Sampling rate
Encyclopedia
The sampling rate, sample rate, or sampling frequency () defines the number of samples per unit of time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

 (usually second
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

s) taken from a continuous signal
Continuous signal
A continuous signal or a continuous-time signal is a varying quantity whose domain, which is often time, is a continuum . That is, the function's domain is an uncountable set. The function itself need not be continuous...

 to make a discrete signal
Discrete signal
A discrete signal or discrete-time signal is a time series consisting of a sequence of qualities...

. For time-domain signals, the unit for sampling rate is hertz
Hertz
The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....

 (inverse seconds, 1/s, s−1), sometimes noted as Sa/s (samples per second). The inverse of the sampling frequency is the sampling period or sampling interval, which is the time between samples.

Sampling theorem

The Nyquist–Shannon sampling theorem
Nyquist–Shannon sampling theorem
The Nyquist–Shannon sampling theorem, after Harry Nyquist and Claude Shannon, is a fundamental result in the field of information theory, in particular telecommunications and signal processing. Sampling is the process of converting a signal into a numeric sequence...

 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, when the Nyquist frequency
Nyquist frequency
The Nyquist frequency, named after the Swedish-American engineer Harry Nyquist or the Nyquist–Shannon sampling theorem, is half the sampling frequency of a discrete signal processing system...

 (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 band limit of 100 Hz, a sampling frequency greater than 200 Hz will avoid aliasing
Aliasing
In signal processing and related disciplines, aliasing refers to an effect that causes different signals to become indistinguishable when sampled...

 and allow theoretically perfect reconstruction.

The full range of human hearing is between 20 Hz and 20 kHz. The minimum sampling rate that satisfies the sampling theorem for this full bandwidth is 40 kHz. The 44.1 kHz sampling rate used for Compact Disc
Compact Disc
The Compact Disc is an optical disc used to store digital data. It was originally developed to store and playback sound recordings exclusively, but later expanded to encompass data storage , write-once audio and data storage , rewritable media , Video Compact Discs , Super Video Compact Discs ,...

 was chosen for this and other technical reasons.

Oversampling

In some cases, it is desirable to have a sampling frequency more than twice the desired system bandwidth so that a digital filter
Digital filter
In electronics, computer science and mathematics, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is...

 can be used in exchange for a weaker analog anti-aliasing filter
Anti-aliasing filter
An anti-aliasing filter is a filter used before a signal sampler, to restrict the bandwidth of a signal to approximately satisfy the sampling theorem....

. This process is known as oversampling
Oversampling
In signal processing, oversampling is the process of sampling a signal with a sampling frequency significantly higher than twice the bandwidth or highest frequency of the signal being sampled...

.

Undersampling

Conversely, one may sample below the Nyquist rate. For a baseband
Baseband
In telecommunications and signal processing, baseband is an adjective that describes signals and systems whose range of frequencies is measured from close to 0 hertz to a cut-off frequency, a maximum bandwidth or highest signal frequency; it is sometimes used as a noun for a band of frequencies...

 signal (one that has components from 0 to the band limit), this introduces aliasing, but for a passband
Passband
A passband is the range of frequencies or wavelengths that can pass through a filter without being attenuated.A bandpass filtered signal , is known as a bandpass signal, as opposed to a baseband signal....

 signal (one that does not have low frequency components), there are no low frequency signals for the aliases of high frequency signals to collide with, and thus one can sample a high frequency (but narrow bandwidth) signal at a much lower sample rate than the Nyquist rate.

Audio

In digital audio
Digital audio
Digital audio is sound reproduction using pulse-code modulation and digital signals. Digital audio systems include analog-to-digital conversion , digital-to-analog conversion , digital storage, processing and transmission components...

 the most common sampling rates are 44.1 kHz, 48 kHz, and 96 kHz. A common frequency in computer sound cards is 48 kHz – many work at only this frequency, offering the use of other sample rates only through resampling
Sample rate conversion
Sample rate conversion is the process of converting a signal from one sampling rate to another, while changing the information carried by the signal as little as possible...

. The earliest add-in cards ran at 22 kHz. High-end audio equipment, such as in SACD
SACD
SACD, founded as Société des Auteurs et Compositeurs Dramatiques on 7 March 1829, is a French collecting society, undertaking collective rights management for authors...

 or DVD-Audio
DVD-Audio
DVD-Audio is a digital format for delivering high-fidelity audio content on a DVD. DVD-Audio is not intended to be a video delivery format and is not the same as video DVDs containing concert films or music videos....

 players or studio equipment, can reach as high as 192 kHz.

A more complete list of common audio sample rates is:
Sampling rate Use
8,000 Hz Telephone
Telephone
The telephone , colloquially referred to as a phone, is a telecommunications device that transmits and receives sounds, usually the human voice. Telephones are a point-to-point communication system whose most basic function is to allow two people separated by large distances to talk to each other...

 and encrypted walkie-talkie
Walkie-talkie
A walkie-talkie is a hand-held, portable, two-way radio transceiver. Its development during the Second World War has been variously credited to Donald L. Hings, radio engineer Alfred J. Gross, and engineering teams at Motorola...

, wireless intercom
Wireless intercom
A wireless intercom is a telecommunications device that enables voice communication without the need to run copper wires between intercom stations. A wired intercom system may incorporate wireless elements....

 and wireless microphone
Wireless microphone
A wireless microphone, as the name implies, is a microphone without a physical cable connecting it directly to the sound recording or amplifying equipment with which it is associated...

 transmission; adequate for human speech but without sibilance; ess sounds like eff (s, f).
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.
16,000 Hz Wideband
Wideband
In communications, wideband is a relative term used to describe a wide range of frequencies in a spectrum. A system is typically described as wideband if the message bandwidth significantly exceeds the channel's coherence bandwidth....

 frequency extension over standard telephone
Telephone
The telephone , colloquially referred to as a phone, is a telecommunications device that transmits and receives sounds, usually the human voice. Telephones are a point-to-point communication system whose most basic function is to allow two people separated by large distances to talk to each other...

 narrowband
Narrowband
In radio, narrowband describes a channel in which the bandwidth of the message does not significantly exceed the channel's coherence bandwidth. It is a common misconception that narrowband refers to a channel which occupies only a "small" amount of space on the radio spectrum.The opposite of...

 8,000 Hz. Used in most modern VoIP and VVoIP communication products.
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.
32,000 Hz miniDV digital video camcorder
Camcorder
A camcorder is an electronic device that combines a video camera and a video recorder into one unit. Equipment manufacturers do not seem to have strict guidelines for the term usage...

, video tapes with extra channels of audio (e.g. DVCAM with 4 Channels of audio), DAT
Digital Audio Tape
Digital Audio Tape is a signal recording and playback medium developed by Sony and introduced in 1987. In appearance it is similar to a compact audio cassette, using 4 mm magnetic tape enclosed in a protective shell, but is roughly half the size at 73 mm × 54 mm × 10.5 mm. As...

 (LP mode), Germany's Digitales Satellitenradio , NICAM
NICAM
Near Instantaneous Companded Audio Multiplex is an early form of lossy compression for digital audio. It was originally developed in the early 1970s for point-to-point links within broadcasting networks...

 digital audio, used alongside analogue television sound in some countries. High-quality digital wireless microphone
Wireless microphone
A wireless microphone, as the name implies, is a microphone without a physical cable connecting it directly to the sound recording or amplifying equipment with which it is associated...

s. Suitable for digitizing FM radio
FM broadcasting
FM broadcasting is a broadcasting technology pioneered by Edwin Howard Armstrong which uses frequency modulation to provide high-fidelity sound over broadcast radio. The term "FM band" describes the "frequency band in which FM is used for broadcasting"...

.
44,056 Hz Used by digital audio locked to NTSC
NTSC
NTSC, named for the National Television System Committee, is the analog television system that is used in most of North America, most of South America , Burma, South Korea, Taiwan, Japan, the Philippines, and some Pacific island nations and territories .Most countries using the NTSC standard, as...

 color video signals (245 lines by 3 samples by 59.94 fields per second = 29.97 frames per second).
44,100 Hz
44,100 Hz
In digital audio, 44,100 Hz is a common sampling frequency: analog audio is recorded by sampling it 44,100 times per second, and then these samples are used to reconstruct the audio signal when playing it back...

Audio CD
Compact Disc
The Compact Disc is an optical disc used to store digital data. It was originally developed to store and playback sound recordings exclusively, but later expanded to encompass data storage , write-once audio and data storage , rewritable media , Video Compact Discs , Super Video Compact Discs ,...

, also most commonly used with MPEG-1
MPEG-1
MPEG-1 is a standard for lossy compression of video and audio. It is designed to compress VHS-quality raw digital video and CD audio down to 1.5 Mbit/s without excessive quality loss, making video CDs, digital cable/satellite TV and digital audio broadcasting possible.Today, MPEG-1 has become...

 audio (VCD
VCD
VCD is a three-letter abbreviation with multiple meanings, as described below:* VCD Athletic, semi-professional football team* Video CD* Voice command device* Value change dump * Vocal cord dysfunction* Visual Communication and Design...

, SVCD, MP3
MP3
MPEG-1 or MPEG-2 Audio Layer III, more commonly referred to as MP3, is a patented digital audio encoding format using a form of lossy data compression...

). Originally chosen by Sony
Sony
, commonly referred to as Sony, is a Japanese multinational conglomerate corporation headquartered in Minato, Tokyo, Japan and the world's fifth largest media conglomerate measured by revenues....

 because it could be recorded on modified video equipment running at either 25 frames per second (PAL) or 30 frame/s (using an NTSC monochrome video recorder) and cover the 20 kHz bandwidth thought necessary to match professional analog recording equipment of the time. A PCM adaptor
PCM adaptor
A PCM adaptor is a device used for recording digital audio in the PCM format, which in turn connects to a video cassette recorder for storage and playback of the digital audio information.-How a PCM adaptor works:...

 would fit digital audio samples into the analog video channel of, for example, PAL
PAL
PAL, short for Phase Alternating Line, is an analogue television colour encoding system used in broadcast television systems in many countries. Other common analogue television systems are NTSC and SECAM. This page primarily discusses the PAL colour encoding system...

 video tapes using 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
Wireless microphone
A wireless microphone, as the name implies, is a microphone without a physical cable connecting it directly to the sound recording or amplifying equipment with which it is associated...

s.
47,250 Hz world's first commercial PCM sound recorder by Nippon Columbia (Denon)
48,000 Hz The standard audio sampling rate used by professional digital video equipment such as tape recorders, video servers, vision mixers and so on. This rate was chosen because it could deliver a 22 kHz frequency response and work with 29.97 frames per second NTSC video - as well as 25 frame/s, 30 frame/s and 24 frame/s systems. With 29.97 frame/s systems it is necessary to handle 1601.6 audio samples per frame delivering an integer number of audio samples only every fifth video frame. Also used for sound with consumer video formats like DV, digital TV, DVD
DVD
A DVD is an optical disc storage media format, invented and developed by Philips, Sony, Toshiba, and Panasonic in 1995. DVDs offer higher storage capacity than Compact Discs while having the same dimensions....

, and films. The professional Serial Digital Interface (SDI)
Serial Digital Interface
Serial digital interface is a family of video interfaces standardized by SMPTE. For example, ITU-R BT.656 and SMPTE 259M define digital video interfaces used for broadcast-grade video...

 and High-definition Serial Digital Interface (HD-SDI)
Serial Digital Interface
Serial digital interface is a family of video interfaces standardized by SMPTE. For example, ITU-R BT.656 and SMPTE 259M define digital video interfaces used for broadcast-grade video...

 used to connect broadcast television equipment together uses this audio sampling frequency. Much professional audio gear uses (or is able to select) 48 kHz sampling, including mixers, EQs, compressors, reverb, crossovers and recording devices such as DAT
Digital Audio Tape
Digital Audio Tape is a signal recording and playback medium developed by Sony and introduced in 1987. In appearance it is similar to a compact audio cassette, using 4 mm magnetic tape enclosed in a protective shell, but is roughly half the size at 73 mm × 54 mm × 10.5 mm. As...

.
50,000 Hz First commercial digital audio recorders from the late 70s from 3M
3M
3M Company , formerly known as the Minnesota Mining and Manufacturing Company, is an American multinational conglomerate corporation based in Maplewood, Minnesota, United States....

 and Soundstream
Soundstream
-The Company:Soundstream Inc. was founded in 1975 in Salt Lake City, Utah by Dr. Thomas G. Stockham, Jr. It was the world’s first audiophile digital audio recording company, providing commercial services for recording and computer-based editing...

.
50,400 Hz Sampling rate used by the Mitsubishi X-80 digital audio recorder.
88,200 Hz Sampling rate used by some 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
DVD-Audio
DVD-Audio is a digital format for delivering high-fidelity audio content on a DVD. DVD-Audio is not intended to be a video delivery format and is not the same as video DVDs containing concert films or music videos....

, some LPCM
LPCM
Linear pulse-code modulation is a method of encoding audio information digitally. The term also refers collectively to formats using this method of encoding...

 DVD tracks, BD-ROM (Blu-ray Disc) audio tracks, HD DVD
HD DVD
HD DVD is a discontinued high-density optical disc format for storing data and high-definition video.Supported principally by Toshiba, HD DVD was envisioned to be the successor to the standard DVD format...

 (High-Definition DVD) audio tracks. Most pro audio gear uses (or is able to select) 96 kHz sampling, including mixers, EQs, compressors, reverb, crossovers and recording devices. This sampling frequency is twice the 48 kHz standard commonly used with audio on professional video equipment.
176,400 Hz Sampling rate used by HDCD recorders and other professional applications for CD production.
192,000 Hz DVD-Audio
DVD-Audio
DVD-Audio is a digital format for delivering high-fidelity audio content on a DVD. DVD-Audio is not intended to be a video delivery format and is not the same as video DVDs containing concert films or music videos....

, some LPCM
LPCM
Linear pulse-code modulation is a method of encoding audio information digitally. The term also refers collectively to formats using this method of encoding...

 DVD tracks, BD-ROM (Blu-ray Disc) audio tracks, and HD DVD
HD DVD
HD DVD is a discontinued high-density optical disc format for storing data and high-definition video.Supported principally by Toshiba, HD DVD was envisioned to be the successor to the standard DVD format...

 (High-Definition DVD) audio tracks, High-Definition audio recording devices and audio editing software. This sampling frequency is four times the 48 kHz standard commonly used with audio on professional video equipment.
352,800 Hz Digital eXtreme Definition
Digital eXtreme Definition
Digital eXtreme Definition is an audio encoding scheme for professional use that was developed for editing high-resolution recordings because DSD, the audio standard used on Super Audio CD is not ideally suited for editing...

, used for recording and editing Super Audio CD
Super Audio CD
Super Audio CD is a high-resolution, read-only optical disc for audio storage. Sony and Philips Electronics jointly developed the technology, and publicized it in 1999. It is designated as the Scarlet Book standard. Sony and Philips previously collaborated to define the Compact Disc standard...

s, as 1-bit DSD is not suited for editing. Eight times the frequency of 44.1 kHz.
2,822,400 Hz SACD
Super Audio CD
Super Audio CD is a high-resolution, read-only optical disc for audio storage. Sony and Philips Electronics jointly developed the technology, and publicized it in 1999. It is designated as the Scarlet Book standard. Sony and Philips previously collaborated to define the Compact Disc standard...

, 1-bit delta-sigma modulation
Delta-sigma modulation
Delta-sigma modulation is a method for encoding high-resolution or analog signals into lower-resolution digital signals. The conversion is done using error feedback, where the difference between the two signals is measured and used to improve the conversion...

 process known as Direct Stream Digital
Direct Stream Digital
Direct-Stream Digital is the trademark name used by Sony and Philips for their system of recreating audible signals which uses pulse-density modulation encoding, a technology to store audio signals on digital storage media which is used for the Super Audio CD .The signal is stored as delta-sigma...

, co-developed by Sony
Sony
, commonly referred to as Sony, is a Japanese multinational conglomerate corporation headquartered in Minato, Tokyo, Japan and the world's fifth largest media conglomerate measured by revenues....

 and Philips
Philips
Koninklijke Philips Electronics N.V. , more commonly known as Philips, is a multinational Dutch electronics company....

.
5,644,800 Hz Double-Rate DSD, 1-bit Direct Stream Digital
Direct Stream Digital
Direct-Stream Digital is the trademark name used by Sony and Philips for their system of recreating audible signals which uses pulse-density modulation encoding, a technology to store audio signals on digital storage media which is used for the Super Audio CD .The signal is stored as delta-sigma...

 at 2x the rate of the SACD. Used in some professional DSD recorders.

Video systems

In digital video
Digital video
Digital video is a type of digital recording system that works by using a digital rather than an analog video signal.The terms camera, video camera, and camcorder are used interchangeably in this article.- History :...

, the temporal sampling rate is defined the frame rate
Frame rate
Frame rate is the frequency at which an imaging device produces unique consecutive images called frames. The term applies equally well to computer graphics, video cameras, film cameras, and motion capture systems...

 – or rather the field rate
Field rate
The field rate of an interlaced video image is twice the effective frame rate, since interlacing draws only half of the image at a time. For example, a field rate of 60 Hertz will correspond to a 30 frames-per-second moving picture...

 – 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
    PAL
    PAL, short for Phase Alternating Line, is an analogue television colour encoding system used in broadcast television systems in many countries. Other common analogue television systems are NTSC and SECAM. This page primarily discusses the PAL colour encoding system...

     video
  • 60 / 1.001 Hz ~= 59.94 Hz – NTSC
    NTSC
    NTSC, named for the National Television System Committee, is the analog television system that is used in most of North America, most of South America , Burma, South Korea, Taiwan, Japan, the Philippines, and some Pacific island nations and territories .Most countries using the NTSC standard, as...

     video


Video digital-to-analog converter
Digital-to-analog converter
In electronics, a digital-to-analog converter is a device that converts a digital code to an analog signal . An analog-to-digital converter performs the reverse operation...

s operate in the megahertz range (from ~3 MHz for low quality composite video scalers in early games consoles, to 250 MHz or more for the highest-resolution VGA output.

When analog video is converted to digital video
Digital video
Digital video is a type of digital recording system that works by using a digital rather than an analog video signal.The terms camera, video camera, and camcorder are used interchangeably in this article.- History :...

, a different sampling process occurs, this time at the pixel frequency, corresponding to a spatial sampling rate along scan line
Scan line
A scan line or scanline is one line, or row, in a raster scanning pattern, such as a line of video on a cathode ray tube display of a television set or computer monitor....

s. A common pixel
Pixel
In digital imaging, a pixel, or pel, is a single point in a raster image, or the smallest addressable screen element in a display device; it is the smallest unit of picture that can be represented or controlled....

 sampling rate is:
  • 13.5 MHz – CCIR 601
    CCIR 601
    ITU-R Recommendation BT.601, more commonly known by the abbreviations Rec. 601 or BT.601 is a standard published in 1982 by International Telecommunication Union - Radiocommunications sector for encoding interlaced analog video signals in digital video form...

    , D1 video


Spatial sampling in the other direction is determined by the spacing of scan lines in the raster
Raster graphics
In computer graphics, a raster graphics image, or bitmap, is a data structure representing a generally rectangular grid of pixels, or points of color, viewable via a monitor, paper, or other display medium...

. The sampling rates and resolutions in both spatial directions can be measured in units of lines per picture height.

Spatial aliasing
Aliasing
In signal processing and related disciplines, aliasing refers to an effect that causes different signals to become indistinguishable when sampled...

 of high-frequency luma
Luma (video)
In video, luma, sometimes called luminance, represents the brightness in an image . Luma is typically paired with chrominance. Luma represents the achromatic image without any color, while the chroma components represent the color information...

 or chroma
Chrominance
Chrominance is the signal used in video systems to convey the color information of the picture, separately from the accompanying luma signal . Chrominance is usually represented as two color-difference components: U = B' − Y' and V = R' − Y'...

 video components shows up as a moiré pattern
Moiré pattern
In physics, a moiré pattern is an interference pattern created, for example, when two grids are overlaid at an angle, or when they have slightly different mesh sizes.- Etymology :...

.

See also

  • Bit rate
    Bit rate
    In telecommunications and computing, bit rate is the number of bits that are conveyed or processed per unit of time....

  • Digital control
    Digital control
    Digital control is a branch of control theory that uses digital computers to act as system controllers.Depending on the requirements, a digital control system can take the form of a microcontroller to an ASIC to a standard desktop computer....

  • Normalized frequency
    Normalized frequency (digital signal processing)
    In digital signal processing, the normalized frequency of a periodic signal is its frequency expressed in units of cycles per sample, rather than in the usual SI units of hertz...

  • Sample and hold
    Sample and hold
    In electronics, a sample and hold circuit is an analog device that samples the voltage of a continuously varying analog signal and holds its value at a constant level for a specified minimal period of time. Sample and hold circuits and related peak detectors are the elementary analog memory...

  • Sample rate conversion
    Sample rate conversion
    Sample rate conversion is the process of converting a signal from one sampling rate to another, while changing the information carried by the signal as little as possible...

  • Signal (information theory)
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