Signals & Systems: Match Task to Principle/Consequence List I A. Detection of a periodic signal in noise B. Recovery of a band-limited signal from its uniformly sampled values C. Finer quantization of a signal D. Delta modulation List II 1. Increase in required channel bandwidth (due to higher bit rate) 2. Slope overload error 3. Nyquist rate 4. Cross-correlation (for detection)

Introduction / Context:
Core operations in signal processing have canonical tools and side effects. This problem matches standard tasks (detection, sampling reconstruction, quantization changes, and delta modulation) to their governing principles or common artifacts.

Given Data / Assumptions:

• Periodic signal detection amidst noise uses correlation-based techniques.
• Sampling theory requires minimum sampling rates for perfect reconstruction.
• Quantization with finer steps increases bits per sample.
• Delta modulation is a one-bit differential scheme susceptible to slope overload.

Concept / Approach:

Cross-correlation maximizes the detection metric for a periodic (or known) signal in noise. Nyquist rate (at least 2 * f_max) is the criterion for reconstructing a band-limited signal from uniform samples. Finer quantization (more bits) increases the coded bit rate for a fixed sampling rate, increasing the required bandwidth on a digital channel. Delta modulation suffers from slope overload when the input slope exceeds the modulator’s step-rate capability.

Step-by-Step Solution:

Verification / Alternative check:

Matched filter theory equates to correlation; Shannon-Nyquist sampling theorem ensures recoverability; bit rate grows linearly with bits/sample; DM textbooks highlight slope overload and granular noise trade-offs.

Why Other Options Are Wrong:

Swapping any pair contradicts foundational theorems (e.g., using Nyquist for detection, or calling DM error an aliasing artifact).

Common Pitfalls:

Confusing correlation with convolution; thinking finer quantization always reduces bandwidth (it reduces quantization noise but increases bit rate).

Final Answer:

A-4, B-3, C-1, D-2