Sampling rate
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The sampling rate, sample rate, or sampling frequency defines the number of samples per second (or per other unit) taken from a continuous signal to make a discrete signal. For time-domain signals, it can be measured in hertz (Hz). The inverse of the sampling frequency is the sampling period or sampling interval, which is the time between samples.
The concept of sampling frequency can only be applied to samplers in which samples are taken periodically. Some samplers may sample at a non-periodic rate.
The common notation for sampling frequency is which stands for frequency (subscript) sampled.
Sampling theorem
The Nyquist–Shannon sampling theorem states that perfect reconstruction of a signal is possible when the sampling frequency is greater than twice the maximum frequency of the signal being sampled, or equivalently, that the Nyquist frequency (half the sample rate) exceeds the bandwidth of the signal being sampled. If lower sampling rates are used, the original signal's information may not be completely recoverable from the sampled signal.
For example, if a signal has a bandwidth of 100 Hz, to avoid aliasing the sampling frequency should be greater than 200 Hz.
Oversampling
In some cases, it is desirable to have a sampling frequency considerably more than twice the desired system bandwidth so that a digital filter can be used in exchange for a weaker analog anti-aliasing filter. This process is known as oversampling.
Audio
In digital audio, common sampling rates are:
| Sampling rate | Use |
|---|---|
| 8,000 Hz | telephone, adequate for human speech |
| 11,025 Hz and 22,050 Hz | one quarter and one half of the sampling rate of audio CDs, respectively (see 44,100 Hz below), used for lower-quality PCM and MPEG audio |
| 32,000 Hz | miniDV digital video camcorder, DAT (LP mode), Germany's Digitales Satellitenradio Template:De icon, NICAM digital audio, used alongside analogue television sound in some countries. |
| 44,056 Hz | PCM adaptor using NTSC video tapes (245 lines by 3 samples by 59.94 frames per second), sometimes misused to play back audio streams sampled at 44,100 Hz (and vice versa) |
| 44,100 Hz | audio CD, also most commonly used with MPEG-1 audio (VCD, SVCD, MP3), adopted from the PCM adaptor using PAL video tapes (294 lines by 3 samples by 50 frames per second) |
| 47,250 Hz | world's first commercial PCM sound recorder by Nippon Columbia (Denon) |
| 48,000 Hz | digital sound used for miniDV, digital TV, DVD, DAT, films and professional audio |
| 50,000 Hz | first commercial digital audio recorders from the late 70's from 3M and Soundstream |
| 50,400 Hz | sampling rate used by the Mitsubishi X-80 digital audio recorder |
| 88,200 or 176,400 Hz | sampling rates used by professional recording equipment when the destination is CD (multiples of 44,100 Hz) |
| 96,000 or 192,000 Hz | DVD-Audio, some LPCM DVD tracks, BD-ROM (Blu-ray Disc) audio tracks, and HD-DVD (High-Definition DVD) audio tracks |
| 2,822,400 Hz | SACD, 1-bit sigma-delta modulation process known as Direct Stream Digital, co-developed by Sony and Philips |
Video systems
In digital video, the temporal sampling rate is defined the frame/field rate, rather than the notional pixel clock. The image sampling frequency is the repetition rate of the sensor integration period. Since the integration period may be significantly shorter than the time between repetitions, the sampling frequency can be different from the inverse of the sample time.
When analog video is converted to digital video, a different sampling process occurs, this time at the pixel frequency, corresponding to a spatial sampling rate along scan lines. Some common pixel sampling rates are:
Spatial sampling in the other direction is determined by the spacing of scan lines in the raster. The sampling rates and resolutions in both spatial directions can be measured in units of lines per picture height.
Spatial aliasing of high-frequency luma or chroma video components shows up as a moiré pattern.
See also
- Continuous signal vs. Discrete signal
- MP3
- Digital control
- Sample and hold
- Sample (signal)
- Sampling (signal processing)
- Signal (information theory)