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.

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:

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.