⚡ ADC Resolution, Noise & Oversampling — Signal Processing Lab

Quatumn Hackathon · Track #4 · Problem Statement #19

A complete, browser-based digital laboratory for studying Analog-to-Digital Conversion, quantization noise, and oversampling.
Record real signals, run controlled experiments, visualise the physics, and export a full lab report — no installation required.

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🌐 Live Website

🔗 https://vertiam.github.io/adc-simulator/

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📽️ Video Demo

🔗 Click This Link to Watch the video demo!!

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Page	URL	Description
🏠 Landing Page	/index.html	Project overview, theory cards, experiment guide
🔬 Lab Environment	/lab.html	Full 5-step guided experiment

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📋 Table of Contents

• Evaluation Criteria Alignment
• What This Project Does
• Problem Statement
• Technologies Used
• Lab Workflow — All 5 Steps
• Core Concepts
• The Algorithm
• Visualization Features
• Chart Interaction Tools
• How to Use
• Real-World Applications
• Project File Structure
• Key Formulas Reference
• Team

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🎯 Evaluation Criteria Alignment

Criterion	How This Project Meets It
Physical / System Correctness	Midtread uniform quantization matches the IEEE standard ADC model. SNR formula 6.02n + 1.76 dB is the exact closed-form theoretical result. Oversampling gain 10·log₁₀(M) is derived from noise power spectral density. FFT uses Cooley-Tukey radix-2 DIT with Hanning windowing — standard DSP practice. All formulas are textbook-accurate.
Visualization Quality	4 live interactive charts: waveform, error signal, SNR curve, FFT spectrum. Staircase fill shows error area even at high bit depths. Quantization level grid lines visible at ≤7 bits. Zoom, pan, markers, comparison snapshots, and text annotations on every chart. Dark/light mode. PNG export.
Conceptual Clarity	Every technical term has a plain-English hover tooltip. Step-by-step guided lab workflow. Pre-filled theory notebook with derivations. Real-world application examples. Designed so a student with zero prior knowledge can complete the full experiment and understand ADC principles end-to-end.

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🎯 What This Project Does

This project models every stage of the ADC pipeline:

Real Signal → Sampling → Quantization → Error Measurement → Oversampling → SNR & FFT Analysis

Students interact with this pipeline through a guided 5-step lab session, recording readings, writing observations, and generating a complete exportable report.

Core deliverables from the problem statement:

Required Outcome	Implementation
Model ADCs with different bit resolutions	2-bit to 16-bit slider, live waveform update
Visualize quantization noise	Error chart + orange fill + FFT spectrum
Demonstrate noise reduction via oversampling	1× to 64× slider, live SNR update
Quantized signal plots	Waveform chart with stepped quantized line
SNR vs ADC resolution graphs	SNR curve chart with operating point dot

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🔍 Problem Statement

Problem Statement #19:

Analog-to-digital conversion introduces quantization noise. Simulate ADC digitization effects and study how oversampling improves signal quality.

• ✅ Model ADCs with different bit resolutions (2–16 bit)
• ✅ Visualize quantization noise (error chart + FFT)
• ✅ Demonstrate noise reduction using oversampling (1× to 64×)
• ✅ Quantization, ADC resolution, oversampling, noise averaging — all implemented and visualized

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🛠 Technologies Used

Technology	Role	Why Chosen
HTML5	Page structure	No framework overhead, works offline
CSS3 + Variables	Shared design system	Single style.css; dark/light via class toggle
JavaScript ES6+	All simulation logic	In-browser, zero-latency slider response
Web Audio API	Microphone recording	Native PCM capture, no libraries
MediaRecorder API	Audio stream capture	Standard across all modern browsers
Chart.js v4.4.1	4 live interactive charts	Fastest JS charting library for real-time data
chartjs-plugin-zoom	Zoom & pan	Built on Hammer.js touch gestures
Custom FFT (JS)	Frequency spectrum	Cooley-Tukey radix-2 DIT, O(N log N)
localStorage	Auto-save student data	No backend required
GitHub Pages	Free HTTPS hosting	getUserMedia requires HTTPS

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🔬 Lab Workflow — All 5 Steps

Step 1 — Student Setup

Required fields (name, reg number, dept, date) with shake-animation validation and live green/red border feedback. Auto-saves to localStorage every 10 seconds. All fields populate the final report.

Step 2 — Signal Source

🎤 Microphone — getUserMedia() → MediaRecorder → WebM blob → decodeAudioData() → Float32Array PCM → normalized to [-1, +1]. Live waveform via AnalyserNode.

⚡ Generator — Sine, Square, Sawtooth, Chirp. Configurable frequency and amplitude.

📂 CSV Upload — Drag-and-drop, single-column or time,value format, linear interpolation resample to 250 points.

Step 3 — Run Experiments

Four live charts, all interactive:

1. Waveform — Original vs Quantized with staircase fill and level grid lines
2. Quantization Error — The noise signal; RMS error shown live
3. SNR vs Bit Depth — Theoretical curve + orange dot at current settings
4. FFT Spectrum — Cooley-Tukey FFT of the error signal; shows noise spectral distribution

Controls: Bit Depth (2–16 bit) · Oversampling (1×–64×) · Noise Floor (0–30%).

Record This Reading logs current settings (bits, OS rate, SNR, ENOB, RMS) to a data table.

Step 4 — Lab Notebook

Aim, Apparatus, Theory, Observations, Analysis, Conclusion — all editable, auto-saved.

Step 5 — Report

Auto-assembled from all previous steps. Print with @media print CSS, or export full CSV.

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📚 Core Concepts

1. Analog vs Digital

Real-world signals are continuous. Computers store only discrete numbers. The ADC bridges this gap.

2. Bit Depth & Quantization Levels

Levels = 2ⁿ          Step = 2 / 2ⁿ    (in [-1, +1] range)

Bits	Levels	Typical Use
4	16	Illustration
8	256	Telephony
12	4,096	Sensors, IoT
16	65,536	CD audio
24	16,777,216	Studio recording

3. Quantization Noise

Q[i]    = round(x[i] / step) × step
error   = Q[i] - x[i]   ∈ [-step/2, +step/2]
RMS     = step / √12

4. Signal-to-Noise Ratio

SNR = 6.02n + 1.76 + 10·log₁₀(osRate)   dB

Every bit adds ~6 dB. Every 4× oversampling adds another ~6 dB.

5. Oversampling

Sample M times faster, average groups of M. Noise variance drops by M, amplitude by √M.

Golden Rule:  4× oversampling = +1 bit = +6 dB SNR
ENOB = n + log₂(M) / 2

6. FFT Spectral Analysis

Quantization noise is ideally white (flat spectrum). The FFT chart shows this. Oversampling lowers the noise floor uniformly across all frequency bins.

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🧮 The Algorithm

Midtread Uniform Quantization

step  = 2 / Math.pow(2, bits)          // one level's width
Q[i]  = Math.round(x[i] / step) * step // snap to nearest level

This is the IEEE-standard ADC model. Rounding error is uniformly distributed in [-step/2, +step/2].

Oversampling + Decimation

// Generate N × osRate super-samples → quantize each → average groups
for (let i = 0; i < N; i++) {
  let sum = 0;
  for (let j = 0; j < osRate; j++) sum += Q_super[i * osRate + j];
  output[i] = sum / osRate;
}

Statistical independence of rounding errors means averaging M values reduces noise variance by M.

Cooley-Tukey FFT

Algorithm:   Radix-2 DIT with bit-reversal permutation
Complexity:  O(N log N) vs O(N²) naive DFT
Window:      Hanning  w[i] = 0.5 × (1 - cos(2πi/N))
Input:       Quantization error signal
Output:      Power spectrum, first N/2 bins

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📊 Visualization Features

Chart	What It Shows	Evaluation Criterion Met
Waveform	Smooth blue original vs stepped orange quantized + fill + level grid	Physical correctness + Visualization quality
Error Signal	Raw quantization noise at each sample point	Visualization quality + Conceptual clarity
SNR Curve	Theoretical 6.02n + 1.76 dB plotted against current operating point	Physical correctness
FFT Spectrum	Noise power distribution across frequency bins (Hanning-windowed)	Physical correctness + Visualization quality

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🔧 Chart Interaction Tools

Button	Function
+ / −	Zoom in/out (also mouse wheel, pinch)
⊙	Reset zoom
📍	Place marker — wave markers sync automatically to error chart
✏️	Add text annotation — click chart, type label
⊞	Snapshot comparison — freeze current state as purple overlay
↓	Download PNG (respects dark/light mode)
Theme toggle	Dark ↔ Light mode, saved to localStorage

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🚀 How to Use

# Hosted: just visit the URL
https://vertiam.github.io/adc-simulator/

# Local (mic needs HTTPS or localhost):
python -m http.server 8000
# open http://localhost:8000

Suggested experiment sequence:

1. Set Bit Depth = 4-bit → Record
2. Set Bit Depth = 8-bit → Record
3. Set Bit Depth = 12-bit → Record  (observe SNR jump)
4. Set Oversampling = 4× → Record   (observe noise floor in FFT)
5. Set Oversampling = 16× → Record
6. Use ⊞ to snapshot 4-bit, switch to 12-bit → direct visual comparison
7. Place marker at a peak → observe it synced to error chart
8. Export lab report

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🌍 Real-World Applications

Domain	ADC Impact
🎵 Music	CD = 16-bit 44.1 kHz · Studio = 24-bit 96 kHz
🏥 Medical	ECG, MRI, pulse oximeters — noisy ADC = wrong diagnosis
📱 Smartphones	Every mic, camera sensor, and touchscreen uses an ADC
🛰 Telecom	5G radio front-ends — ADC limits channel capacity
🌡 IoT	Temperature, pressure sensors — bit depth = precision
🔬 Science	Oscilloscopes — limited by ADC resolution

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📁 Project File Structure

adc-simulator/
├── index.html              ← Landing page
├── lab.html                ← Full lab (2083 lines)
│   ├── 4 chart system      waveform, error, SNR, FFT
│   ├── Marker system       wave→error sync
│   ├── Comparison mode     snapshot overlay
│   ├── Text annotations    click-to-place labels
│   ├── FFT engine          Cooley-Tukey + Hanning
│   └── Theme toggle        dark/light + localStorage
├── style.css               ← Shared design system
├── csv_data_generator.py   ← Python test data generator
└── README.md               ← This file

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🔑 Key Formulas

Levels     = 2ⁿ
Step       = 2 / 2ⁿ
RMS noise  = step / √12
SNR (ideal)= 6.02n + 1.76  dB
SNR (OS)   = 6.02n + 1.76 + 10·log₁₀(M)  dB
ENOB       = n + log₂(M) / 2
Nyquist    : f_s ≥ 2 × f_max
FFT        : O(N log N),  Hanning window

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👥 Team

Team Name: Qt π's · Quatumn Hackathon · Problem Statement #19 · Mechanical Engineering

Role	Name	Reg. No.
Team Leader	Swayam Viral Marfatia	RA2511002010080
Member	Narayan Murthy	RA2511002010124
Member	Shirly Oviya	RA2511054010030
Member	Mithasha P Sishaj	RA2511053050040

"The goal is to turn invisible noise into something you can see, drag a slider, and understand." — Qt π's