🔬 SignalLab

An interactive, offline-first Intelligent Tutoring System (ITS) and practice laboratory for university-level Analog Signal Processing & Linear Systems.

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✨ Overview

SignalLab provides undergraduate and graduate engineering students with an interactive, step-by-step practice environment for mastering continuous-time signals and systems. Designed around cognitive tutoring principles, SignalLab breaks complex signal processing problems into structured sub-steps, evaluates student inputs with exact symbolic math normalization, and delivers real-time diagnostic feedback.

Key Capabilities

• 🧩 Zero-Guesswork Step Solvers: Step-by-step problem workflows showing characteristic roots, differential trial ansatzes, systems of linear equations, and partial fraction expansions.
• 📐 Symbolic Math Normalization: Powered by @cortex-js/compute-engine with AST normalization tolerant of student shorthand, equivalent algebraic groupings, and fractional forms.
• 💡 Adaptive Diagnostic Feedback: Real-time syntax checking, multi-tiered hints, and step-specific error classification.
• 📊 Interactive Canvas Visualizers: Dynamic canvas plots for Fourier harmonic series synthesis and continuous-time signal analysis.
• 🔒 100% Client-Side & Private: Practice runs entirely in the browser with zero external telemetry or tracking, with PWA asset caching for offline use and theme preferences saved in localStorage when available. Solver sessions and practice history are not persisted across reloads.
• 📱 Fluid & Accessible: Fully accessible via keyboard (:focus-visible), with responsive layouts verified down to $320\text{px}$ viewports (WCAG 2.1 Reflow).

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📚 Practice Modules

Module	Core Topics & Capabilities	Route
Differential Equations	Characteristic equation roots, zero-input response ($y_{ZI}$), zero-state response ($y_{ZS}$), total response ($y_{\text{total}}$), and BIBO stability.	/odes
Continuous-Time Convolution	Graphical convolution, sliding window integration, interval partitioning, and composite piece-wise response computation.	/convolution
Fourier Series Representation	Trigonometric & compact exponential Fourier series, Dirichlet conditions, line spectra, and harmonic synthesis.	/fourier-series
Continuous-Time Fourier Transform	Forward and inverse CTFT, spectral density $\lvert X(j\omega) \rvert$, phase spectra, duality, modulation, and differentiation properties.	/fourier-transform
Laplace Transform & ROC	Unilateral/bilateral Laplace transforms, pole-zero constellations, Region of Convergence ($\text{ROC}$), and Partial Fraction Decomposition ($\text{PFD}$).	/laplace
Analog Circuit Analysis	$s$-domain impedance equivalence, nodal/mesh analysis, transfer function $H(s)$ derivation, and transient step/impulse responses.	/circuits

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📸 Visual Showcase

Fourier Series Analysis & Live Harmonic Synthesis	Second-Order ODE Response Solver

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🚀 Quickstart

Prerequisites

• Node.js 22.x from v22.22.1, or v24.12.0 and higher (24.x is recommended for the resolved dependencies).
• npm v10.0.0 or higher

Local Setup

# Clone the repository
git clone <repository-url>
cd "Analog Signal Processing Practice"

# Install dependencies
npm install

# Start development server
npm run dev

Open http://localhost:5173 in your browser to start practicing.

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GitHub Pages deployment

Configure Settings → Pages → Source → GitHub Actions once. Pushes to main and manual dispatch build with the Pages BASE_PATH, verify the artifact using npm run test:pages, and deploy only after verification passes. PR checks exercise both root and project hosting. See the Pages verification guide.

📖 Technical Documentation

• 🛠️ Development & Testing Guide — Contributor setup, dual-runtime Vitest architecture (ADR 0025), Playwright E2E suites, AST math testing, and formatting standards.
• 📐 Terminology & Mathematical Standards — Canonical signal processing symbols, operator conventions, and notation rules.
• 🏛️ Architectural Decision Records (ADRs) — Index of 33 ADRs recording foundational design, mathematical engine, and UI decisions.
• 🤖 Workspace Agent Rules — Development guidelines for LaTeX math formatting, component styling, and code quality.

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📄 License

This project is licensed for non-commercial educational use under the PolyForm Noncommercial License 1.0.0.