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shannon-hartley.js

/**
 * Shannon-Hartley Theorem: Channel Capacity Calculator
 * 
 * Formula: C = B * log2(1 + SNR)
 * 
 * Where:
 *  - C   = Channel Capacity (bits per second)
 *  - B   = Bandwidth (Hz)
 *  - SNR = Signal-to-Noise Ratio (linear)
 */

function dbToLinear(db) {
  return 10 ** (db / 10);
}

function calculateCapacity(bandwidthHz, snrdB) {
  const snrLinear = dbToLinear(snrdB);
  const capacityBps = bandwidthHz * Math.log2(1 + snrLinear);
  return {
    bps: capacityBps,
    kbps: capacityBps / 1000,
    bytesPerSec: capacityBps / 8
  };
}

// ----------------------------------------------------
// Acoustic Link Simulation (e.g. 2 kHz to 12 kHz)
// ----------------------------------------------------
const BANDWIDTH = 10000; // 10 kHz
const SNR_DB = 30;       // 30 dB (typical quiet room)

const capacity = calculateCapacity(BANDWIDTH, SNR_DB);

console.log(`=== Shannon-Hartley Theorem ===`);
console.log(`Bandwidth:   ${(BANDWIDTH / 1000).toFixed(1)} kHz`);
console.log(`SNR:         ${SNR_DB} dB (Linear ratio: ${dbToLinear(SNR_DB).toFixed(0)}:1)`);
console.log(`Capacity:    ${capacity.kbps.toFixed(2)} kbps (${capacity.bytesPerSec.toFixed(0)} B/s)`);

console.log('\nCapacity at different SNR levels:');
console.log('SNR (dB)  | Ratio    | Capacity (kbps)');
console.log('----------+----------+----------------');
[0, 10, 20, 30, 40, 50].forEach(db => {
  const ratio = dbToLinear(db);
  const cap = calculateCapacity(BANDWIDTH, db);
  const dbStr = `${db} dB`.padEnd(9);
  const ratioStr = `${ratio.toFixed(0)}:1`.padEnd(9);
  console.log(`${dbStr} | ${ratioStr} | ${cap.kbps.toFixed(2)} kbps`);
});