Concept Taxonomy
This document defines the categorical taxonomy for organizing the 200 signal processing concepts into 12 logical groups.
Taxonomy Categories
MATH - Mathematical Foundations
TaxonomyID: MATH
Core mathematical concepts that form the foundation for signal processing, including: - Real and complex numbers - Calculus (differential and integral) - Linear algebra (vectors, matrices, eigenvalues) - Probability and statistics - Trigonometry and special functions
Target Distribution: ~15-20 concepts
SIG - Signal Fundamentals
TaxonomyID: SIG
Basic signal types, properties, and characteristics, including: - Signal classifications (continuous/discrete, analog/digital, periodic/aperiodic) - Signal properties (energy, power, amplitude, frequency, phase) - Basic signal operations and transformations
Target Distribution: ~20-25 concepts
SYS - System Properties
TaxonomyID: SYS
System characteristics and behaviors, including: - Linear/nonlinear, time-invariant/time-varying systems - Causality, stability, memory properties - System responses and interconnections - Transfer functions and system identification
Target Distribution: ~15-20 concepts
CONV - Convolution and Correlation
TaxonomyID: CONV
Convolution operations and correlation analysis, including: - Continuous and discrete convolution - Circular convolution and convolution theorems - Autocorrelation and cross-correlation - Matched and Wiener filters
Target Distribution: ~8-10 concepts
SAMP - Sampling and Quantization
TaxonomyID: SAMP
Analog-to-digital conversion concepts, including: - Sampling theory and Nyquist criteria - Aliasing and anti-aliasing - Quantization methods and errors - Signal reconstruction
Target Distribution: ~12-15 concepts
FOUR - Fourier Analysis
TaxonomyID: FOUR
Fourier-based frequency analysis techniques, including: - Fourier series and transforms - DFT and FFT algorithms - Frequency/time domain representations - Spectral analysis and windowing
Target Distribution: ~20-25 concepts
XFRM - Advanced Transforms
TaxonomyID: XFRM
Transform methods beyond basic Fourier, including: - Laplace and Z-transforms - Pole-zero analysis - Wavelet transforms - Time-frequency analysis methods
Target Distribution: ~15-18 concepts
FILT - Filter Design
TaxonomyID: FILT
Filter types, design methods, and implementation, including: - Filter classifications (low-pass, high-pass, band-pass, etc.) - FIR and IIR filter design - Classical filter approximations (Butterworth, Chebyshev, etc.) - Multirate and polyphase filters
Target Distribution: ~25-30 concepts
ADAP - Adaptive Processing
TaxonomyID: ADAP
Adaptive signal processing techniques, including: - Adaptive filter algorithms (LMS, RLS, Kalman) - Adaptive applications (noise cancellation, equalization) - System identification methods
Target Distribution: ~10-12 concepts
RAND - Stochastic Processes
TaxonomyID: RAND
Random signal analysis and statistical signal processing, including: - Random processes and stochastic signals - Noise types and characteristics - Power spectral density - Statistical signal processing methods
Target Distribution: ~10-12 concepts
ADVN - Advanced Topics
TaxonomyID: ADVN
Multirate processing, compression, and time-frequency analysis, including: - Decimation, interpolation, upsampling, downsampling - Signal compression and coding - Spectrograms and advanced time-frequency methods - Compressed sensing
Target Distribution: ~15-18 concepts
APPL - Applications and AI
TaxonomyID: APPL
Practical applications and modern AI integration, including: - Digital signal processors and FPGA implementation - Audio, image, and video processing - Machine learning and deep learning for signals - AI-driven signal analysis
Target Distribution: ~10-12 concepts
Category Summary
| TaxonomyID | Category Name | Description | Target Count |
|---|---|---|---|
| MATH | Mathematical Foundations | Core math prerequisites | 15-20 |
| SIG | Signal Fundamentals | Basic signal types and properties | 20-25 |
| SYS | System Properties | System characteristics and behaviors | 15-20 |
| CONV | Convolution and Correlation | Convolution operations and correlation | 8-10 |
| SAMP | Sampling and Quantization | ADC and sampling theory | 12-15 |
| FOUR | Fourier Analysis | Frequency domain analysis | 20-25 |
| XFRM | Advanced Transforms | Laplace, Z, wavelet transforms | 15-18 |
| FILT | Filter Design | Filter types and design methods | 25-30 |
| ADAP | Adaptive Processing | Adaptive algorithms and applications | 10-12 |
| RAND | Stochastic Processes | Random signals and noise | 10-12 |
| ADVN | Advanced Topics | Multirate, compression, TF analysis | 15-18 |
| APPL | Applications and AI | Practical applications and ML/AI | 10-12 |
Total Categories: 12 Total Concepts: 200
This taxonomy provides balanced distribution across signal processing domains while maintaining logical groupings that support the course structure.