Insignal processing,sampling is the reduction of acontinuous-time signal to adiscrete-time signal. A common example is the conversion of asound wave to a sequence of "samples".Asample is a value of thesignal at a point in time and/or space; this definition differs fromthe term's usage in statistics, which refers to a set of such values.[A]
Asampler is a subsystem or operation that extracts samples from acontinuous signal. A theoreticalideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points.
The original signal can be reconstructed from a sequence of samples, up to theNyquist limit, by passing the sequence of samples through areconstruction filter.
Functions of space, time, or any other dimension can be sampled, and similarly in two or more dimensions.
For functions that vary with time, let be a continuous function (or "signal") to be sampled, and let sampling be performed by measuring the value of the continuous function every seconds, which is called thesampling interval orsampling period.[1][2] Then the sampled function is given by the sequence:
Thesampling frequency orsampling rate,, is the average number of samples obtained in one second, thus, with the unitsamples per second, sometimes referred to ashertz, for example 48 kHz is 48,000samples per second.
Reconstructing a continuous function from samples is done by interpolation algorithms. TheWhittaker–Shannon interpolation formula is mathematically equivalent to an ideallow-pass filter whose input is a sequence ofDirac delta functions that are modulated (multiplied) by the sample values. When the time interval between adjacent samples is a constant, the sequence of delta functions is called aDirac comb. Mathematically, the modulated Dirac comb is equivalent to the product of the comb function with. That mathematical abstraction is sometimes referred to asimpulse sampling.[3]
Most sampled signals are not simply stored and reconstructed. The fidelity of a theoretical reconstruction is a common measure of the effectiveness of sampling. That fidelity is reduced when contains frequency components whose cycle length (period) is less than 2 sample intervals (seeAliasing). The corresponding frequency limit, incycles per second (hertz), is cycle/sample × samples/second =, known as theNyquist frequency of the sampler. Therefore, is usually the output of alow-pass filter, functionally known as ananti-aliasing filter. Without an anti-aliasing filter, frequencies higher than the Nyquist frequency will influence the samples in a way that is misinterpreted by the interpolation process.[4]
In practice, the continuous signal is sampled using ananalog-to-digital converter (ADC), a device with various physical limitations. This results in deviations from the theoretically perfect reconstruction, collectively referred to asdistortion.
Various types of distortion can occur, including:
Although the use ofoversampling can completely eliminate aperture error and aliasing by shifting them out of the passband, this technique cannot be practically used above a few GHz, and may be prohibitively expensive at much lower frequencies. Furthermore, while oversampling can reduce quantization error and non-linearity, it cannot eliminate these entirely. Consequently, practical ADCs at audio frequencies typically do not exhibit aliasing or aperture error, and are not limited by quantization error. Instead, analog noise dominates. At RF and microwave frequencies, where oversampling is impractical and filters are expensive, aperture error, quantization error and aliasing can be significant limitations.
Jitter, noise, and quantization are often analyzed by modeling them as random errors added to the sample values. Integration and zero-order hold effects can be analyzed as a form oflow-pass filtering. The non-linearities of either ADC or DAC are analyzed by replacing the ideallinear function mapping with a proposednonlinear function.
Digital audio systems typically employpulse-code modulation (PCM) to encode sound as a series of discrete samples of the electrical level of an analog audio signal. Analog signals are captured (encoded) as PCM samples in analog-to-digital conversion (ADC), and reproduced (decoded) using digital-to-analog conversion (DAC). The encoding used for the storage and transmission of digitised sound data within the system may differ.
When it is necessary to capture audio covering the entire 20–20,000 Hz range ofhuman hearing[6] such as when recording music or many types of acoustic events, audio waveforms are typically sampled at 44.1 kHz (CD), 48 kHz, 88.2 kHz, or 96 kHz.[7] The approximately double-rate requirement is a consequence of theNyquist theorem. Sampling rates higher than about 50 kHz to 60 kHz cannot supply more usable information for human listeners. Earlyprofessional audio equipment manufacturers chose sampling rates in the region of 40 to 50 kHz for this reason.
There has been an industry trend towards sampling rates well beyond the basic requirements: such as 96 kHz and even 192 kHz[8] Even thoughultrasonic frequencies are inaudible to humans, recording and mixing at higher sampling rates is effective in eliminating the distortion that can be caused byfoldback aliasing. Conversely, ultrasonic sounds may interact with and modulate the audible part of the frequency spectrum (intermodulation distortion),degrading the fidelity.[9][10][11][12]One advantage of higher sampling rates is that they can relax the low-pass filter design requirements forADCs andDACs, but with modern oversamplingdelta-sigma-converters this advantage is less important.
TheAudio Engineering Society recommends 48 kHz sampling rate for most applications but gives recognition to 44.1 kHz for CD and other consumer uses, 32 kHz for transmission-related applications, and 96 kHz for higher bandwidth or relaxedanti-aliasing filtering.[13] Both Lavry Engineering and J. Robert Stuart state that the ideal sampling rate would be about 60 kHz, but since this is not a standard frequency, recommend 88.2 or 96 kHz for recording purposes.[14][15][16][17]A more complete list of common audio sample rates is:
| Sampling rate | Use |
|---|---|
| 5,512.5 Hz | Supported inFlash.[18] |
| 8,000 Hz | Telephone and encryptedwalkie-talkie,wireless intercom andwireless microphone transmission; adequate for human speech but withoutsibilance (ess sounds likeeff (/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 standardtelephonenarrowband 8,000 Hz. Used in most modernVoIP andVVoIP communication products.[19][unreliable source?] |
| 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 as78s andAM Radio.[20] |
| 32,000 Hz | miniDV digital videocamcorder, video tapes with extra channels of audio (e.g.DVCAM with four channels of audio),DAT (LP mode), Germany'sDigitales Satellitenradio,NICAM digital audio, used alongside analogue television sound in some countries. High-quality digitalwireless microphones.[21] Suitable for digitizingFM radio.[citation needed] |
| 37,800 Hz | CD-XA audio |
| 44,055.9 Hz | Used by digital audio locked toNTSCcolor video signals (3 samples per line, 245 lines per field, 59.94 fields per second = 29.97frames per second). |
| 44,100 Hz | Audio CD, also most commonly used withMPEG-1 audio (VCD,SVCD,MP3). Originally chosen bySony because it could be recorded on modified video equipment running at either 25 frames per second (PAL) or 30 frame/s (using an NTSCmonochrome video recorder) and cover the 20 kHz bandwidth thought necessary to match professional analog recording equipment of the time. APCM adaptor would fit digital audio samples into the analog video channel of, for example,PAL video tapes using 3 samples per line, 588 lines per frame, 25 frames per second. |
| 47,250 Hz | world's first commercialPCM sound recorder byNippon 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 reconstruct frequencies up to 22 kHz and work with 29.97 frames per second NTSC video, as well as25 frame/s,30 frame/s and24 frame/s systems. With29.97 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.[13] Also used for sound with consumer video formats like DV,digital TV,DVD, and films. The professionalserial digital interface (SDI) andHigh-definition Serial Digital Interface (HD-SDI) used to connect broadcast television equipment together use this audio sampling frequency. Most professional audio gear uses 48 kHz sampling, includingmixing consoles, anddigital recording devices. |
| 50,000 Hz | First commercial digital audio recorders from the late 70s from3M andSoundstream. |
| 50,400 Hz | Sampling rate used by theMitsubishi X-80 digital audio recorder. |
| 64,000 Hz | Uncommonly used, but supported by some hardware[22][23] and software.[24][25] |
| 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, someLPCM DVD tracks,BD-ROM (Blu-ray Disc) audio tracks,HD DVD (High-Definition DVD) audio tracks. Some professional recording and production equipment is able to select 96 kHz sampling. This sampling frequency is twice the 48 kHz standard commonly used with audio on professional equipment. |
| 176,400 Hz | Sampling rate used byHDCD recorders and other professional applications for CD production. Four times the frequency of 44.1 kHz. |
| 192,000 Hz | DVD-Audio, someLPCM DVD tracks,BD-ROM (Blu-ray Disc) audio tracks, andHD 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 editingSuper Audio CDs, as 1-bitDirect Stream Digital (DSD) is not suited for editing. 8 times the frequency of 44.1 kHz. |
| 384,000 Hz | Maximum sample rate available in common software.[citation needed] |
| 2,822,400 Hz | SACD, 1-bitdelta-sigma modulation process known asDirect Stream Digital, co-developed bySony andPhilips. |
| 5,644,800 Hz | Double-Rate DSD, 1-bitDirect Stream Digital at 2× the rate of the SACD. Used in some professional DSD recorders. |
| 11,289,600 Hz | Quad-Rate DSD, 1-bitDirect Stream Digital at 4× the rate of the SACD. Used in some uncommon professional DSD recorders. |
| 22,579,200 Hz | Octuple-Rate DSD, 1-bitDirect Stream Digital at 8× the rate of the SACD. Used in rare experimental DSD recorders. Also known as DSD512. |
| 45,158,400 Hz | Sexdecuple-Rate DSD, 1-bitDirect Stream Digital at 16× the rate of the SACD. Used in rare experimental DSD recorders. Also known as DSD1024.[B] |
Audio is typically recorded at 8-, 16-, and 24-bit depth; which yield a theoretical maximumsignal-to-quantization-noise ratio (SQNR) for a puresine wave of, approximately; 49.93 dB, 98.09 dB, and 122.17 dB.[26] CD quality audio uses 16-bit samples.Thermal noise limits the true number of bits that can be used in quantization. Few analog systems havesignal to noise ratios (SNR) exceeding 120 dB. However,digital signal processing operations can have very high dynamic range, consequently, it is common to perform mixing and mastering operations at 32-bitfloating-point precision and then convert to 16- or 24-bit for distribution.
Speech signals, i.e., signals intended to carry only humanspeech, can usually be sampled at a much lower rate. For mostphonemes, almost all of the energy is contained in the 100 Hz – 4 kHz range, allowing a sampling rate of 8 kHz. This is the sampling rate used by nearly alltelephony systems, which use theG.711 sampling and quantization specifications.[citation needed]
 | This sectionneeds additional citations forverification. Please helpimprove this article byadding citations to reliable sources in this section. Unsourced material may be challenged and removed.(June 2007) (Learn how and when to remove this message) |
Standard-definition television (SDTV) uses either 720 by 480pixels (USNTSC 525-line) or 720 by 576 pixels (UKPAL 625-line) for the visible picture area.
High-definition television (HDTV) uses720p (progressive),1080i (interlaced), and1080p (progressive, also known as Full-HD).
Indigital video, the temporal sampling rate is defined as theframe rate – or rather thefield rate – rather than the notionalpixel 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:
Videodigital-to-analog converters operate in the megahertz range (from ~3 MHz for low-quality composite video scalers in early game consoles, to 250 MHz or more for the highest-resolution VGA output).
When analog video is converted todigital video, a different sampling process occurs, this time at the pixel frequency, corresponding to a spatial sampling rate alongscan lines. A common pixel sampling rate is:
Spatial sampling in the other direction is determined by the spacing of scan lines in theraster. The sampling rates and resolutions in both spatial directions can be measured in units of lines per picture height.
Spatialaliasing of high-frequencyluma orchroma video components shows up as amoiré pattern.
The process ofvolume rendering samples a 3D grid ofvoxels to produce 3D renderings of sliced (tomographic) data. The 3D grid is assumed to represent a continuous region of 3D space. Volume rendering is common in medical imaging,X-ray computed tomography (CT/CAT),magnetic resonance imaging (MRI),positron emission tomography (PET) are some examples. It is also used forseismic tomography and other applications.
When abandpass signal is sampled slower than itsNyquist rate, the samples are indistinguishable from samples of a low-frequencyalias of the high-frequency signal. That is often done purposefully in such a way that the lowest-frequency alias satisfies theNyquist criterion, because the bandpass signal is still uniquely represented and recoverable. Suchundersampling is also known asbandpass sampling,harmonic sampling,IF sampling, anddirect IF to digital conversion.[27]
Oversampling is used in most modern analog-to-digital converters to reduce the distortion introduced by practicaldigital-to-analog converters, such as azero-order hold instead of idealizations like theWhittaker–Shannon interpolation formula.[28]
Complex sampling (orI/Q sampling) is the simultaneous sampling of two different, but related, waveforms, resulting in pairs of samples that are subsequently treated ascomplex numbers.[C] When one waveform,, is theHilbert transform of the other waveform,, the complex-valued function,, is called ananalytic signal, whose Fourier transform is zero for all negative values of frequency. In that case, theNyquist rate for a waveform with no frequencies ≥ B can be reduced to justB (complex samples/sec), instead of (real samples/sec).[D] More apparently, theequivalent baseband waveform,, also has a Nyquist rate of, because all of its non-zero frequency content is shifted into the interval.
Although complex-valued samples can be obtained as described above, they are also created by manipulating samples of a real-valued waveform. For instance, the equivalent baseband waveform can be created without explicitly computing, by processing the product sequence,,[E] through a digital low-pass filter whose cutoff frequency is.[F] Computing only every other sample of the output sequence reduces the sample rate commensurate with the reduced Nyquist rate. The result is half as many complex-valued samples as the original number of real samples. No information is lost, and the original waveform can be recovered, if necessary.
in many cases, we can hear the sound of higher sample rates not because they are more transparent, but because they are less so. They can actually introduce unintended distortion in the audible spectrum
be very careful about any claims that 192 kHz sounds better than 96 kHz. Our experience points in the opposite direction.
We are often asked why the iD and EVO interfaces don't support 192 kHZ, because after all, aren't higher-spec numbers better? Well, in this case, not always…
So while 192 kHz may look impressive on a spec sheet, it often leads to more system strain, more distortion, and less clarity, all in service of frequencies no human can actually hear.
Although 60 KHz would be closer to the ideal; given the existing standards, 88.2 KHz and 96 KHz are closest to the optimal sample rate.
I am trying to accommodate all ears, and there are reports of few people that can actually hear slightly above 20KHz. I do think that 48 KHz is pretty good compromise, but 88.2 or 96 KHz yields some additional margin.
Nowdays [sic] there are a number of good designers and ear people that find 60-70KHz sample rate to be the optimal rate for the ear. It is fast enough to include what we can hear, yet slow enough to do it pretty accurately.
both psychoacoustic analysis and experience tell us that the minimum rectangular channel necessary to ensure transparency uses linear PCM with 18.2-bit samples at 58 kHz. ... there are strong arguments for maintaining integer relationships with existing sampling rates – which suggests that 88.2 kHz or 96 kHz should be adopted.
For most records a sample rate of 22050 in stereo is adequate. An exception is likely to be recordings made in the second half of the century, which may need a sample rate of 44100.
Supported sample frequencies: Internally 32, 44.1, 48, 64, 88.2, 96, 176.4, 192 kHz.
Supported sampling rates: 44.1 kHz, 48 kHz, 64 kHz, 88.2 kHz, 96 kHz, 176.4 kHz, 192 kHz
Common Sample Rates: 64 000 Hz
[Screenshot of Cubase]
