Sampling Rate Calculation

Digital Sampling Rate Calculator

The highest frequency component in your analog signal (e.g., 20,000 Hz for human hearing).

The rate at which samples are captured (Common: 44100, 48000, 96000).

8-bit 16-bit (CD Quality) 24-bit (High Res) 32-bit (Floating Point)

Mono (1) Stereo (2) 5.1 Surround (6)

Calculation Results

Nyquist Frequency:

Nyquist Rate (Min Required):

Aliasing Risk:

Total Bitrate:

Uncompressed File Size:

function calculateSampling() { var maxFreq = parseFloat(document.getElementById('maxFrequency').value); var sampleRate = parseFloat(document.getElementById('samplingRate').value); var bitDepth = parseFloat(document.getElementById('bitDepth').value); var channelVal = document.getElementById('channels').value; var channels = (channelVal === "5.1") ? 6 : parseFloat(channelVal); var duration = parseFloat(document.getElementById('duration').value); if (isNaN(maxFreq) || isNaN(sampleRate) || isNaN(duration)) { alert("Please enter valid numerical values."); return; } // 1. Nyquist Math var nyquistFreq = sampleRate / 2; var minRequiredRate = maxFreq * 2; // 2. Bitrate: Rate * BitDepth * Channels var bitrateBps = sampleRate * bitDepth * channels; var bitrateKbps = bitrateBps / 1000; // 3. File Size: (Bitrate * Time) / 8 (for bytes) var totalBits = bitrateBps * duration; var totalBytes = totalBits / 8; var sizeMB = totalBytes / (1024 * 1024); // UI Updates document.getElementById('nyquistFreq').innerText = nyquistFreq.toLocaleString() + " Hz"; document.getElementById('nyquistRate').innerText = minRequiredRate.toLocaleString() + " Hz"; var statusEl = document.getElementById('aliasingStatus'); if (sampleRate < minRequiredRate) { statusEl.innerText = "HIGH (Aliasing will occur)"; statusEl.style.color = "#dc3545"; } else { statusEl.innerText = "LOW (Safe Sampling)"; statusEl.style.color = "#28a745"; } document.getElementById('bitrateResult').innerText = bitrateKbps.toLocaleString() + " kbps"; document.getElementById('fileSizeResult').innerText = sizeMB.toFixed(2) + " MB"; document.getElementById('resultsArea').style.display = "block"; }

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Understanding Sampling Rate and the Nyquist Theorem

In digital signal processing and audio engineering, the sampling rate (or sampling frequency) defines how many times per second an analog signal is measured to convert it into a digital format. This process is the foundation of everything from professional music production to VoIP calls and medical imaging.

The Nyquist-Shannon Sampling Theorem

The core principle governing digital audio is the Nyquist-Shannon theorem. It states that to accurately reconstruct an analog signal, the sampling rate must be at least double the highest frequency contained within the signal.

• The Nyquist Rate: The minimum sampling frequency ($2 \times f_{max}$).
• The Nyquist Frequency: Half of the actual sampling rate ($f_s / 2$). This represents the highest frequency a digital system can accurately record.

If you attempt to record a signal frequency that exceeds the Nyquist frequency, a phenomenon called aliasing occurs. This introduces artificial, low-frequency distortions into the recording that were not present in the original source.

Calculating Bitrate and Data Requirements

Beyond the sampling rate, the quality and size of a digital file are determined by the Bit Depth and the number of Channels. The formula for the bitrate of uncompressed pulse-code modulation (PCM) audio is:

Bitrate = Sampling Rate (Hz) × Bit Depth (bits) × Number of Channels

Common Real-World Examples

Standard	Sample Rate	Bit Depth	Typical Use
CD Audio	44.1 kHz	16-bit	Consumer Music
DVD/Film	48 kHz	24-bit	Professional Video
High-Res Audio	96/192 kHz	24-bit	Studio Mastering
Telephony	8 kHz	8-bit	Voice Communication

Why choose 44.1 kHz?

The standard 44.1 kHz sampling rate for CDs was chosen because the upper limit of human hearing is roughly 20,000 Hz (20 kHz). According to Nyquist, we need at least 40 kHz to capture this. The extra 4.1 kHz allows for "roll-off" filters that prevent aliasing without affecting the audible frequencies.