Learning Graph for Signal Processing

Welcome to the learning graph section for Introduction to Signal Processing with AI. This section contains a comprehensive knowledge graph of 200 concepts that map the learning dependencies and structure of this course.

What is a Learning Graph?

A learning graph is a directed acyclic graph (DAG) that represents:

• Concepts: The key topics and ideas in the course (nodes)
• Dependencies: Prerequisites relationships between concepts (edges)
• Taxonomies: Categorical groupings for organizing concepts
• Learning Paths: Multiple routes through the material based on your goals

Course Learning Graph

This learning graph contains:

• 200 Concepts organized into 12 taxonomies
• 262 Dependency Relationships showing prerequisite connections
• 12 Concept Categories for logical organization
• Quality Score: 75/100 - Valid DAG with good structure

Files in this Section

Core Learning Graph Files

• learning-graph.json - Complete learning graph in vis-network.js JSON format
• learning-graph.csv - Tabular format with ConceptID, Label, Dependencies, and TaxonomyID

Documentation and Reports

• concept-list.md - Numbered list of all 200 concepts
• concept-taxonomy.md - Definitions of the 12 taxonomic categories
• course-description-assessment.md - Quality assessment (Score: 93/100)
• quality-metrics.md - Graph structure analysis and validation
• taxonomy-distribution.md - Distribution analysis across categories

Configuration Files

• metadata.json - Course metadata (Dublin Core fields)
• taxonomy-config.json - Color scheme and category names

The 12 Taxonomies

TaxonomyID	Category	Concepts	Percentage
MATH	Mathematical Foundations	25	12.5%
SIG	Signal Fundamentals	25	12.5%
FILT	Filter Design	25	12.5%
SYS	System Properties	20	10.0%
FOUR	Fourier Analysis	20	10.0%
SAMP	Sampling and Quantization	15	7.5%
XFRM	Advanced Transforms	15	7.5%
ADVN	Advanced Topics	15	7.5%
CONV	Convolution and Correlation	10	5.0%
ADAP	Adaptive Processing	10	5.0%
RAND	Stochastic Processes	10	5.0%
APPL	Applications and AI	10	5.0%

Key Metrics

Foundational Concepts

There is 1 foundational concept with no prerequisites:

• Real Numbers - The starting point for all mathematical concepts

Most Important Concepts

Top 10 concepts by number of dependent concepts:

1. Signals (28 dependencies) - Core concept for signal types
2. Filters (19 dependencies) - Essential for signal processing
3. Systems (19 dependencies) - Foundation for system analysis
4. Real Numbers (13 dependencies) - Mathematical foundation
5. Fourier Transform (8 dependencies) - Key frequency analysis tool
6. Discrete-Time Signals (7 dependencies) - Digital signal foundation
7. Z-Transform (6 dependencies) - Discrete system analysis
8. Discrete Fourier Transform (6 dependencies) - Practical frequency analysis
9. Quantization (6 dependencies) - ADC foundation
10. Sampling Rate (6 dependencies) - Digital signal theory

Dependency Chain

The maximum dependency chain length is 11 concepts, meaning the deepest learning path requires mastering 11 sequential concepts.

Using the Learning Graph

For Students

• Identify Prerequisites: See what concepts you need to learn before tackling advanced topics
• Find Learning Paths: Discover multiple routes through the material
• Track Progress: Mark concepts as you master them
• Understand Connections: See how concepts relate to each other

For Instructors

• Course Planning: Design curriculum based on concept dependencies
• Assessment Design: Create tests that respect prerequisite relationships
• Personalized Learning: Adapt content to student backgrounds
• Gap Analysis: Identify missing prerequisites for struggling students

Interactive Visualization

To explore the learning graph interactively:

1. Open the Graph Viewer (if available)
2. Load learning-graph.json
3. Filter by taxonomy to focus on specific topic areas
4. Search for concepts by name
5. Visualize dependency paths

Quality Assessment

Course Description Quality: 93/100 - Excellent

• Complete Bloom's Taxonomy coverage (all 6 levels)
• 50 well-defined topics
• Clear prerequisites and boundaries
• Sufficient depth for 200+ concepts

Learning Graph Quality: 75/100 - Acceptable

• ✅ Valid DAG (no cycles)
• ✅ Balanced taxonomy distribution
• ✅ Meaningful dependency relationships
• ⚠️ 112 orphaned nodes (concepts that lead to no higher concepts)
• ⚠️ Low average dependencies (1.31) - graph could be more interconnected

Generation Process

This learning graph was generated using AI assistance through the following steps:

1. Course Description Analysis - Assessed completeness and quality
2. Concept Enumeration - Generated 200 pedagogically sound concepts
3. Dependency Mapping - Created prerequisite relationships
4. Quality Validation - Verified DAG structure and metrics
5. Taxonomy Creation - Organized into 12 balanced categories
6. JSON Generation - Created vis-network.js compatible format

Next Steps

Recommended Improvements

1. Add More Cross-Dependencies: Connect orphaned concepts to advanced applications
2. Create Learning Modules: Group related concepts into teachable units
3. Add Concept Descriptions: Provide detailed definitions for each concept
4. Create Assessment Items: Map quiz questions to specific concepts
5. Build Interactive Viewer: Enable graph exploration and filtering

Integration with Course Materials

• Link concepts to chapter sections
• Create concept-specific MicroSims
• Add glossary terms for each concept
• Map learning objectives to concept clusters
• Create pre-assessment based on foundational concepts

License

This learning graph is licensed under CC BY-NC-SA 4.0 DEED (Creative Commons Attribution-NonCommercial-ShareAlike 4.0).

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Generated: 2025-11-13 Version: 1.0 Course: Introduction to Signal Processing with AI