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FFT Benchmarking Course Taxonomy

Taxonomy Categories

The 200 concepts are organized into 12 pedagogically-sound categories with balanced distribution.

1. MATH - Mathematical Foundations (16 concepts, 8%)

Abbreviation: MATH Description: Core mathematical concepts underlying FFT and signal processing

Concept IDs: 1-16

Concepts:

  • Complex Numbers, Imaginary Unit, Euler's Formula
  • Sine Wave, Cosine Wave, Amplitude, Frequency, Phase
  • Periodic Functions, Harmonics
  • Complex Conjugate, Magnitude, Unit Circle
  • Hertz, Time Domain, Frequency Domain

2. SIGP - Signal Processing Fundamentals (16 concepts, 8%)

Abbreviation: SIGP Description: Basic signal processing concepts including sampling, filtering, and windowing

Concept IDs: 17-32

Concepts:

  • Analog Signals, Digital Signals
  • Sampling, Sampling Rate, Nyquist Theorem, Aliasing
  • Quantization, Bit Depth, ADC Conversion
  • Signal Noise, Signal To Noise Ratio, Bandwidth
  • Low Pass Filter, Band Pass Filter
  • Windowing Functions, Spectral Leakage

3. FOUR - Fourier Theory (16 concepts, 8%)

Abbreviation: FOUR Description: Theoretical foundations of Fourier transforms including DFT and spectral analysis

Concept IDs: 33-48

Concepts:

  • Jean Baptiste Fourier, Fourier Series
  • Continuous Fourier Transform, Discrete Fourier Transform
  • DFT Definition, DFT Complexity, Inverse DFT
  • Frequency Bins, Bin Resolution
  • Spectral Analysis, Power Spectrum, Magnitude Spectrum, Phase Spectrum
  • Frequency Resolution, Zero Padding, Orthogonality

4. FFTA - FFT Algorithm (24 concepts, 12%)

Abbreviation: FFTA Description: FFT algorithm implementations, variants, and computational structures

Concept IDs: 49-72

Concepts:

  • FFT Algorithm, FFT History, Cooley Tukey Algorithm
  • Radix-2 FFT, Radix-4 FFT, Split Radix FFT
  • Butterfly Operation, Butterfly Diagram, Twiddle Factors
  • Bit Reversal, In Place FFT
  • Decimation In Time, Decimation In Frequency
  • FFT Stages, FFT Complexity, O(N log N)
  • FFT Size, Power Of Two Sizes
  • Real FFT, Complex FFT, Inverse FFT, IFFT Algorithm
  • Normalization Factor, FFT Scaling

5. HARD - Hardware Platforms (16 concepts, 8%)

Abbreviation: HARD Description: Microcontrollers, processors, and embedded systems used for FFT computation

Concept IDs: 73-88

Concepts:

  • Microcontroller, ARM Architecture, ARM Cortex M Series
  • ARM Cortex M4, ARM Cortex M33
  • Raspberry Pi Pico, Raspberry Pi Pico 2
  • RP2040 Chip, RP2350 Chip
  • DSP Chip, General Purpose CPU
  • Clock Speed, CPU Cycles
  • Memory Architecture, Cache Memory, Embedded Systems

6. DSPI - DSP Instructions (16 concepts, 8%)

Abbreviation: DSPI Description: Digital signal processing instructions and hardware acceleration features

Concept IDs: 89-104

Concepts:

  • DSP Instructions, SIMD Instructions
  • MAC Instruction, Multiply Accumulate
  • Saturating Arithmetic, Fixed Point Arithmetic
  • Floating Point Unit, FPU Operations, Single Precision Float
  • Q Format Numbers, Q15 Format, Q31 Format
  • Hardware Multiplier, Pipelining, Instruction Latency
  • Real Time Constraints

7. PROG - Programming (16 concepts, 8%)

Abbreviation: PROG Description: Programming languages, compilers, and development tools

Concept IDs: 105-120

Concepts:

  • C Language, C Compiler, GCC Compiler, ARM Compiler
  • Compiler Optimization, Optimization Flags
  • Assembly Language, ARM Assembly, Thumb Instructions
  • Python Language, NumPy Library, SciPy FFT, MicroPython
  • Memory Management, Reading Assembly Code, Disassembly

8. LIBS - FFT Libraries (12 concepts, 6%)

Abbreviation: LIBS Description: Software libraries for FFT computation and their licensing

Concept IDs: 121-132

Concepts:

  • FFT Libraries, CMSIS DSP Library, Kiss FFT, FFTW Library
  • Arm Math Library, Pico SDK FFT, Open Source FFT
  • Library Licensing, MIT License, GPL License
  • Library Integration, API Documentation

9. BNCH - Benchmarking (18 concepts, 9%)

Abbreviation: BNCH Description: Benchmarking methodology, metrics, and measurement frameworks

Concept IDs: 133-150

Concepts:

  • Benchmarking, Performance Metrics
  • Execution Time, Clock Cycles
  • Microseconds Per FFT, FFTs Per Second
  • Throughput Metric, Latency Metric, Memory Usage, Code Size
  • Test Harness, Warm Up Runs, Statistical Sampling
  • Mean Execution Time, Standard Deviation
  • Reproducibility, Fair Comparison, Benchmarking Framework

10. PERF - Performance Optimization (14 concepts, 7%)

Abbreviation: PERF Description: Performance factors, optimization techniques, and real-time processing

Concept IDs: 151-164

Concepts:

  • Integer FFT, Floating Point FFT, Fixed Point FFT
  • Precision Tradeoffs, Speed Accuracy Tradeoff
  • Cache Effects, Memory Access Patterns
  • Loop Unrolling, Vectorization
  • Real Time Processing, Streaming FFT, Block Processing
  • Double Buffering, Compiler Settings

11. PIPE - Signal Pipeline (12 concepts, 6%)

Abbreviation: PIPE Description: Signal preprocessing and post-processing operations

Concept IDs: 165-176

Concepts:

  • Signal Preprocessing, DC Offset Removal, Normalization
  • Window Application, Zero Padding Input
  • Post Processing, Magnitude Calculation, Phase Calculation
  • Decibel Conversion, Peak Detection
  • Frequency Estimation, Dominant Frequency

12. VAPP - Visualization and Applications (24 concepts, 12%)

Abbreviation: VAPP Description: Data visualization, reporting, and practical FFT applications

Concept IDs: 177-200

Concepts:

  • Data Visualization, Spectrum Plot, Spectrogram, Waterfall Display
  • Time Domain Plot, Performance Charts, Comparison Tables
  • Performance Dashboard, Benchmark Results, Report Generation
  • Audio Processing, Music Analysis, Voice Recognition
  • Noise Cancellation, Spectrum Analyzer, Pitch Detection
  • Vibration Analysis, Machine Monitoring, Radar Processing
  • Communication Systems, Software Defined Radio, Biomedical Signals
  • Sound Processing, Capstone Project, Benchmark Suite

Distribution Summary

Category Code Count Percentage Status
Mathematical Foundations MATH 16 8.0% ✓ Under 30%
Signal Processing SIGP 16 8.0% ✓ Under 30%
Fourier Theory FOUR 16 8.0% ✓ Under 30%
FFT Algorithm FFTA 24 12.0% ✓ Under 30%
Hardware Platforms HARD 16 8.0% ✓ Under 30%
DSP Instructions DSPI 16 8.0% ✓ Under 30%
Programming PROG 16 8.0% ✓ Under 30%
FFT Libraries LIBS 12 6.0% ✓ Under 30%
Benchmarking BNCH 18 9.0% ✓ Under 30%
Performance Optimization PERF 14 7.0% ✓ Under 30%
Signal Pipeline PIPE 12 6.0% ✓ Under 30%
Visualization & Applications VAPP 24 12.0% ✓ Under 30%
Total 200 100% ✓ Balanced

Category Relationships

Mathematical Foundation: MATH → FOUR → SIGP Algorithm Path: FOUR → FFTA → PERF Hardware Platform: HARD → DSPI Software Path: PROG → LIBS → BNCH Processing Pipeline: SIGP → PIPE → VAPP

Pedagogical Flow

  1. Weeks 1-2: MATH and SIGP foundations
  2. Weeks 3-4: FOUR and FFTA algorithm concepts
  3. Weeks 5-6: HARD and DSPI hardware
  4. Week 7: PROG programming and LIBS libraries
  5. Week 8: BNCH benchmarking methodology
  6. Week 9: PERF optimization and PIPE signal pipeline
  7. Week 10: VAPP applications and capstone project

Quality Metrics

  • 12 categories (target: ~12)
  • All categories < 30% of total (largest: FFTA and VAPP at 12%)
  • Balanced distribution across theoretical and practical domains
  • Clear abbreviations (3-5 letters)
  • Pedagogically coherent category groupings