120π) / (2π) = 60 Hz. Similarly: 240π → 120 Hz; 360π → 180 Hz; 480π → 240 Hz; 600π → 300 Hz; 720π → 360 Hz.All individual tones (60 to 360 Hz) lie below 600 Hz, so the folding limit is simply 600 Hz.
Verification / Alternative check:
Nyquist theorem requires fs ≥ 2 fmax. Here fmax = 360 Hz, so fs ≥ 720 Hz is sufficient. Since fs = 1200 Hz, it satisfies the criterion, and fN = 600 Hz by definition.
Why Other Options Are Wrong:
300 Hz and 360 Hz: These are actual spectral components or arbitrary values, not fs/2.480 Hz and 720 Hz: 480 Hz is below fN but is not the folding frequency; 720 Hz equals fmax*2 and relates to minimum sampling rate, not fN for given fs.
Common Pitfalls:
Confusing the highest sinusoidal frequency present with the folding frequency; forgetting that fN depends only on fs.
Final Answer:
600 Hz
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