Sampling rate

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.

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, 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.

Audio

In digital audio, common sampling rates are:
Sampling rate Use
8,000 Hz telephone and encrypted walkie-talkie, wireless intercom and wireless microphone 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
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 , NICAM digital audio, used alongside analogue television sound in some countries. High-quality digital wireless microphones.
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.
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:

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

References

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