Sampling Rate Calculator
Min sampling rate (Hz)
20000
How it works
Sampling rate (or sample rate) is the number of samples taken per second from an analog signal for digital conversion, measured in Hz or samples/second. It determines the highest frequency that can be represented in the digital signal.
**Nyquist-Shannon theorem** The sampling theorem states: a signal can be perfectly reconstructed from its samples if the sampling rate is greater than twice the highest frequency component: f_s > 2 × f_max. The minimum required sampling rate is the Nyquist rate (2 × f_max). The highest representable frequency at a given sample rate is f_max = f_s / 2 (Nyquist frequency).
**Common sampling rates** Telephone audio: 8 kHz (adequate for voice up to 4 kHz). CD audio: 44.1 kHz (covers 20 Hz–20 kHz audible range). Professional audio: 48 kHz (broadcast standard), 96 kHz, 192 kHz. ECG: 250–1000 Hz (cardiac signals < 100 Hz). EEG: 256–512 Hz. Vibration monitoring: 10–100 kHz depending on frequencies of interest.
**Anti-aliasing filters** Before sampling, an analog low-pass filter must remove all frequency components above f_s/2. Without this, high-frequency components fold back (alias) into the baseband — for example, a 5 kHz signal sampled at 8 kHz appears as a 3 kHz artifact. Anti-aliasing filters are the most critical component in ADC front-end design.
**Oversampling and noise shaping** Sampling at a higher rate than necessary (oversampling) spreads quantization noise across a wider bandwidth — averaging or filtering reduces noise in the band of interest. Delta-sigma ADCs oversample massively (e.g., 64× or 256×) and use noise shaping to achieve 24-bit effective resolution from 1-bit conversion.
Frequently Asked Questions
- 44.1 kHz was chosen for practical reasons: early CD development relied on video tape recorders (VTRs) to store digital audio before dedicated media existed. NTSC video has 245 lines × 3 samples/line × 60 fields/s = 44,100 samples/s. This rate covers the full audible range (up to 20 kHz) with margin. The choice was also partly historical accident — Sony and Philips converged on this rate during CD standardization. 48 kHz is the professional broadcast standard (chosen later, providing more margin above 20 kHz and aligning with video frame rates in digital broadcasting).
- Sample rate conversion (SRC) is required. Without SRC: playing a 48 kHz file at 44.1 kHz sample rate plays back 8.5% slower and lower pitched (44.1/48 = 0.919). With SRC: a digital filter interpolates new sample values between existing samples (upsampling or downsampling), changing the effective sample rate while preserving pitch and speed. Quality of SRC varies enormously: simple linear interpolation causes aliasing; polyphase FIR filters achieve transparent conversion. DAW software and professional interfaces include high-quality SRC. The 44.1 kHz ↔ 48 kHz conversion is particularly challenging because 44.1 = 441 × 100 and 48,000 = 480 × 100 — a 147:160 ratio requiring a very long filter.
- Claimed benefits: headroom for processing (filtering and pitch shifting avoid fold-back artifacts), ultrasonic content captured for mixing (though audibility is disputed), and higher Nyquist (96 kHz at 192 kHz sample rate) means anti-aliasing filters can have gentler slopes — less phase distortion in the audible range. Practical reality: blind listening tests consistently fail to show audible benefit of >48 kHz. The main concrete benefit is processing headroom — during heavy DSP (convolution reverb, heavy EQ), artifacts accumulate less at higher sample rates. Down-sample to 44.1 or 48 kHz for final release.
- Quantization noise power is spread across 0 to f_Nyquist. Oversampling by factor OSR spreads the same noise across a wider bandwidth: noise in audio band = total noise / √OSR. Each doubling of sample rate gains 3 dB SNR improvement = 0.5 bits of effective resolution. Delta-sigma ADCs oversample at 64×–512× and use noise shaping to push quantization noise to high frequencies, then apply a digital low-pass filter to remove it. This achieves 24-bit effective resolution from a 1-bit comparator — noise shaping plus oversampling. A 192 kHz ADC oversampled at 4× compared to 48 kHz gives 6 dB (1 bit) of theoretical improvement in the audio band.