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FAQ Coverage Gaps

Concepts from the 200-concept core learning graph not explicitly named in docs/faq.md, ranked by centrality (number of other concepts that depend on each one). See faq-quality-report.md for full coverage statistics and a note on why exact-phrase matching understates true thematic coverage.

Critical Gaps (High Priority)

High-centrality concepts (3+ downstream dependents) without a dedicated FAQ entry:

  1. Performance Metrics (BENCH, 7 dependents) Sub-concepts (execution time, throughput, speedup factor) are covered individually, but no question defines the umbrella term itself. Suggested question: "What performance metrics does this course use to compare FFT implementations?" (Core Concepts)

  2. Statistical Analysis (BENCH, 6 dependents) Mean and standard deviation are covered under What statistics should a trustworthy benchmark report?, but variance, confidence intervals, and outlier detection are not. Suggested question: "How do you detect and handle an outlier measurement in a set of benchmark trials?" (Best Practices)

  3. Compiler Optimization Levels (OPT, 6 dependents) -O2/-O3/-Os flags are mentioned in passing but have no dedicated question. Suggested question: "What do compiler optimization flags like -O2 and -Os actually change?" (Technical Details)

  4. Fixed Point Numbers (FXP, 5 dependents) Q15/Q31 are covered specifically, but the general fixed-point-versus-floating-point framing has no standalone entry. Suggested question: "What is fixed-point arithmetic, and how does it differ from floating point?" (Technical Details)

  5. Q Format Notation (FXP, 5 dependents) Covered implicitly via the Q15/Q31 question but the general Q-format notation convention isn't named directly. Suggested question: "What does 'Q15' or 'Q31' notation actually mean?" (Technical Details)

  6. Input Signal Generation (BENCH, 5 dependents) Test signal design (sine, chirp, white noise, impulse) used for benchmarking isn't covered. Suggested question: "What kinds of test signals are used to benchmark a spectrum analyzer, and why not just use real audio?" (Best Practices)

  7. Sine Wave Representation (MATH, 3 dependents) The general sine wave equation is covered inside the time/frequency domain and Euler's formula answers but has no standalone entry. Suggested question: "What is the general equation for a sine wave, and what does each term mean?" (Core Concepts)

  8. DSP Extension Instructions (ARM, 3 dependents) VMLA and other specific instructions are covered; the general ARM DSP extension category is not named. Suggested question: "What are ARM's DSP extension instructions, and which Cortex-M cores support them?" (Technical Details)

  9. Memory Alignment (MEM, 3 dependents) Not currently covered; relevant to the assembly and typed-array chapters. Suggested question: "Why does memory alignment matter when working with typed arrays in assembly?" (Technical Details)

  10. Data Layout (MEM, 3 dependents) Not currently covered. Suggested question: "How does data layout in memory affect FFT performance?" (Advanced Topics)

  11. Test Case Design (BENCH, 3 dependents) Related to validation (covered) but the general practice of designing a good test case isn't a standalone question. Suggested question: "What makes a good test case for validating a DFT or FFT implementation?" (Best Practices)

  12. Linking Libraries (LIB, 3 dependents) Static vs. dynamic linking, header files, and library dependencies are not covered — this course leans on licensing and library choice more than the mechanics of linking. Suggested question: "What's the difference between static and dynamic linking when integrating a C library like CMSIS-DSP?" (Advanced Topics)

Medium Priority Gaps

Moderate-centrality concepts (1–2 downstream dependents) without dedicated FAQ coverage — 40 concepts. Grouped by taxonomy category:

Mathematical foundations (MATH): Continuous Fourier Transform, Convolution Theorem, Symmetry Properties

FFT algorithms (FFT): Radix-4 FFT (discussed but not as an exact phrase — see quality report), Computational Complexity, Zero Padding

Signal processing (SIG): Analog To Digital Conversion, Overlap Add Method, Spectrum Analysis

ARM architecture (ARM): Pipeline Architecture, Instruction Pipeline, Interrupt Handling, Memory Mapped IO, Clock Configuration, Direct Memory Access

Memory (MEM): Stack Memory, Heap Memory, Buffer Management, Cache Hit Rate, Memory Bandwidth, Dynamic Memory Allocation, Double Buffering

Fixed-point (FXP): Integer Representation, Fixed Point Multiplication, Overflow Detection, Rounding Modes, Truncation Error, Precision Analysis

Benchmarking (BENCH): Code Profiling, System Timer, High Resolution Timer, Profiling Tools, Function Profiling, Chirp Signal, Baseline Measurement, Comparative Analysis, Benchmark Automation

Libraries (LIB): Library API Design, Library Integration, GitHub Repositories

Low Priority Gaps

Leaf concepts with zero downstream dependents in the planning DAG — 100 concepts, distributed across taxonomy categories as follows: ARM (17), Memory (14), Benchmarking (14), Libraries (14), FFT (10), Signal Processing (9), Fixed-Point (9), Math (7), Optimization (6). These are mostly fine-grained implementation details (specific register names, specific library functions, specific window-function variants like the Kaiser window) that the glossary already defines individually and that a curated FAQ isn't expected to enumerate one by one.

Recommendations

  1. Add questions for the 12 critical gaps above — each is a genuinely distinct concept not addressed elsewhere in the FAQ, not just a phrasing mismatch. This would raise 200-concept DAG coverage from 24.0% to roughly 30% and close every remaining gap in the top-25-by-centrality list.
  2. The 40 medium-priority gaps are reasonable candidates for a second-wave FAQ expansion if this document is revisited after the Instructor's Guide and any additional lab content stabilize, but are not urgent — most are already implicitly touched on through the concepts that depend on them.
  3. The 100 low-priority leaf concepts can be addressed in future updates only if student questions actually arise about them in practice; they are better served by the glossary's existing per-term definitions than by dedicated FAQ entries.