Sampling rate

Analog signal and resulting sampled signal.

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.^[1]

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 $f_{s}$ 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,^[2] 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 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.^[3]

Audio

In digital audio, common sampling rates are:

Sampling rate	Use
8,000 Hz	telephone and encrypted walkie-talkie, wireless intercom^[4]^[5] and wireless microphone^[6] transmission; adequate for human speech but without sibilance; ess sounds like eff
Sims has a little willy lol	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^[7]
32,000 Hz	miniDV digital video camcorder, video tapes with extra channels of audio (eg. DVCAM with 4 Channels of audio), DAT (LP mode), Germany's Digitales Satellitenradio Template:De icon, NICAM digital audio, used alongside analogue television sound in some countries. High-quality digital wireless microphones.^[8]
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 (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.^[9]
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 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	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.

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 lines. 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 or chroma video components shows up as a moiré pattern.

References

^ Martin H. Weik (1996). Communications Standard Dictionary. Springer. ISBN 0412083914.
^ 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)
^ William Morris Hartmann (1997). Signals, Sound, and Sensation. Springer. ISBN 1563962837.
^ HME DX200 encrypted wireless intercom
^ Telex BTR-1 encrypted wireless intercom
^ Telex SAFE-1000 wireless microphone
^ The restoration procedure - part 1
^ Zaxcom digital wireless transmitters
^ Lectrosonics UDR700 Encrypted wireless receiver

Template:Link FA

[1] Martin H. Weik (1996). Communications Standard Dictionary. Springer. ISBN 0412083914.

[2] 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)

[3] William Morris Hartmann (1997). Signals, Sound, and Sensation. Springer. ISBN 1563962837.

[4] HME DX200 encrypted wireless intercom

[5] Telex BTR-1 encrypted wireless intercom

[6] Telex SAFE-1000 wireless microphone

[7] The restoration procedure - part 1

[8] Zaxcom digital wireless transmitters

[9] Lectrosonics UDR700 Encrypted wireless receiver

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v t e Digital signal processing
Theory	Detection theory Discrete signal Estimation theory Nyquist–Shannon sampling theorem
Sub-fields	Audio signal processing Digital image processing Speech processing Statistical signal processing
Techniques	Z-transform Advanced z-transform Matched Z-transform method Bilinear transform Constant-Q transform Discrete cosine transform (DCT) Discrete Fourier transform (DFT) Discrete-time Fourier transform (DTFT) Impulse invariance Integral transform Laplace transform Post's inversion formula Starred transform Zak transform
Sampling	Aliasing Anti-aliasing filter Downsampling Nyquist rate / frequency Oversampling Quantization Sampling rate Undersampling Upsampling

Sampling theorem

Oversampling

Audio

Video systems

See also

References