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#REDIRECT [[Sampling (signal processing)#Sampling rate]]
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|valign="top"|[[Image:Analog signal.png|Analog signal]]
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|valign="bottom"|[[Image:Sampled signal.png|Digital signal]]
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<div class="thumbcaption" style="width:260px;">Analog signal and resulting sampled signal.</div>
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The '''sampling rate''', '''sample rate''', or '''sampling frequency''' defines the number of [[sample (signal)|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 [[sample (signal)|samples]].<ref>{{cite book | title = Communications Standard Dictionary | author = Martin H. Weik | publisher = Springer | year = 1996 | isbn = 0412083914 | url = http://books.google.com/books?id=ND2c1uq53TIC&pg=PA866&ots=jyC7vyPLLQ&dq=%22sampling+rate%22+frequency+period&sig=40Pw5vlPE-hXuM4-Rh3lpONQ6g4 }}</ref>


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The concept of sampling frequency can only be applied to [[Sampler (signal)|sampler]]s in which samples are taken periodically. Some samplers may sample at a non-periodic rate.
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The common notation for sampling frequency is <math>f_s</math> which stands for frequency (subscript) sampled.


[[Category:Temporal rates]]
==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,<ref>[[Claude E. Shannon|C. E. Shannon]], "Communication in the presence of noise", Proc. Institute of Radio Engineers, vol. 37, no.1, pp. 10–21, Jan. 1949. [http://www.stanford.edu/class/ee104/shannonpaper.pdf Reprint as classic paper in: ''Proc. IEEE'', Vol. 86, No. 2, (Feb 1998)]</ref> or equivalently, that the [[Nyquist frequency]] (half the sample rate) exceeds the highest frequency 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 an upper [[Bandwidth (signal processing)|band limit]] of 100 Hz, a sampling frequency greater than 200 Hz will avoid [[aliasing]] and allow theoretically perfect reconstruction.

==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]].<ref>{{cite book | title = Signals, Sound, and Sensation | author = William Morris Hartmann | publisher = Springer | year = 1997 | isbn = 1563962837 | url = http://books.google.com/books?id=3N72rIoTHiEC&pg=PA485&ots=GT7aaJK5vq&dq=over-sampling+digital-filter+audio&sig=0ZvXTWSZNb0E1Ugm0_qoF8z-Z7E }}</ref>



==Audio==
In [[digital audio]], common sampling rates are:
{| class="wikitable"
|-
! Sampling rate
! Use
|-
| 8,000 Hz
| [[telephone]] and encrypted [[walkie-talkie]], [[wireless intercom]]<ref>[http://www.hme.com/proDX200.cfm HME DX200 encrypted wireless intercom]</ref><ref>[http://www.telexradiocom.com/product.php?id=71897XX Telex BTR-1 encrypted wireless intercom]</ref> and [[wireless microphone]]<ref>[http://www.telex.com/wirelessmicrophones/Product.aspx?MarketID=14&CategoryID=59&ProductID=141 Telex SAFE-1000 wireless microphone]</ref> transmission; adequate for human speech but without [[sibilance]]; ''ess'' sounds like ''eff''
|-
| 11,025 Hz
| one quarter the sampling rate of audio CDs; used for lower-quality PCM, MPEG audio and for audio analysis of subwoofer bandpasses
|-
| 22,050 Hz
| one half the sampling rate of audio CDs; used for lower-quality PCM and MPEG audio and for audio analysis of low frequency energy. Suitable for digitizing early 20th century audio formats such as 78s<ref>[http://www.restoring78s.co.uk/Procedure%20Part%201.htm The restoration procedure - part 1]</ref>
|-
| 32,000 Hz
| [[miniDV]] digital video [[camcorder]], video tapes with extra channels of audio (eg. [[DVCAM]] with 4 Channels of audio), [[Digital Audio Tape|DAT]] (LP mode), Germany's [[:de:Digitales Satellitenradio|Digitales Satellitenradio]] {{de icon}}, [[NICAM]] digital audio, used alongside analogue television sound in some countries. High-quality digital [[wireless microphone]]s.<ref>[http://www.zaxcom.com/transmitters.htm Zaxcom digital wireless transmitters]</ref>
|-
| 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
| [[compact disc|audio CD]], also most commonly used with [[MPEG-1]] audio ([[VCD]], [[SVCD]], [[MP3]]), adopted from the [[PCM adaptor]] using [[PAL]] video tapes (588 lines by 3 samples by 25 frames per second). Much pro audio gear uses (or is able to select) 44.1 kHz sampling, including mixers, EQs, compressors, reverb, crossovers, recording devices and CD-quality encrypted [[wireless microphone]]s.<ref>[http://www.lectrosonics.com/wireless/700/udr700.htm Lectrosonics UDR700 Encrypted wireless receiver]</ref>
|-
| 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]], and films. Much pro audio gear uses (or is able to select) 48 kHz sampling, including mixers, EQs, compressors, reverb, crossovers and recording devices such as [[Digital Audio Tape|DAT]].
|-
| 50,000 Hz
| first commercial digital audio recorders from the late 70s from [[3M]] and [[Soundstream]]
|-
| 50,400 Hz
| sampling rate used by the [[Mitsubishi]] X-80 digital audio recorder
|-
| 88,200 Hz
| sampling rate used by professional recording equipment when the destination is CD (multiples of 44,100 Hz). Some pro audio gear uses (or is able to select) 88.2 kHz sampling, including mixers, EQs, compressors, reverb, crossovers and recording devices.
|-
| 96,000 Hz
| [[DVD-Audio]], some [[LPCM]] DVD tracks, [[BD-ROM]] (Blu-ray Disc) audio tracks, and [[HD DVD]] (High-Definition DVD) audio tracks. Some pro audio gear uses (or is able to select) 96 kHz sampling, including mixers, EQs, compressors, reverb, crossovers and recording devices.
|-
| 176,400 Hz
| sampling rate used by professional recording equipment when the destination is CD (multiples of 44,100 Hz)
|-
| 192,000 Hz
| [[DVD-Audio]], some [[LPCM]] DVD tracks, [[BD-ROM]] (Blu-ray Disc) audio tracks, and [[HD DVD]] (High-Definition DVD) audio tracks, High-Definition audio recording devices and audio editing software
|-
| 2,822,400 Hz
| [[Super Audio CD|SACD]], 1-bit [[sigma-delta modulation]] process known as [[Direct Stream Digital]], co-developed by [[Sony]] and [[Philips]]
|}

==Video systems==
{{refimprove|section|date=June 2007}}
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.
* 50 Hz - [[PAL]] video
* 60 / 1.001 Hz - [[NTSC]] video

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 line]]s. Some common [[pixel]] sampling rates are:
*13.5 MHz - [[CCIR 601]], [[D1 video]]
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 (video)|luma]] or [[chrominance|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)]]
* [[Sample rate conversion]]
* [[Signal (information theory)]]
* [[Bit rate]]

==References==
{{reflist}}

{{DSP}}

[[Category:Digital signal processing]]
[[Category:Signal processing]]

{{Link FA|es}}

[[ca:Freqüència de mostreig]]
[[da:Samplingsfrekvens]]
[[de:Abtastrate]]
[[es:Frecuencia de muestreo]]
[[fr:Fréquence d'échantillonnage]]
[[ga:Ráta samplála]]
[[it:Frequenza di campionamento]]
[[hu:Mintavételezési frekvencia]]
[[nl:Bemonsteringsfrequentie]]
[[ja:サンプリング周波数]]
[[ru:Частота дискретизации]]
[[fi:Näytteenottotaajuus]]
[[sv:Samplingsfrekvens]]
[[uk:Частота дискретизації]]
[[zh:采样率]]

Latest revision as of 17:12, 13 July 2021

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