Taxonomy Distribution Report

Overview

• Total Concepts: 200
• Number of Taxonomies: 12
• Average Concepts per Taxonomy: 16.7

Distribution Summary

Category	TaxonomyID	Count	Percentage	Status
MATH	MATH	25	12.5%	✅
SIG	SIG	25	12.5%	✅
FILT	FILT	25	12.5%	✅
SYS	SYS	20	10.0%	✅
FOUR	FOUR	20	10.0%	✅
SAMP	SAMP	15	7.5%	✅
XFRM	XFRM	15	7.5%	✅
ADVN	ADVN	15	7.5%	✅
CONV	CONV	10	5.0%	✅
ADAP	ADAP	10	5.0%	✅
RAND	RAND	10	5.0%	✅
APPL	APPL	10	5.0%	✅

Visual Distribution

MATH   ██████  25 ( 12.5%)
SIG    ██████  25 ( 12.5%)
FILT   ██████  25 ( 12.5%)
SYS    █████  20 ( 10.0%)
FOUR   █████  20 ( 10.0%)
SAMP   ███  15 (  7.5%)
XFRM   ███  15 (  7.5%)
ADVN   ███  15 (  7.5%)
CONV   ██  10 (  5.0%)
ADAP   ██  10 (  5.0%)
RAND   ██  10 (  5.0%)
APPL   ██  10 (  5.0%)

Balance Analysis

✅ No Over-Represented Categories

All categories are under the 30% threshold. Good balance!

Category Details

MATH (MATH)

Count: 25 concepts (12.5%)

Concepts:

• 1. Real Numbers
• 1. Complex Numbers
• 1. Imaginary Unit
• 1. Euler's Formula
• 1. Phasors
• 1. Vectors
• 1. Matrices
• 1. Linear Algebra
• 1. Differential Calculus
• 1. Integral Calculus
• 1. Differential Equations
• 1. Partial Derivatives
• 1. Probability Theory
• 1. Random Variables
• 1. Statistical Distributions
• ...and 10 more

SIG (SIG)

Count: 25 concepts (12.5%)

Concepts:

• 1. Signals
• 1. Systems
• 1. Continuous-Time Signals
• 1. Discrete-Time Signals
• 1. Analog Signals
• 1. Digital Signals
• 1. Periodic Signals
• 1. Aperiodic Signals
• 1. Even Signals
• 1. Odd Signals
• 1. Energy Signals
• 1. Power Signals
• 1. Unit Step Function
• 1. Unit Impulse Function
• 1. Sinusoidal Signals
• ...and 10 more

FILT (FILT)

Count: 25 concepts (12.5%)

Concepts:

• 1. Filters
• 1. Low-Pass Filters
• 1. High-Pass Filters
• 1. Band-Pass Filters
• 1. Band-Stop Filters
• 1. Notch Filters
• 1. Comb Filters
• 1. All-Pass Filters
• 1. FIR Filters
• 1. IIR Filters
• 1. Filter Order
• 1. Filter Coefficients
• 1. Filter Stability
• 1. Filter Design Methods
• 1. Butterworth Filter
• ...and 10 more

SYS (SYS)

Count: 20 concepts (10.0%)

Concepts:

• 1. Linear Systems
• 1. Nonlinear Systems
• 1. Time-Invariant Systems
• 1. Time-Varying Systems
• 1. Causality
• 1. Non-Causal Systems
• 1. Stability
• 1. Unstable Systems
• 1. Memory Systems
• 1. Memoryless Systems
• 1. Invertible Systems
• 1. System Response
• 1. Impulse Response
• 1. Step Response
• 1. Frequency Response
• ...and 5 more

FOUR (FOUR)

Count: 20 concepts (10.0%)

Concepts:

• 1. Fourier Series
• 1. Fourier Coefficients
• 1. Fourier Transform
• 1. Inverse Fourier Transform
• 1. Discrete Fourier Transform
• 1. Inverse DFT
• 1. Fast Fourier Transform
• 1. FFT Algorithms
• 1. Radix-2 FFT
• 1. Cooley-Tukey Algorithm
• 1. Frequency Domain
• 1. Time Domain
• 1. Spectrum
• 1. Magnitude Spectrum
• 1. Phase Spectrum
• ...and 5 more

SAMP (SAMP)

Count: 15 concepts (7.5%)

Concepts:

• 1. Sampling
• 1. Sampling Rate
• 1. Sampling Theorem
• 1. Nyquist Rate
• 1. Nyquist Frequency
• 1. Aliasing
• 1. Anti-Aliasing Filter
• 1. Oversampling
• 1. Undersampling
• 1. Quantization
• 1. Quantization Error
• 1. Quantization Noise
• 1. Uniform Quantization
• 1. Non-Uniform Quantization
• 1. Signal Reconstruction

XFRM (XFRM)

Count: 15 concepts (7.5%)

Concepts:

• 1. Laplace Transform
• 1. Z-Transform
• 1. Inverse Z-Transform
• 1. Region of Convergence
• 1. Poles
• 1. Zeros
• 1. Pole-Zero Plot
• 1. Pole-Zero Analysis
• 1. S-Plane
• 1. Z-Plane
• 1. Discrete Cosine Transform
• 1. Wavelet Transform
• 1. Discrete Wavelet Transform
• 1. Continuous Wavelet Transform
• 1. Short-Time Fourier Transform

ADVN (ADVN)

Count: 15 concepts (7.5%)

Concepts:

• 1. Multirate Signal Processing
• 1. Decimation
• 1. Interpolation
• 1. Upsampling
• 1. Downsampling
• 1. Signal Compression
• 1. Lossy Compression
• 1. Lossless Compression
• 1. Transform Coding
• 1. Huffman Coding
• 1. Time-Frequency Analysis
• 1. Spectrogram
• 1. Wigner-Ville Distribution
• 1. Ambiguity Function
• 1. Compressed Sensing

CONV (CONV)

Count: 10 concepts (5.0%)

Concepts:

• 1. Convolution
• 1. Discrete Convolution
• 1. Circular Convolution
• 1. Convolution Theorem
• 1. Correlation
• 1. Autocorrelation
• 1. Cross-Correlation
• 1. Correlation Coefficient
• 1. Matched Filter
• 1. Wiener Filter

ADAP (ADAP)

Count: 10 concepts (5.0%)

Concepts:

• 1. Adaptive Filters
• 1. Adaptive Algorithms
• 1. Least Mean Squares
• 1. Normalized LMS
• 1. Recursive Least Squares
• 1. Kalman Filter
• 1. Adaptive Noise Cancellation
• 1. Echo Cancellation
• 1. Adaptive Equalization
• 1. System Identification

RAND (RAND)

Count: 10 concepts (5.0%)

Concepts:

• 1. Random Processes
• 1. Stochastic Signals
• 1. White Noise
• 1. Colored Noise
• 1. Gaussian Noise
• 1. Signal-to-Noise Ratio
• 1. Noise Reduction
• 1. Statistical Signal Processing
• 1. Power Spectral Density
• 1. Wiener-Khinchin Theorem

APPL (APPL)

Count: 10 concepts (5.0%)

Concepts:

• 1. Digital Signal Processors
• 1. FPGA Implementation
• 1. Real-Time Processing
• 1. Audio Signal Processing
• 1. Image Processing
• 1. Video Processing
• 1. Machine Learning in DSP
• 1. Convolutional Neural Networks
• 1. Deep Learning for Signals
• 1. AI-Driven Signal Analysis

Recommendations

• ✅ Excellent balance: Categories are evenly distributed (spread: 7.5%)
• ✅ MISC category minimal: Good categorization specificity

Educational Use Recommendations

• Use taxonomy categories for color-coding in graph visualizations
• Design curriculum modules based on taxonomy groupings
• Create filtered views for focused learning paths
• Use categories for assessment organization
• Enable navigation by topic area in interactive tools

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Report generated by learning-graph-reports/taxonomy_distribution.py