Sampling rate
The sampling rate, sample rate, or sampling frequency (fs) defines the number of samples per unit of time (usually seconds) taken from a continuous signal to make a discrete signal. For time-domain signals, the unit for sampling rate is hertz (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.[1]
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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, when 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.[2] For example, if a signal has an upper band limit of 100 Hz, a sampling frequency greater than 200 Hz will avoid aliasing and allow theoretically perfect reconstruction.
The full range of human hearing is between 20 Hz and 20 kHz.[3] 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 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 can be used in exchange for a weaker analog anti-aliasing filter. This process is known as oversampling.[4]
Undersampling
Conversely, one may sample below the Nyquist rate. For a baseband signal (one that has components from 0 to the band limit), this introduces aliasing, but for a passband 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 the most common sampling rates are 44.1 kHz, 48 kHz, and 96 kHz.[citation needed] 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. The earliest add-in cards ran at 22 kHz.[citation needed] High-end audio equipment, such as in SACD or DVD-Audio 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 and encrypted walkie-talkie, wireless intercom[5][6] and wireless microphone[7] 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.[citation needed] |
| 16,000 Hz | Wideband frequency extension over standard telephone narrowband 8,000 Hz. Used in most modern VoIP and VVoIP communication products.[citation needed] |
| 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.[8] |
| 32,000 Hz | miniDV digital video camcorder, video tapes with extra channels of audio (e.g. DVCAM with 4 Channels of audio), DAT (LP mode), Germany's Digitales Satellitenradio (German), NICAM digital audio, used alongside analogue television sound in some countries. High-quality digital wireless microphones.[9] Suitable for digitizing FM radio.[citation needed] |
| 44,056 Hz | Used by digital audio locked to NTSC color video signals (245 lines by 3 samples by 59.94 fields per second = 29.97 frames per second). |
| 44,100 Hz | Audio CD, also most commonly used with MPEG-1 audio (VCD, SVCD, MP3). Originally chosen by Sony 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 would fit digital audio samples into the analog video channel of, for example, PAL 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 microphones.[10] |
| 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.[11] Also used for sound with consumer video formats like DV, digital TV, DVD, and films. The professional Serial Digital Interface (SDI) and High-definition Serial Digital Interface (HD-SDI) 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. |
| 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 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, some LPCM DVD tracks, BD-ROM (Blu-ray Disc) audio tracks, HD DVD (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, 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. This sampling frequency is four times the 48 kHz standard commonly used with audio on professional video equipment. |
| 352,800 Hz | Digital eXtreme Definition, used for recording and editing Super Audio CDs, as 1-bit DSD is not suited for editing. Eight times the frequency of 44.1 kHz. |
| 2,822,400 Hz | SACD, 1-bit delta-sigma modulation process known as Direct Stream Digital, co-developed by Sony and Philips. |
| 5,644,800 Hz | Double-Rate DSD, 1-bit Direct Stream Digital at 2x the rate of the SACD. Used in some professional DSD recorders. |
Video systems
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This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (June 2007) |
In digital video, the temporal sampling rate is defined the frame rate – or rather the 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:
Video digital-to-analog converters 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, a different sampling process occurs, this time at the pixel frequency, corresponding to a spatial sampling rate along scan lines. A common pixel sampling rate is:
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
- Bit rate
- Digital control
- Normalized frequency
- Sample and hold
- Sample rate conversion
- Signal (information theory)
References
- ^ Martin H. Weik (1996). Communications Standard Dictionary. Springer. ISBN 0412083914. http://books.google.com/books?id=ND2c1uq53TIC&pg=PA866&ots=jyC7vyPLLQ&dq=%22sampling+rate%22+frequency+period&sig=40Pw5vlPE-hXuM4-Rh3lpONQ6g4.
- ^ C. E. Shannon, "Communication in the presence of noise", Proc. Institute of Radio Engineers, vol. 37, no.1, pp. 10–21, Jan. 1949. Reprint as classic paper in: Proc. IEEE, Vol. 86, No. 2, (Feb 1998)
- ^ "Frequency Range of Human Hearing". The Physics Factbook. http://hypertextbook.com/facts/2003/ChrisDAmbrose.shtml.
- ^ William Morris Hartmann (1997). Signals, Sound, and Sensation. Springer. ISBN 1563962837. http://books.google.com/books?id=3N72rIoTHiEC&pg=PA485&ots=GT7aaJK5vq&dq=over-sampling+digital-filter+audio&sig=0ZvXTWSZNb0E1Ugm0_qoF8z-Z7E.
- ^ HME DX200 encrypted wireless intercom[dead link]
- ^ "Telex BTR-1 encrypted wireless intercom". Telexradiocom.com. http://www.telexradiocom.com/product.php?id=71897XX. Retrieved 2011-01-18.
- ^ "Telex SAFE-1000 wireless microphone". Telex.com. http://www.telex.com/wirelessmicrophones/Product.aspx?MarketID=14&CategoryID=59&ProductID=141. Retrieved 2011-01-18.
- ^ "The restoration procedure - part 1". Restoring78s.co.uk. http://www.restoring78s.co.uk/Procedure%20Part%201.htm. Retrieved 2011-01-18.
- ^ "Zaxcom digital wireless transmitters". Zaxcom.com. http://www.zaxcom.com/transmitters.htm. Retrieved 2011-01-18.
- ^ Lectrosonics UDR700 Encrypted wireless receiver[dead link]
- ^ AES5-2008: AES recommended practice for professional digital audio - Preferred sampling frequencies for applications employing pulse-code modulation, Audio Engineering Society, 2008, http://www.aes.org/publications/standards/search.cfm?docID=14, retrieved 2010-01-18
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