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Concept List

This document contains 550 concepts for the Benchmarking FFT course, regenerated from the current docs/course-description.md and the full 35-lab series in docs/labs/. Each concept is numbered with a unique ConceptID for use in the learning graph. This numbering also matches the taxonomy category blocks used in concept-taxonomy.md and learning-graph.csv.

Concepts are grouped into 12 categories that mirror the course's 8 lab modules plus 4 cross-cutting themes (math foundations, benchmarking, ARM assembly, and course logistics).

Foundations & Tools (FOUND) — 45 concepts

  1. Microcontroller
  2. Thonny IDE
  3. MicroPython
  4. Read Eval Print Loop
  5. USB Serial Connection
  6. Interpreter Selection
  7. Device Filesystem
  8. File Transfer
  9. Script Execution
  10. Print Statement
  11. Keyboard Interrupt
  12. Soft Reset
  13. BOOTSEL Button
  14. Firmware
  15. Firmware Update
  16. Float Precision
  17. Integer Precision
  18. While Loop
  19. Try Except Block
  20. General Purpose IO
  21. GPIO Pin
  22. Pin Object
  23. Digital Output
  24. Digital Input
  25. Onboard LED
  26. Logic Level
  27. Pin Toggle
  28. Sleep Delay
  29. Pulse Width Modulation
  30. CPU Clock Frequency
  31. RAM
  32. Flash Memory
  33. Memory Mapped Register
  34. CPUID Register
  35. Bit Shift Operator
  36. Bit Mask
  37. CPU Cycle Budget
  38. Register Address
  39. Garbage Collection
  40. Free Memory Query
  41. Board Identification
  42. Silicon Revision
  43. Unique Device ID
  44. Prediction Before Measurement
  45. Mascot Pedagogical Device

Peripherals & Hardware I/O (HWIO) — 40 concepts

  1. Serial Peripheral Interface
  2. SPI Clock Line
  3. Chip Select Line
  4. Display Driver Chip
  5. SSD1306 Controller
  6. Framebuffer
  7. Monochrome Display
  8. Pixel Coordinate
  9. Text Rendering
  10. Display Refresh
  11. Data Command Pin
  12. Display Reset Pin
  13. Shared Configuration Module
  14. Draw Show Loop Pattern
  15. Coordinate System Origin
  16. Character Grid
  17. Digital Input Pin
  18. Pull Up Resistor
  19. Active Low Logic
  20. Switch Bounce
  21. Debouncing
  22. Polling Loop
  23. Edge Detection
  24. Event Loop
  25. Mode Switching
  26. Floating Pin
  27. Long Press Detection
  28. Tactile Switch
  29. mpremote Tool
  30. Library Directory
  31. Import Path
  32. Module Import
  33. Autorun Main Script
  34. Standalone Operation
  35. Code Organization
  36. Boot Script
  37. Board Recovery Procedure
  38. Escape Hatch Delay
  39. Deployment Workflow
  40. Untethered Operation

Digital Audio & Sampling (AUDIO) — 50 concepts

  1. MEMS Microphone
  2. I2S Protocol
  3. Bit Clock
  4. Word Select Line
  5. I2S Serial Data
  6. Audio Buffer
  7. Buffered Read
  8. Sample Word Format
  9. Arithmetic Right Shift
  10. Binary Data Unpacking
  11. DC Offset
  12. DC Offset Removal
  13. Signed Integer Conversion
  14. Full Scale Value
  15. Channel Select Pin
  16. Root Mean Square
  17. Sound Level
  18. Loudness Perception
  19. Moving Average
  20. Exponential Smoothing
  21. Auto Calibration
  22. Bar Graph Display
  23. Decibel Scale
  24. Level Meter
  25. Noise Floor
  26. Peak Hold Marker
  27. Sample Period
  28. Sampling Theorem
  29. Nyquist Frequency
  30. Aliasing
  31. Frequency Folding
  32. Anti Aliasing Filter
  33. Undersampling
  34. Tone Generator
  35. Sample Rate Selection
  36. Productive Failure
  37. Zero Crossing Counting
  38. Dynamic Range
  39. Headroom
  40. Clipping
  41. Clipping Distortion
  42. Quantization Error
  43. Amplitude Normalization
  44. Integer Overflow
  45. Bit Depth
  46. 6 dB Per Bit Rule
  47. Flat Top Waveform
  48. Harmonic Distortion
  49. Live VU Meter
  50. Settling Time Discard

Waves & Signal Math Foundations (WAVE) — 45 concepts

  1. Radians
  2. Angular Frequency
  3. Period Of A Wave
  4. Phase Offset
  5. Sine Wave
  6. Cosine Function
  7. Sine Synthesis
  8. Waveform Plotting
  9. Peak Amplitude
  10. DC Component
  11. Signal Synthesis
  12. Samples Per Cycle
  13. Superposition Principle
  14. Wave Addition
  15. Constructive Interference
  16. Destructive Interference
  17. Beat Frequency
  18. Amplitude Envelope
  19. Fundamental Frequency
  20. Overtone
  21. Timbre
  22. Additive Synthesis
  23. Square Wave
  24. Sawtooth Wave
  25. Complex Numbers
  26. Imaginary Unit
  27. Euler's Formula
  28. Complex Exponential
  29. Real Part
  30. Imaginary Part
  31. Magnitude Of A Complex Number
  32. Phase Angle
  33. Unit Circle
  34. Roots Of Unity
  35. Orthogonality
  36. Basis Function
  37. Projection Onto Basis
  38. Frequency Domain
  39. Time Domain
  40. Algebra Of Sine And Cosine
  41. Amplitude Parameter
  42. Frequency Parameter
  43. Wave Interference Pattern
  44. Harmonic Series
  45. Signal Envelope

Correlation & the DFT (DFT) — 55 concepts

  1. Correlation
  2. Multiply And Sum
  3. Dot Product
  4. Test Frequency
  5. Similarity Measure
  6. In Phase Component
  7. Quadrature Component
  8. Phase Independence
  9. Correlation Magnitude
  10. Hidden Frequency Detection
  11. Sine Only Detector Blind Spot
  12. Arctangent Phase Recovery
  13. Frequency Candidate Sweep
  14. Frequency Sweep
  15. Bin Index
  16. Bin Center Frequency
  17. Bin Width
  18. Spectrum Array
  19. 8-Point DFT Example
  20. Real And Imaginary Parts
  21. Spectrum Symmetry
  22. Negative Frequency
  23. DC Bin
  24. Nyquist Bin
  25. Two-Tone Signal
  26. Mirror Spectrum
  27. Forward Transform Convention
  28. Inverse Transform Convention
  29. Discrete Fourier Transform
  30. Fourier Transform
  31. Ground Truth Signal
  32. Known Signal Test
  33. Validation Before Trust
  34. Numerical Tolerance
  35. Absolute Error
  36. Relative Error
  37. Bin Exact Frequency
  38. Expected Peak
  39. Debugging By Bisection
  40. Test Signal Design
  41. Impulse Response Test
  42. Single Precision Float
  43. Parseval's Theorem
  44. Test Suite Blind Spot
  45. Sign Error
  46. Algorithmic Complexity
  47. Quadratic Complexity
  48. Operation Counting
  49. Scaling Behavior
  50. Real Time Budget
  51. Frame Duration
  52. Processing Deadline
  53. Performance Bottleneck
  54. Big O Notation
  55. Trigonometric Function Cost

The FFT Algorithm (FFT) — 50 concepts

  1. Fast Fourier Transform
  2. Divide And Conquer
  3. Even Odd Split
  4. Recursive Decomposition
  5. Subproblem
  6. Recombination Step
  7. Logarithmic Stages
  8. Complexity Reduction
  9. Power Of Two Constraint
  10. Redundant Computation
  11. Symmetry Exploitation
  12. Twiddle Factor
  13. Radix 2 Algorithm
  14. Mixed Radix FFT
  15. Cooley-Tukey Algorithm
  16. Bit Reversal Permutation
  17. Index Reversal
  18. Permutation Table
  19. Twiddle Factor Table
  20. Precomputation
  21. Lookup Table
  22. Loop Invariant Hoisting
  23. In Place Reordering
  24. Swap Operation
  25. Interleaved Storage
  26. Butterfly Operation
  27. Complex Multiplication
  28. Four Multiply Form
  29. Three Multiply Trick
  30. Butterfly Pair
  31. Stage Span
  32. Data Flow Graph
  33. Butterfly Count
  34. Stage Loop
  35. Cross Add And Subtract
  36. Iterative FFT
  37. Reference Implementation
  38. Cross Validation
  39. Speedup Factor
  40. Correctness Before Speed
  41. Function Decomposition
  42. Inverse FFT
  43. Table Hoisting Optimization
  44. FFT DFT Crossover Point
  45. In Place Computation
  46. O(N Log N) Complexity
  47. Real Input Transform
  48. Decimation In Time
  49. Bluestein's Algorithm
  50. Radix 4 FFT

Spectral Analysis & Real Spectra (SPEC) — 55 concepts

  1. Magnitude Computation
  2. Fast Magnitude Approximation
  3. Power Versus Magnitude
  4. Bin Averaging
  5. Logarithmic Scaling
  6. Square Root Scaling
  7. Spectrum Bars
  8. Frame Capture
  9. Live Spectrum Display
  10. Whistle Test
  11. Half Spectrum Display
  12. Rumble Rejection
  13. Peak Ratio Threshold
  14. Resolution Speed Tradeoff
  15. Spectral Leakage
  16. Rectangular Window
  17. Hanning Window
  18. Hamming Window
  19. Blackman Window
  20. Main Lobe Width
  21. Side Lobe Level
  22. Window Tradeoff
  23. Coherent Gain
  24. Edge Discontinuity
  25. Window Table
  26. Periodic Extension Assumption
  27. On Bin Tone
  28. Off Bin Tone
  29. Argmax Search
  30. Peak Bin
  31. Bin To Frequency Mapping
  32. Frequency Resolution Limit
  33. Parabolic Interpolation
  34. Sub Bin Accuracy
  35. Local Maximum
  36. Threshold Rejection
  37. Pitch
  38. Musical Note Mapping
  39. Octave
  40. Cents Deviation
  41. Semitone Formula
  42. Chromatic Tuner
  43. Reference Pitch
  44. Frame Rate
  45. Stage Profiling
  46. Capture Time
  47. Compute Time
  48. Draw Time
  49. Overlap Processing
  50. Hop Size
  51. Buffer Swapping
  52. Processing Latency
  53. Bottleneck Identification
  54. Amdahl's Law
  55. Stage Percentage Breakdown

Benchmarking & Measurement Methodology (BENCH) — 50 concepts

  1. Millisecond Timer
  2. Microsecond Timer
  3. Timer Resolution
  4. Counter Wraparound
  5. Cycle Counter
  6. DWT Unit
  7. Cycle Count Register
  8. Debug Exception Register
  9. Register Bit Manipulation
  10. Cycles To Time Conversion
  11. Counter Verification
  12. Trace Enable Bit
  13. Cycle Count Enable Bit
  14. Nanosecond Resolution
  15. Overflow Masking
  16. Empty Loop Baseline
  17. Cold Start Effect
  18. Warm Up Discard
  19. Best Of N Sampling
  20. Minimum Sample Statistic
  21. Variance Sources
  22. Interrupt Interference
  23. Observer Effect
  24. Timing Overhead
  25. Measurement Discipline
  26. Honest Reporting
  27. Benchmark Exclusions
  28. Negative Result
  29. Benchmark Report Format
  30. Cold Start Baseline Mismatch
  31. Bytecode Interpretation
  32. Native Code Emitter
  33. Viper Code Emitter
  34. Boxed Value
  35. Unboxed Value
  36. Type Annotation
  37. Machine Type
  38. Abstraction Cost
  39. Language Tradeoff Analysis
  40. Calling C From MicroPython
  41. Library Over Handwritten Code
  42. Native Decorator
  43. Viper Decorator
  44. Typed Pointer
  45. Abstraction Ladder
  46. Reading Versus Writing Skill
  47. Benchmarking Methodology
  48. Fair Comparison
  49. Reproducibility
  50. Instrumentation Overhead

ARM Architecture & Assembly Language (ASM) — 55 concepts

  1. Instruction Set Architecture
  2. ARMv6-M
  3. ARMv7-M
  4. ARMv8-M
  5. Cortex M0 Plus
  6. Cortex M33 Processor
  7. ARM Cortex M Architecture
  8. FPU Presence Detection
  9. Feature Register
  10. FPv5 Floating Point Unit
  11. Capability Probing
  12. Hardware Feature Gate
  13. Portability Constraint
  14. Failure Root Cause
  15. Inline Assembler
  16. Assembly Decorator
  17. CPU Register
  18. General Purpose Register
  19. Register Allocation
  20. Move Instruction
  21. Add Instruction
  22. Compare Instruction
  23. Conditional Branch
  24. Assembly Label
  25. Assembly Loop
  26. Argument Passing Convention
  27. Return Value Register
  28. Machine Code
  29. Instruction Mnemonic
  30. Core Register Set
  31. Array Sum Speedup
  32. Floating Point Register
  33. Register Bank
  34. Load Store Architecture
  35. VLDR Instruction
  36. VSTR Instruction
  37. VADD Instruction
  38. VSUB Instruction
  39. VMUL Instruction
  40. VNEG Instruction
  41. Memory Address
  42. Pointer Arithmetic
  43. Byte Offset
  44. Typed Array
  45. Address Of Buffer
  46. Assembly Butterfly
  47. Register Pressure
  48. Register Spilling
  49. Scratch Register
  50. Stage Parameter Block
  51. Python Assembly Boundary
  52. Work Split Strategy
  53. Assembly Debugging
  54. Bit For Bit Match
  55. Hot Loop

Optimization & Instruction Encoding (OPT) — 45 concepts

  1. Special Case Optimization
  2. Trivial Twiddle
  3. Multiply By One Shortcut
  4. Multiply By I Shortcut
  5. Branch Prediction
  6. Unpredictable Branch
  7. Branchless Code
  8. Precomputed Swap List
  9. Code Size Tradeoff
  10. Loop Overhead
  11. Address Computation Cost
  12. Optimization Attribution
  13. Heap Fragmentation
  14. Instruction Encoding
  15. Opcode
  16. Encoding Bit Field
  17. Encoding Table
  18. Halfword
  19. Thumb Instruction Set
  20. Thumb-2 Encoding
  21. Data Directive
  22. Raw Machine Word
  23. Fused Multiply Add
  24. Fused Rounding
  25. Assembler Limitation
  26. ISA Versus Toolchain
  27. Encoding Verification
  28. Instruction Reference Manual
  29. Variant Comparison
  30. Controlled Variable
  31. Comparison Matrix
  32. Ranking Prediction
  33. Optimization Composition
  34. Sub Linear Composition
  35. Integration Cost
  36. Kernel Versus Total Time
  37. Data Marshalling Cost
  38. Surprising Result
  39. 6-Way Variant Matrix
  40. Dual Core Processing
  41. Interleaved Layout Variant
  42. Fixed Point Q15 Arithmetic
  43. Instruction Encoding Error
  44. Calling Convention
  45. Stack Frame

Capstone, Experimental Design & Pedagogy (CAPS) — 35 concepts

  1. Experimental Design
  2. Research Question
  3. Independent Variable
  4. Dependent Variable
  5. Methodology Section
  6. Results Presentation
  7. Limitations Statement
  8. Conclusion Drawing
  9. Project Scoping
  10. Peer Review
  11. Hypothesis Statement
  12. Harness Noise Floor
  13. Capstone Track Selection
  14. Retrofitted Hypothesis Error
  15. Spectrogram Project
  16. DTMF Decoder Project
  17. Vibration Monitor Project
  18. Instrument Identifier Project
  19. Voice Activity Detector Project
  20. Bloom's Taxonomy
  21. Remember Level Outcome
  22. Understand Level Outcome
  23. Apply Level Outcome
  24. Analyze Level Outcome
  25. Evaluate Level Outcome
  26. Create Level Outcome
  27. Lab Demonstrated Outcome
  28. Engineered Productive Failure
  29. Predict Then Measure Pattern
  30. Optimistic Prediction Pattern
  31. Real Mistake As Teaching Tool
  32. Load Bearing Module
  33. 45-Minute Lab Format
  34. Self Paced Study Option
  35. Capstone Report

Course Logistics, Hardware Kit & Scope (KIT) — 25 concepts

  1. Raspberry Pi Pico 2
  2. Pico 2 W Variant
  3. Original Pico Incompatibility
  4. OLED Display Module
  5. Push Button Component
  6. INMP441 Microphone Module
  7. Breadboard
  8. Jumper Wire
  9. Hardware Kit Cost
  10. Software Toolchain
  11. No Compiler Required
  12. Non ARM Instruction Sets
  13. FPGA FFT Implementation
  14. ASIC FFT Implementation
  15. Multi Dimensional Transform
  16. Non Power Of Two Transform
  17. Filter Design Scope
  18. Midterm Assessment
  19. Laboratory Work Grading
  20. Homework And Quiz Grading
  21. Capstone Project Weight
  22. Final Exam Weight
  23. Grading Rubric
  24. Instructor's Guide
  25. Weekly Milestone Schedule