# Difference Equation Analyzer (DEA) - Architecture & Functionality

## Overview
DEA is a specialized tool for designing, visualizing, and validating discrete-time filters. It bridges the gap between theoretical filter design (floating-point) and hardware implementation (fixed-point/MCU).

## 🏗 System Architecture

### 1. Backend (Python 3.12 + FastAPI)
The backend is responsible for heavy mathematical computations and data processing.

- **API Entry (`dea_api.py`)**: Routes requests to appropriate modules and serves the Vue.js frontend from `static/`.
- **Computation Engine (`dea/`)**:
    - `filter_design.py`: Uses `scipy.signal` to calculate coefficients for various filter topologies.
    - `bode.py`: Computes magnitude and phase response. Supports comparing "Ideal" (float) vs "Fixed" (quantized) responses.
    - `csv_processing.py`: Processes time-domain CSV data. It applies the current filter to the signal and downsamples the result for efficient visualization.
    - `validation.py`: Protects against unstable filter designs and invalid inputs.

### 2. Frontend (Vue 3 + Vite + Tailwind)
A reactive "Single Page Application" (SPA) approach.

- **Reactive Logic (`src/app-options.js`)**:
    - Manages the state of all coefficients.
    - Implements "Fine-tuning" sliders that allow real-time adjustment of poles/zeros.
    - Handles Fixed-Point conversion logic (Q-format shifting).
- **UI Components (`src/App.vue`)**:
    - **Control Sidebar**: Interactive inputs for all filter parameters.
    - **Visualization**: Dual-plot system using Plotly.js for Bode plots and Time-domain waveforms.
- **Hardware Bridge**: Uses the **Web Serial API** to send commands directly to connected MCUs (requires HTTPS).

## 🚀 Execution Flow
1. **Design**: User selects a filter type or enters coefficients manually.
2. **Quantize**: User adjusts Q-format bits to see how quantization affects the frequency response.
3. **Verify**: User uploads a CSV to see how the filter behaves with real-world signals.
4. **Deploy**: User clicks "Write to MCU" to send the coefficients to their hardware.

## 🛠 Tech Stack
- **Backend**: FastAPI, NumPy, SciPy, Pandas, Uvicorn.
- **Frontend**: Vue 3, Vite, Tailwind CSS, Plotly.js.
- **Security**: Restricted to LAN/Loopback; implemented security headers and HTTPS support.