FFT Benchmarking Course Taxonomy
Taxonomy Categories
The 200 concepts are organized into 12 pedagogically-sound categories with balanced distribution.
1. MATH - Mathematical Foundations (20 concepts, 10%)
Abbreviation: MATH Description: Core mathematical concepts underlying FFT and signal processing
Concepts: - Complex Numbers, Euler's Formula, Sine Wave Representation - Frequency Domain, Time Domain - Discrete Fourier Transform, Continuous Fourier Transform - Transform Pairs, Linearity Property - Time Shifting, Frequency Shifting, Convolution Theorem - Parseval's Theorem, Symmetry Properties - Magnitude Spectrum, Phase Spectrum - Rectangular Form, Polar Form - Sampling Theorem, Nyquist Frequency
2. FFT - FFT Algorithm & Implementation (25 concepts, 12.5%)
Abbreviation: FFT Description: Fast Fourier Transform algorithms, variants, and computational techniques
Concepts: - Fast Fourier Transform, Cooley-Tukey Algorithm - Divide And Conquer, Butterfly Operation - Radix-2 FFT, Radix-4 FFT, Radix-8 FFT, Mixed Radix FFT - Decimation In Time, Decimation In Frequency - Bit Reversal Permutation, Twiddle Factors - In-Place Computation, Computational Complexity - FFT Size Selection, Power Of Two Constraint - Inverse FFT, FFT Scaling - Real FFT, Complex FFT - Half-Spectrum Property, Zero Padding - Frequency Resolution, Time Resolution Tradeoff - Circular Convolution
3. SIG - Signal Processing (25 concepts, 12.5%)
Abbreviation: SIG Description: Digital signal processing concepts, windowing, and frame-based analysis
Concepts: - Digital Signal Processing - Analog To Digital Conversion, Digital To Analog Conversion - Sample Rate, Quantization, Bit Depth - Dynamic Range, Signal To Noise Ratio - Windowing Functions (Rectangular, Hanning, Hamming, Blackman, Kaiser) - Window Sidelobe Levels, Spectral Leakage, Scalloping Loss - Overlap Add Method, Overlap Save Method - Frame Size, Hop Size - Frequency Bins, Bin Width - Spectrum Analysis, Spectrogram
4. ARM - ARM Architecture & DSP Hardware (30 concepts, 15%)
Abbreviation: ARM Description: ARM Cortex-M processors, DSP instructions, and hardware features
Concepts: - ARM Cortex M Series, Cortex M4 Processor, Cortex M33 Processor - Instruction Set Architecture, Thumb Instructions - DSP Extension Instructions, Single Instruction Multiple Data - MAC Instructions, Saturating Arithmetic - Floating Point Unit, Single Precision Float, Double Precision Float - Hardware Floating Point, Software Floating Point - FPU Register File, Pipeline Architecture - Instruction Pipeline, Branch Prediction - Interrupt Handling, Exception Handling - Memory Mapped IO, Peripheral Access - Clock Configuration, Clock Cycles - Instruction Cycle Count, Wait States - Flash Memory Access, RAM Access Patterns - Direct Memory Access, DMA Channels
5. MEM - Memory Management & Optimization (25 concepts, 12.5%)
Abbreviation: MEM Description: Memory architecture, cache, buffers, and data layout strategies
Concepts: - Cache Memory, Cache Hit Rate, Cache Miss Penalty - Data Cache, Instruction Cache, Cache Line Size - Memory Alignment, Aligned Data Access, Unaligned Data Access - Memory Bandwidth, Memory Latency - Stack Memory, Heap Memory - Static Memory Allocation, Dynamic Memory Allocation - Buffer Management, Double Buffering - Ping Pong Buffers, Circular Buffers - Memory Copy Operations, Data Layout - Structure Packing, Array Of Structures - Structure Of Arrays, Memory Fragmentation
6. FXP - Fixed-Point Arithmetic (18 concepts, 9%)
Abbreviation: FXP Description: Fixed-point number representation and arithmetic operations
Concepts: - Fixed Point Numbers, Q Format Notation - Integer Representation, Fractional Representation - Scaling Factor - Fixed Point Multiplication, Fixed Point Division, Fixed Point Addition - Overflow Detection, Saturation Handling - Rounding Modes, Truncation Error - Quantization Noise, Dynamic Range Management - Precision Analysis, Bit Width Selection - Sign Extension, Fixed To Float Conversion
7. BENCH - Benchmarking & Testing (30 concepts, 15%)
Abbreviation: BENCH Description: Performance measurement, profiling, statistical analysis, and test design
Concepts: - Performance Metrics, Execution Time - Clock Cycle Measurement, System Timer - High Resolution Timer, Timestamp Counter - Profiling Tools, Code Profiling - Function Profiling, Instruction Profiling - Statistical Analysis, Mean Execution Time - Standard Deviation, Variance Analysis - Outlier Detection, Confidence Intervals - Benchmark Repeatability, Test Case Design - Input Signal Generation - Sine Wave Test Signal, Chirp Signal - White Noise Signal, Impulse Response - Frequency Sweep, Amplitude Scaling - Baseline Measurement, Comparative Analysis - Performance Regression, Benchmark Automation - Test Harness Design
8. LIB - FFT Libraries & Integration (20 concepts, 10%)
Abbreviation: LIB Description: FFT libraries, APIs, licensing, and integration techniques
Concepts: - CMSIS DSP Library, FFTW Library, Kiss FFT - FFT Library Licensing - Open Source Libraries, Proprietary Libraries - Library API Design, Function Call Overhead - Initialization Functions, Configuration Parameters - Library Documentation, Example Code - GitHub Repositories, Version Control - Library Integration, Header Files - Linking Libraries, Static Linking - Dynamic Linking, Library Dependencies
9. OPT - Optimization Techniques (7 concepts, 3.5%)
Abbreviation: OPT Description: Compiler and code optimization strategies
Concepts: - Compiler Optimization Levels - Loop Unrolling, Function Inlining - Code Size Optimization, Speed Optimization - Constant Propagation, Dead Code Elimination
10. PROG - Programming & Development (15 concepts, 7.5%)
Abbreviation: PROG Description: Programming languages, tools, and development practices (Optional Extension)
Concepts: - C Programming Language, Python For Analysis - NumPy Library, SciPy FFT Functions - Matplotlib Visualization - Assembly Language, Reading Assembly Code - Hand Coded Optimization, Intrinsic Functions - Volatile Keyword, Register Variables - Pointer Arithmetic, Makefile Build System - Cross Compilation, Debugging Embedded Code
11. APP - Applications & Context (10 concepts, 5%)
Abbreviation: APP Description: Real-world applications and hardware platforms (Optional Extension)
Concepts: - Audio Signal Processing, Speech Compression - Frequency Analysis, Real Time Processing - Latency Requirements - Raspberry Pi Pico, RP2350 Microcontroller - ADC Configuration, DAC Configuration - Audio Sampling Rates
12. DOC - Documentation & Workflows (0 concepts - Extension Available)
Abbreviation: DOC Description: Project documentation, collaboration tools, and workflows
Note: Core 200 concepts focus on technical content. Documentation concepts can be added as extensions.
Distribution Summary
| Category | Code | Count | Percentage | Status |
|---|---|---|---|---|
| Math | MATH | 20 | 10.0% | ✓ Under 30% |
| FFT | FFT | 25 | 12.5% | ✓ Under 30% |
| Signal | SIG | 25 | 12.5% | ✓ Under 30% |
| ARM | ARM | 30 | 15.0% | ✓ Under 30% |
| Memory | MEM | 25 | 12.5% | ✓ Under 30% |
| Fixed | FXP | 18 | 9.0% | ✓ Under 30% |
| Bench | BENCH | 30 | 15.0% | ✓ Under 30% |
| Library | LIB | 20 | 10.0% | ✓ Under 30% |
| Optimize | OPT | 7 | 3.5% | ✓ Under 30% |
| Total | 200 | 100% | ✓ Balanced |
Category Relationships
Mathematical Foundation: MATH → FFT → SIG Hardware Platform: ARM → MEM Numeric Precision: FXP (alternative to hardware float) Performance: BENCH → OPT Software Integration: LIB → PROG Real Applications: APP
Pedagogical Flow
- Weeks 1-2: MATH foundations
- Weeks 3-4: FFT + SIG concepts
- Weeks 5-6: ARM + MEM hardware
- Week 7: FXP arithmetic + BENCH methodology
- Week 8: LIB integration + OPT techniques
- Weeks 9-10: PROG + APP capstone project
Quality Metrics
✓ 12 categories (target: ~12) ✓ All categories < 30% of total (largest: ARM and BENCH at 15%) ✓ Balanced distribution across theoretical and practical domains ✓ Clear abbreviations (3-5 letters) ✓ Pedagogically coherent category groupings