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FFT Benchmarking Course: 200 Core Concepts

Mathematical Foundations (20 concepts)

  1. Complex Numbers
  2. Euler's Formula
  3. Sine Wave Representation
  4. Frequency Domain
  5. Time Domain
  6. Discrete Fourier Transform
  7. Continuous Fourier Transform
  8. Transform Pairs
  9. Linearity Property
  10. Time Shifting
  11. Frequency Shifting
  12. Convolution Theorem
  13. Parseval's Theorem
  14. Symmetry Properties
  15. Magnitude Spectrum
  16. Phase Spectrum
  17. Rectangular Form
  18. Polar Form
  19. Sampling Theorem
  20. Nyquist Frequency

FFT Algorithm Fundamentals (25 concepts)

  1. Fast Fourier Transform
  2. Cooley-Tukey Algorithm
  3. Divide And Conquer
  4. Butterfly Operation
  5. Radix-2 FFT
  6. Radix-4 FFT
  7. Radix-8 FFT
  8. Mixed Radix FFT
  9. Decimation In Time
  10. Decimation In Frequency
  11. Bit Reversal Permutation
  12. Twiddle Factors
  13. In-Place Computation
  14. Computational Complexity
  15. FFT Size Selection
  16. Power Of Two Constraint
  17. Inverse FFT
  18. FFT Scaling
  19. Real FFT
  20. Complex FFT
  21. Half-Spectrum Property
  22. Zero Padding
  23. Frequency Resolution
  24. Time Resolution Tradeoff
  25. Circular Convolution

Signal Processing Concepts (25 concepts)

  1. Digital Signal Processing
  2. Analog To Digital Conversion
  3. Digital To Analog Conversion
  4. Sample Rate
  5. Quantization
  6. Bit Depth
  7. Dynamic Range
  8. Signal To Noise Ratio
  9. Windowing Functions
  10. Rectangular Window
  11. Hanning Window
  12. Hamming Window
  13. Blackman Window
  14. Kaiser Window
  15. Window Sidelobe Levels
  16. Spectral Leakage
  17. Scalloping Loss
  18. Overlap Add Method
  19. Overlap Save Method
  20. Frame Size
  21. Hop Size
  22. Frequency Bins
  23. Bin Width
  24. Spectrum Analysis
  25. Spectrogram

ARM Architecture & DSP (30 concepts)

  1. ARM Cortex M Series
  2. Cortex M4 Processor
  3. Cortex M33 Processor
  4. Instruction Set Architecture
  5. Thumb Instructions
  6. DSP Extension Instructions
  7. Single Instruction Multiple Data
  8. MAC Instructions
  9. Saturating Arithmetic
  10. Floating Point Unit
  11. Single Precision Float
  12. Double Precision Float
  13. Hardware Floating Point
  14. Software Floating Point
  15. FPU Register File
  16. Pipeline Architecture
  17. Instruction Pipeline
  18. Branch Prediction
  19. Interrupt Handling
  20. Exception Handling
  21. Memory Mapped IO
  22. Peripheral Access
  23. Clock Configuration
  24. Clock Cycles
  25. Instruction Cycle Count
  26. Wait States
  27. Flash Memory Access
  28. RAM Access Patterns
  29. Direct Memory Access
  30. DMA Channels

Memory & Performance (25 concepts)

  1. Cache Memory
  2. Cache Hit Rate
  3. Cache Miss Penalty
  4. Data Cache
  5. Instruction Cache
  6. Cache Line Size
  7. Memory Alignment
  8. Aligned Data Access
  9. Unaligned Data Access
  10. Memory Bandwidth
  11. Memory Latency
  12. Stack Memory
  13. Heap Memory
  14. Static Memory Allocation
  15. Dynamic Memory Allocation
  16. Buffer Management
  17. Double Buffering
  18. Ping Pong Buffers
  19. Circular Buffers
  20. Memory Copy Operations
  21. Data Layout
  22. Structure Packing
  23. Array Of Structures
  24. Structure Of Arrays
  25. Memory Fragmentation

Fixed-Point Arithmetic (18 concepts)

  1. Fixed Point Numbers
  2. Q Format Notation
  3. Integer Representation
  4. Fractional Representation
  5. Scaling Factor
  6. Fixed Point Multiplication
  7. Fixed Point Division
  8. Fixed Point Addition
  9. Overflow Detection
  10. Saturation Handling
  11. Rounding Modes
  12. Truncation Error
  13. Quantization Noise
  14. Dynamic Range Management
  15. Precision Analysis
  16. Bit Width Selection
  17. Sign Extension
  18. Fixed To Float Conversion

Benchmarking Methodology (30 concepts)

  1. Performance Metrics
  2. Execution Time
  3. Clock Cycle Measurement
  4. System Timer
  5. High Resolution Timer
  6. Timestamp Counter
  7. Profiling Tools
  8. Code Profiling
  9. Function Profiling
  10. Instruction Profiling
  11. Statistical Analysis
  12. Mean Execution Time
  13. Standard Deviation
  14. Variance Analysis
  15. Outlier Detection
  16. Confidence Intervals
  17. Benchmark Repeatability
  18. Test Case Design
  19. Input Signal Generation
  20. Sine Wave Test Signal
  21. Chirp Signal
  22. White Noise Signal
  23. Impulse Response
  24. Frequency Sweep
  25. Amplitude Scaling
  26. Baseline Measurement
  27. Comparative Analysis
  28. Performance Regression
  29. Benchmark Automation
  30. Test Harness Design

FFT Libraries & Tools (20 concepts)

  1. CMSIS DSP Library
  2. FFTW Library
  3. Kiss FFT
  4. FFT Library Licensing
  5. Open Source Libraries
  6. Proprietary Libraries
  7. Library API Design
  8. Function Call Overhead
  9. Initialization Functions
  10. Configuration Parameters
  11. Library Documentation
  12. Example Code
  13. GitHub Repositories
  14. Version Control
  15. Library Integration
  16. Header Files
  17. Linking Libraries
  18. Static Linking
  19. Dynamic Linking
  20. Library Dependencies

Optimization Techniques (15 concepts)

  1. Compiler Optimization Levels
  2. Loop Unrolling
  3. Function Inlining
  4. Code Size Optimization
  5. Speed Optimization
  6. Constant Propagation
  7. Dead Code Elimination

Development & Programming (15 concepts - Optional Extensions)

  1. C Programming Language
  2. Python For Analysis
  3. NumPy Library
  4. SciPy FFT Functions
  5. Matplotlib Visualization
  6. Assembly Language
  7. Reading Assembly Code
  8. Hand Coded Optimization
  9. Intrinsic Functions
  10. Volatile Keyword
  11. Register Variables
  12. Pointer Arithmetic
  13. Makefile Build System
  14. Cross Compilation
  15. Debugging Embedded Code

Applications & Context (10 concepts - Optional Extensions)

  1. Audio Signal Processing
  2. Speech Compression
  3. Frequency Analysis
  4. Real Time Processing
  5. Latency Requirements
  6. Raspberry Pi Pico
  7. RP2350 Microcontroller
  8. ADC Configuration
  9. DAC Configuration
  10. Audio Sampling Rates