🔬 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: PWA with IndexedDB persistence—runs entirely in the browser with zero external telemetry, tracking, or network dependencies.
• 📱 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 v20.0.0 or higher
• 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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📖 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.