Skip to content

Concept List

This document contains 200 concepts for the Benchmarking FFT course. Each concept is numbered with a unique ConceptID for use in the learning graph.

Mathematical Foundations (1-16)

  1. Complex Numbers
  2. Imaginary Unit
  3. Euler's Formula
  4. Sine Wave
  5. Cosine Wave
  6. Amplitude
  7. Frequency
  8. Phase
  9. Periodic Functions
  10. Harmonics
  11. Complex Conjugate
  12. Magnitude
  13. Unit Circle
  14. Hertz
  15. Time Domain
  16. Frequency Domain

Signal Processing Fundamentals (17-32)

  1. Analog Signals
  2. Digital Signals
  3. Sampling
  4. Sampling Rate
  5. Nyquist Theorem
  6. Aliasing
  7. Quantization
  8. Bit Depth
  9. ADC Conversion
  10. Signal Noise
  11. Signal To Noise Ratio
  12. Bandwidth
  13. Low Pass Filter
  14. Band Pass Filter
  15. Windowing Functions
  16. Spectral Leakage

Fourier Transform Theory (33-48)

  1. Jean Baptiste Fourier
  2. Fourier Series
  3. Continuous Fourier Transform
  4. Discrete Fourier Transform
  5. DFT Definition
  6. DFT Complexity
  7. Inverse DFT
  8. Frequency Bins
  9. Bin Resolution
  10. Spectral Analysis
  11. Power Spectrum
  12. Magnitude Spectrum
  13. Phase Spectrum
  14. Frequency Resolution
  15. Zero Padding
  16. Orthogonality

FFT Algorithm (49-72)

  1. FFT Algorithm
  2. FFT History
  3. Cooley Tukey Algorithm
  4. Radix-2 FFT
  5. Radix-4 FFT
  6. Split Radix FFT
  7. Butterfly Operation
  8. Butterfly Diagram
  9. Twiddle Factors
  10. Bit Reversal
  11. In Place FFT
  12. Decimation In Time
  13. Decimation In Frequency
  14. FFT Stages
  15. FFT Complexity
  16. O(N log N)
  17. FFT Size
  18. Power Of Two Sizes
  19. Real FFT
  20. Complex FFT
  21. Inverse FFT
  22. IFFT Algorithm
  23. Normalization Factor
  24. FFT Scaling

Hardware Platforms (73-88)

  1. Microcontroller
  2. ARM Architecture
  3. ARM Cortex M Series
  4. ARM Cortex M4
  5. ARM Cortex M33
  6. Raspberry Pi Pico
  7. Raspberry Pi Pico 2
  8. RP2040 Chip
  9. RP2350 Chip
  10. DSP Chip
  11. General Purpose CPU
  12. Clock Speed
  13. CPU Cycles
  14. Memory Architecture
  15. Cache Memory
  16. Embedded Systems

DSP Instructions (89-104)

  1. DSP Instructions
  2. SIMD Instructions
  3. MAC Instruction
  4. Multiply Accumulate
  5. Saturating Arithmetic
  6. Fixed Point Arithmetic
  7. Floating Point Unit
  8. FPU Operations
  9. Single Precision Float
  10. Q Format Numbers
  11. Q15 Format
  12. Q31 Format
  13. Hardware Multiplier
  14. Pipelining
  15. Instruction Latency
  16. Real Time Constraints

Programming Languages (105-120)

  1. C Language
  2. C Compiler
  3. GCC Compiler
  4. ARM Compiler
  5. Compiler Optimization
  6. Optimization Flags
  7. Assembly Language
  8. ARM Assembly
  9. Thumb Instructions
  10. Python Language
  11. NumPy Library
  12. SciPy FFT
  13. MicroPython
  14. Memory Management
  15. Reading Assembly Code
  16. Disassembly

FFT Libraries (121-132)

  1. FFT Libraries
  2. CMSIS DSP Library
  3. Kiss FFT
  4. FFTW Library
  5. Arm Math Library
  6. Pico SDK FFT
  7. Open Source FFT
  8. Library Licensing
  9. MIT License
  10. GPL License
  11. Library Integration
  12. API Documentation

Benchmarking Methodology (133-150)

  1. Benchmarking
  2. Performance Metrics
  3. Execution Time
  4. Clock Cycles
  5. Microseconds Per FFT
  6. FFTs Per Second
  7. Throughput Metric
  8. Latency Metric
  9. Memory Usage
  10. Code Size
  11. Test Harness
  12. Warm Up Runs
  13. Statistical Sampling
  14. Mean Execution Time
  15. Standard Deviation
  16. Reproducibility
  17. Fair Comparison
  18. Benchmarking Framework

Performance Factors (151-164)

  1. Integer FFT
  2. Floating Point FFT
  3. Fixed Point FFT
  4. Precision Tradeoffs
  5. Speed Accuracy Tradeoff
  6. Cache Effects
  7. Memory Access Patterns
  8. Loop Unrolling
  9. Vectorization
  10. Real Time Processing
  11. Streaming FFT
  12. Block Processing
  13. Double Buffering
  14. Compiler Settings

Signal Processing Pipeline (165-176)

  1. Signal Preprocessing
  2. DC Offset Removal
  3. Normalization
  4. Window Application
  5. Zero Padding Input
  6. Post Processing
  7. Magnitude Calculation
  8. Phase Calculation
  9. Decibel Conversion
  10. Peak Detection
  11. Frequency Estimation
  12. Dominant Frequency

Visualization and Reporting (177-186)

  1. Data Visualization
  2. Spectrum Plot
  3. Spectrogram
  4. Waterfall Display
  5. Time Domain Plot
  6. Performance Charts
  7. Comparison Tables
  8. Performance Dashboard
  9. Benchmark Results
  10. Report Generation

Applications (187-198)

  1. Audio Processing
  2. Music Analysis
  3. Voice Recognition
  4. Noise Cancellation
  5. Spectrum Analyzer
  6. Pitch Detection
  7. Vibration Analysis
  8. Machine Monitoring
  9. Radar Processing
  10. Communication Systems
  11. Software Defined Radio
  12. Sound Processing

Capstone Projects (199-200)

  1. Capstone Project
  2. Benchmark Suite