Signals and systems – Match each task with the appropriate principle or artifact List I (Task / Concept) A. Detection of a periodic signal buried in noise B. Recover a band-limited signal from uniformly sampled values C. Use finer quantization in waveform coding D. Delta modulation behavior List II (Principle / Artifact) Increase in required channel bandwidth (higher bit rate) Slope-overload error Nyquist sampling (at or above Nyquist rate) Cross-correlation (matched detection for periodic patterns) Choose the correct mapping.
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AA-4, B-3, C-1, D-2
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BA-3, B-2, C-1, D-4
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CA-4, B-3, C-2, D-1
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DA-3, B-2, C-4, D-1
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EA-1, B-4, C-3, D-2
Answer
Correct Answer: A-4, B-3, C-1, D-2
Explanation
Introduction / Context:This problem links classic signal-processing tasks to the corresponding theoretical tools and common artifacts in sampling and quantization. Such mapping is core to communication system design and detection theory.
Given Data / Assumptions:
- Periodic signal detection in noise benefits from correlation.
- Uniform sampling of band-limited signals follows the Nyquist–Shannon theorem.
- Increasing quantization resolution raises bit rate for fixed sampling rate, thus increasing required bandwidth for digital transmission.
- Delta modulation is prone to slope-overload for fast-varying inputs if step size is too small.
Concept / Approach:
Match each task with the most relevant principle or artifact: cross-correlation for periodic detection; Nyquist rate for perfect reconstruction; finer quantization implies more bits per sample → higher bit rate → more bandwidth; delta modulation → slope-overload when input slope exceeds step capability.
Step-by-Step Solution:
A → 4 (cross-correlation).B → 3 (Nyquist rate).C → 1 (increased bandwidth).D → 2 (slope-overload).Verification / Alternative check:
These are standard results in detection and sampling theory; textbooks and lab exercises confirm the pairings.
Why Other Options Are Wrong:
Relating delta modulation to Nyquist or cross-correlation mixes unrelated concepts; claiming finer quantization reduces bandwidth is incorrect for fixed sampling rate digital links.
Common Pitfalls:
Confusing quantization step size with sampling rate; mixing matched filtering/correlation with envelope detection.
Final Answer:
A-4, B-3, C-1, D-2.