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706:(PCM) and digital signals for sound reproduction. This includes analog-to-digital conversion (ADC), digital-to-analog conversion (DAC), storage, and transmission. In effect, the system commonly referred to as digital is in fact a discrete-time, discrete-level analog of a previous electrical analog. While modern systems can be quite subtle in their methods, the primary usefulness of a digital system is the ability to store, retrieve and transmit signals without any loss of quality.
1317:
38:
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cannot eliminate these entirely. Consequently, practical ADCs at audio frequencies typically do not exhibit aliasing, 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.
1536:
The top two graphs depict
Fourier transforms of two different functions that produce the same results when sampled at a particular rate. The baseband function is sampled faster than its Nyquist rate, and the bandpass function is undersampled, effectively converting it to baseband. The lower graphs
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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
670:
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
1020:
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 as
1021:
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,
1085:
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.
2119:. 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
1421:. 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:
2386:
The sequence of complex numbers is convolved with the impulse response of a filter with real-valued coefficients. That is equivalent to separately filtering the sequences of real parts and imaginary parts and reforming complex pairs at the
1109:(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.
1972:
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
763:
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 relaxed
1144:(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.
2703:
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
1033:(SDI) and High-definition Serial Digital Interface (HD-SDI) used to connect broadcast television equipment together uses this audio sampling frequency. Most professional audio gear uses 48 kHz sampling, including
768:. 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.
2732:
Nowdays 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
1782:
2625:
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
627:
circuit, aperture errors are introduced by multiple mechanisms. For example, the capacitor cannot instantly track the input signal and the capacitor can not instantly be isolated from the input signal.
1896:
873:
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
413:
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
1279:
operations can have very high dynamic range, consequently it is common to perform mixing and mastering operations at 32-bit precision and then convert to 16- or 24-bit for distribution.
674:
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 of
2804:
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.
1444:
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).
619:
results from the fact that the sample is obtained as a time average within a sampling region, rather than just being equal to the signal value at the sampling instant. In a
605:. Some amount of aliasing is inevitable because only theoretical, infinitely long, functions can have no frequency content above the Nyquist frequency. Aliasing can be made
2009:
1668:
1513:
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,
579:. 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.
318:
536:
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2089:
1295:, 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 all
501:
277:
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591:(ADC), a device with various physical limitations. This results in deviations from the theoretically perfect reconstruction, collectively referred to as
2675:
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.
2525:
H.O. Johansson and C. Svensson, "Time resolution of NMOS sampling switches", IEEE J. Solid-State
Circuits Volume: 33, Issue: 2, pp. 237–245, Feb 1998.
2609:
2642:
AES5-2008: AES recommended practice for professional digital audio – Preferred sampling frequencies for applications employing pulse-code modulation
732:
frequencies are inaudible to humans, recording and mixing at higher sampling rates is effective in eliminating the distortion that can be caused by
2216:
728:
There has been an industry trend towards sampling rates well beyond the basic requirements: such as 96 kHz and even 192 kHz Even though
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1418:
1334:
157:
be a continuous function (or "signal") to be sampled, and let sampling be performed by measuring the value of the continuous function every
2248:
Even higher DSD sampling rates exist, but the benefits of those are likely imperceptible, and the size of those files would be humongous.
1610:
336:
1628:) is the simultaneous sampling of two different, but related, waveforms, resulting in pairs of samples that are subsequently treated as
2663:
986:
video recorder) and cover the 20 kHz bandwidth thought necessary to match professional analog recording equipment of the time. A
3069:
2788:
982:
because it could be recorded on modified video equipment running at either 25 frames per second (PAL) or 30 frame/s (using an NTSC
839:
One quarter the sampling rate of audio CDs; used for lower-quality PCM, MPEG audio and for audio analysis of subwoofer bandpasses.
2510:
1706:
3090:
862:
2923:
2181:
721:. Sampling rates higher than about 50 kHz to 60 kHz cannot supply more usable information for human listeners. Early
1830:
2977:
3072: – an interactive presentation in a web-demo at the Institute of Telecommunications, University of Stuttgart
3135:
2883:
Supported sampling rates: 44.1 kHz, 48 kHz, 64 kHz, 88.2 kHz, 96 kHz, 176.4 kHz, 192 kHz
120:
2408:
1564:
of the high-frequency signal. That is often done purposefully in such a way that the lowest-frequency alias satisfies the
1451:, a different sampling process occurs, this time at the pixel frequency, corresponding to a spatial sampling rate along
744:
the fidelity. One advantage of higher sampling rates is that they can relax the low-pass filter design requirements for
3335:
3083:
3038:
2571:
2499:
2177:
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such as when recording music or many types of acoustic events, audio waveforms are typically sampled at 44.1 kHz (
17:
1478:. The sampling rates and resolutions in both spatial directions can be measured in units of lines per picture height.
3125:
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that are modulated (multiplied) by the sample values. When the time interval between adjacent samples is a constant
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3280:
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Oversampling is used in most modern analog-to-digital converters to reduce the distortion introduced by practical
3221:
826:
717:), 48 kHz, 88.2 kHz, or 96 kHz. The approximately double-rate requirement is a consequence of the
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616:
3011:
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2157:
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effects of the mapping of input voltage to converted output value (in addition to the effects of quantization).
49:) is represented with a green colored line while the discrete samples are indicated by the blue vertical lines.
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1121:
recorders and other professional applications for CD production. Four times the frequency of 44.1 kHz.
1522:
905:
818:
736:. Conversely, ultrasonic sounds may interact with and modulate the audible part of the frequency spectrum (
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125:
Functions of space, time, or any other dimension can be sampled, and similarly in two or more dimensions.
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1602:
1441:
749:
745:
588:
3340:
3215:
3192:
2950:"MT-001: Taking the Mystery out of the Infamous Formula, "SNR=6.02N + 1.76dB," and Why You Should Care"
1518:
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produces samples equivalent to the instantaneous value of the continuous signal at the desired points.
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2282:, which is unambiguous because of the constraint that the pre-sampled signal was analytic. Also see
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31:
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1976:
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377:. Mathematically, the modulated Dirac comb is equivalent to the product of the comb function with
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1327:
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equipment manufacturers chose sampling rates in the region of 40 to 50 kHz for this reason.
444:
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912:
digital audio, used alongside analogue television sound in some countries. High-quality digital
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contains frequency components whose cycle length (period) is less than 2 sample intervals (see
282:
62:
3001:
2587:
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1824:
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at 16× the rate of the SACD. Used in rare experimental DSD recorders. Also known as DSD1024.
1235:
1223:
1211:
1199:
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Audio is typically recorded at 8-, 16-, and 24-bit depth, which yield a theoretical maximum
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2014:
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indicate how identical spectral results are created by the aliases of the sampling process.
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1226:
at 8× the rate of the SACD. Used in rare experimental DSD recorders. Also known as DSD512.
765:
649:
limit error, caused by the inability of the ADC input value to change sufficiently rapidly.
479:
335:
Reconstructing a continuous function from samples is done by interpolation algorithms. The
255:
191:
66:
2122:
1788:, whose Fourier transform is zero for all negative values of frequency. In that case, the
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Spatial sampling in the other direction is determined by the spacing of scan lines in the
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380:
131:
8:
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Supported sample frequencies: Internally 32, 44.1, 48, 64, 88.2, 96, 176.4, 192 kHz.
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limits the true number of bits that can be used in quantization. Few analog systems have
913:
800:
459:
350:
1803:
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video signals (3 samples per line, 245 lines per field, 59.94 fields per second = 29.97
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3227:
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1901:
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as a consequence of the finite precision of words that represent the converted values.
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When it is necessary to capture audio covering the entire 20–20,000 Hz range of
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1568:, because the bandpass signal is still uniquely represented and recoverable. Such
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video tapes using 3 samples per line, 588 lines per frame, 25 frames per second.
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For example, "number of samples" in signal processing is roughly equivalent to "
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1034:
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would fit digital audio samples into the analog video channel of, for example,
678:. The non-linearities of either ADC or DAC are analyzed by replacing the ideal
640:
103:
The original signal can be reconstructed from a sequence of samples, up to the
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1214:
at 4× the rate of the SACD. Used in some uncommon professional DSD recorders.
3329:
3309:
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1918:, because all of its non-zero frequency content is shifted into the interval
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1267:, 98.09 dB and 122.17 dB. CD quality audio uses 16-bit samples.
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987:
3314:
2610:"The Science of Sample Rates (When Higher Is Better—And When It Isn't)"
2191:
2167:
1414:
1410:
1341: in this section. Unsourced material may be challenged and removed.
1022:
854:
729:
659:
592:
374:
70:
2535:
D'Ambrose, Christoper; Choudhary, Rizwan (2003). Elert, Glenn (ed.).
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at 2× the rate of the SACD. Used in some professional DSD recorders.
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893:
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1560:, the samples are indistinguishable from samples of a low-frequency
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is not suited for editing. 8 times the frequency of 44.1 kHz.
959:
847:
602:
3031:
Physically Based
Rendering: From Theory to Implementation, 3rd ed.
37:
1292:
1264:
1187:
1049:
First commercial digital audio recorders from the late 70s from
279:, is the average number of samples obtained in one second, thus
3045:) is nicely written with diagrams, core theory and code sample.
1373:
1141:
1137:
1106:
1102:
963:
889:
874:
630:
78:
2091:, through a digital low-pass filter whose cutoff frequency is
1077:
Uncommonly used, but supported by some hardware and software.
81:
at a point in time and/or space; this definition differs from
2775:"Cisco VoIP Phones, Networking and Accessories - VoIP Supply"
1510:
1456:
1399:
1395:
1300:
909:
897:
453:
325:
1777:{\displaystyle s_{a}(t)\triangleq s(t)+i\cdot {\hat {s}}(t)}
406:. That mathematical abstraction is sometimes referred to as
1433:
1391:
1377:
1287:
Speech signals, i.e., signals intended to carry only human
1183:
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979:
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939:
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1426:
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is a subsystem or operation that extracts samples from a
3063: – a page trying to answer the question
1891:{\displaystyle s_{a}(t)\cdot e^{-i2\pi {\frac {B}{2}}t}}
1291:, can usually be sampled at a much lower rate. For most
3055:
2999:
1050:
587:
In practice, the continuous signal is sampled using an
2895:
Cristina
Bachmann, Heiko Bischoff; Schütte, Benjamin.
2534:
2257:
Sample-pairs are also sometimes viewed as points on a
771:
A more complete list of common audio sample rates is:
633:
or deviation from the precise sample timing intervals.
185:. Then the sampled function is given by the sequence:
41:
Signal sampling representation. The continuous signal
2924:"M Track 2x2M Cubase Pro 9 can ́t change Sample Rate"
2440:. Springer International Publishing AG. p. 459.
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2017:
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transmission; adequate for human speech but without
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2140:
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2003:
1961:
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598:Various types of distortion can occur, including:
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27:Measurement of a signal at discrete time intervals
896:, video tapes with extra channels of audio (e.g.
3327:
2278:, for instance, will have an alias at −0.4
2762:88.2 kHz or 96 kHz should be adopted.
1409:, the temporal sampling rate is defined as the
107:, by passing the sequence of samples through a
2566:. Taylor & Francis US. pp. 200, 446.
2406:
373:, the sequence of delta functions is called a
3105:
3091:
3029:Matt Pharr, Wenzel Jakob and Greg Humphreys,
1525:(PET) are some examples. It is also used for
2498:, "Communication in the presence of noise",
2965:
2689:"The Optimal Sample Rate for Quality Audio"
2664:"The Optimal Sample Rate for Quality Audio"
2433:
1432:60 / 1.001 Hz ~= 59.94 Hz –
1417: – rather than the notional
582:
3098:
3084:
2437:Rudiments of Signal Processing and Systems
1792:for a waveform with no frequencies ≥
1303:sampling and quantization specifications.
69:. A common example is the conversion of a
2754:
2303:) is sampled at the Nyquist frequency (1/
2148:waveform can be recovered, if necessary.
1823:(real samples/sec). More apparently, the
1357:Learn how and when to remove this message
448:). The corresponding frequency limit, in
339:is mathematically equivalent to an ideal
2607:
1531:
1384:625-line) for the visible picture area.
1380:525-line) or 720 by 576 pixels (UK
85:, which refers to a set of such values.
36:
2635:
2633:
2502:, vol. 37, no.1, pp. 10–21, Jan. 1949.
2475:. Prentice-Hall Of India Pvt. Limited.
2468:
1611:Whittaker–Shannon interpolation formula
337:Whittaker–Shannon interpolation formula
128:For functions that vary with time, let
14:
3328:
2969:Mixed-signal and DSP design techniques
2817:"Zaxcom digital wireless transmitters"
2744:
2311:), the product sequence simplifies to
2011:, by processing the product sequence,
1402:(progressive, also known as Full-HD).
1275:(SNR) exceeding 120 dB. However,
3079:
2661:
2608:Colletti, Justin (February 4, 2013).
2791:. Restoring78s.co.uk. Archived from
2789:"The restoration procedure – part 1"
2630:
2559:
2274:, a frequency component at 0.6
1339:adding citations to reliable sources
1310:
328:, for example 48 kHz is 48,000
2427:
1616:
1372:(SDTV) uses either 720 by 480
857:8,000 Hz. Used in most modern
24:
3056:Journal devoted to Sampling Theory
3033:, Morgan Kaufmann, November 2016.
3023:
2537:"Frequency range of human hearing"
2500:Proc. Institute of Radio Engineers
2410:Communications Standard Dictionary
2178:In-phase and quadrature components
1800:(complex samples/sec), instead of
1609:instead of idealizations like the
1556:signal is sampled slower than its
1447:When analog video is converted to
1282:
1257:signal-to-quantization-noise ratio
850:frequency extension over standard
756:this advantage is less important.
639:, including thermal sensor noise,
613:order of the anti-aliasing filter.
25:
3352:
3049:
2747:Coding High Quality Digital Audio
2715:
2686:
2645:, Audio Engineering Society, 2008
2284:Aliasing § Complex sinusoids
1306:
1155:, used for recording and editing
1140:(Blu-ray Disc) audio tracks, and
694:
3136:Nyquist–Shannon sampling theorem
3000:William Morris Hartmann (1997).
2270:When the complex sample-rate is
1586:direct IF to digital conversion.
1541:
1413: – or rather the
1315:
938:Used by digital audio locked to
121:Nyquist–Shannon sampling theorem
3222:Discrete-time Fourier transform
2993:
2959:
2942:
2916:
2888:
2861:
2834:
2809:
2781:
2767:
2738:
2709:
2680:
2655:
2601:
2380:
2289:
2264:
2251:
2242:
1703:, the complex-valued function,
1590:
1493:video components shows up as a
1326:needs additional citations for
962:, also most commonly used with
752:, but with modern oversampling
689:
2911:Common Sample Rates: 64 000 Hz
2580:
2553:
2528:
2519:
2489:
2462:
2400:
2351:
2341:
2335:
2326:
2229:
2158:Crystal oscillator frequencies
2135:
2129:
2035:
2026:
1998:
1992:
1986:
1956:
1925:
1850:
1844:
1771:
1765:
1759:
1741:
1735:
1726:
1720:
1690:
1684:
1657:
1651:
1645:
1500:
1370:Standard-definition television
1263:of, approximately, 49.93
1029:, and films. The professional
900:with four channels of audio),
558:
552:
429:
423:
393:
387:
360:
354:
207:
198:
144:
138:
83:the term's usage in statistics
73:to a sequence of "samples". A
13:
1:
3167:Statistical signal processing
3003:Signals, Sound, and Sensation
2504:Reprint as classic paper in:
2394:
2004:{\displaystyle {\hat {s}}(t)}
1898:, also has a Nyquist rate of
1663:{\displaystyle {\hat {s}}(t)}
1105:(Blu-ray Disc) audio tracks,
343:whose input is a sequence of
177:seconds, which is called the
2897:"Customize Sample Rate Menu"
2819:. Zaxcom.com. Archived from
2508:, Vol. 86, No. 2, (Feb 1998)
1825:equivalent baseband waveform
1603:digital-to-analog converters
1523:positron emission tomography
1442:digital-to-analog converters
1244:
7:
3041:. The chapter on sampling (
2563:Audio Engineering Explained
2151:
1234:Sexdecuple-Rate DSD, 1-bit
1161:Direct Stream Digital (DSD)
589:analog-to-digital converter
575:, functionally known as an
571:is usually the output of a
542:of the sampler. Therefore,
324:, sometimes referred to as
10:
3357:
3216:Discrete Fourier transform
3193:Matched Z-transform method
3070:Sampling of analog signals
2873:www.pioneer-audiovisual.eu
2842:"RME: Hammerfall DSP 9632"
2745:Stuart, J. Robert (1998).
2662:Lavry, Dan (May 3, 2012).
1594:
1545:
1519:magnetic resonance imaging
1388:High-definition television
1248:
1153:Digital eXtreme Definition
1065:Sampling rate used by the
916:. Suitable for digitizing
738:intermodulation distortion
118:
29:
3336:Digital signal processing
3261:
3210:Discrete cosine transform
3175:
3144:
3113:
3107:Digital signal processing
2446:10.1007/978-3-030-76947-5
2173:Multidimensional sampling
1515:X-ray computed tomography
1277:digital signal processing
1002:world's first commercial
906:Digitales Satellitenradio
761:Audio Engineering Society
313:{\displaystyle f_{s}=1/T}
114:
32:Sampling (disambiguation)
3243:Post's inversion formula
3157:Digital image processing
2614:Trust Me I'm a Scientist
2222:
1529:and other applications.
1222:Octuple-Rate DSD, 1-bit
1069:digital audio recorder.
1031:serial digital interface
978:). Originally chosen by
865:communication products.
682:mapping with a proposed
583:Practical considerations
220:, for integer values of
3152:Audio signal processing
2718:"To mix at 96k or not?"
2407:Martin H. Weik (1996).
1796:can be reduced to just
1674:of the other waveform,
1299:systems, which use the
1198:Double-Rate DSD, 1-bit
766:anti-aliasing filtering
531:{\displaystyle f_{s}/2}
2972:. Newnes. p. 20.
2560:Self, Douglas (2012).
2372:
2371:{\displaystyle \left.}
2187:Sample rate conversion
2142:
2113:
2085:
2005:
1963:
1912:
1892:
1817:
1778:
1697:
1664:
1538:
1273:signal to noise ratios
1176:delta-sigma modulation
1117:Sampling rate used by
754:delta-sigma-converters
565:
532:
497:
470:
436:
400:
367:
314:
273:
234:
214:
171:
151:
63:continuous-time signal
61:is the reduction of a
50:
2901:Steinberg WaveLab Pro
2869:"SX-S30DAB | Pioneer"
2671:Lavry Engineering Inc
2373:
2259:constellation diagram
2143:
2114:
2086:
2084:{\displaystyle \left}
2006:
1964:
1913:
1893:
1818:
1779:
1698:
1665:
1632:. When one waveform,
1535:
1509:samples a 3D grid of
1463:13.5 MHz –
1236:Direct Stream Digital
1224:Direct Stream Digital
1212:Direct Stream Digital
1210:Quad-Rate DSD, 1-bit
1200:Direct Stream Digital
1180:Direct Stream Digital
904:(LP mode), Germany's
704:pulse-code modulation
566:
533:
498:
496:{\displaystyle f_{s}}
471:
437:
401:
368:
345:Dirac delta functions
315:
274:
272:{\displaystyle f_{s}}
235:
215:
213:{\displaystyle s(nT)}
172:
152:
109:reconstruction filter
40:
3276:Anti-aliasing filter
3205:Constant-Q transform
3188:Advanced z-transform
3061:I/Q Data for Dummies
2966:Walt Kester (2003).
2541:The Physics Factbook
2434:Tom J. Moir (2022).
2315:
2217:Normalized frequency
2141:{\displaystyle s(t)}
2123:
2095:
2015:
1977:
1922:
1902:
1831:
1804:
1707:
1696:{\displaystyle s(t)}
1678:
1636:
1335:improve this article
914:wireless microphones
666:Although the use of
577:anti-aliasing filter
564:{\displaystyle s(t)}
546:
507:
480:
476:cycle/sample ×
460:
435:{\displaystyle s(t)}
417:
399:{\displaystyle s(t)}
381:
351:
283:
256:
224:
192:
161:
150:{\displaystyle s(t)}
132:
67:discrete-time signal
30:For other uses, see
2588:"Digital Pro Sound"
2472:Signals and Systems
2112:{\displaystyle B/2}
1231:45,158,400 Hz
1219:22,579,200 Hz
1207:11,289,600 Hz
801:wireless microphone
658:Error due to other
469:{\displaystyle 0.5}
366:{\displaystyle (T)}
3233:Integral transform
3228:Impulse invariance
3200:Bilinear transform
2513:2010-02-08 at the
2368:
2138:
2109:
2081:
2001:
1959:
1908:
1888:
1816:{\displaystyle 2B}
1813:
1774:
1693:
1660:
1539:
1527:seismic tomography
1485:of high-frequency
1459:sampling rate is:
1425:50 Hz –
1398:(interlaced), and
1259:(SQNR) for a pure
1195:5,644,800 Hz
1182:, co-developed by
1168:2,822,400 Hz
1006:sound recorder by
723:professional audio
684:nonlinear function
676:low-pass filtering
611:sufficiently large
561:
528:
493:
466:
432:
396:
363:
330:samples per second
322:samples per second
310:
269:
246:sampling frequency
230:
210:
167:
147:
77:is a value of the
51:
18:Sampling frequency
3341:Signal processing
3323:
3322:
3248:Starred transform
3238:Laplace transform
3162:Speech processing
3131:Estimation theory
2979:978-0-7506-7611-3
2066:
1989:
1911:{\displaystyle B}
1881:
1762:
1672:Hilbert transform
1648:
1617:Complex sampling
1578:harmonic sampling
1574:bandpass sampling
1572:is also known as
1566:Nyquist criterion
1367:
1366:
1359:
1242:
1241:
1178:process known as
1039:digital recording
947:frames per second
797:wireless intercom
734:foldback aliasing
607:arbitrarily small
540:Nyquist frequency
503:samples/second =
450:cycles per second
233:{\displaystyle n}
179:sampling interval
170:{\displaystyle T}
94:continuous signal
55:signal processing
16:(Redirected from
3348:
3121:Detection theory
3100:
3093:
3086:
3077:
3076:
3043:available online
3018:
3017:
2997:
2991:
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2988:
2986:
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2957:
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2940:
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2935:
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2914:
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2908:
2907:
2892:
2886:
2885:
2880:
2879:
2865:
2859:
2858:
2853:
2852:
2846:www.rme-audio.de
2838:
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2551:
2550:
2548:
2547:
2532:
2526:
2523:
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2493:
2487:
2486:
2469:Rao, R. (2008).
2466:
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2459:
2431:
2425:
2424:
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2388:
2384:
2378:
2377:
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2360:
2359:
2358:
2293:
2287:
2268:
2262:
2255:
2249:
2246:
2240:
2239:" in statistics.
2233:
2147:
2145:
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2115:
2110:
2105:
2090:
2088:
2087:
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2074:
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2059:
2010:
2008:
2007:
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1991:
1990:
1982:
1968:
1966:
1965:
1962:{\displaystyle }
1960:
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1702:
1700:
1699:
1694:
1669:
1667:
1666:
1661:
1650:
1649:
1641:
1622:Complex sampling
1507:volume rendering
1362:
1355:
1351:
1348:
1342:
1319:
1311:
1149:352,800 Hz
1126:192,000 Hz
1114:176,400 Hz
830:
822:
774:
773:
570:
568:
567:
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467:
441:
439:
438:
433:
408:impulse sampling
405:
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372:
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364:
320:, with the unit
319:
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156:
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148:
96:. A theoretical
21:
3356:
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3349:
3347:
3346:
3345:
3326:
3325:
3324:
3319:
3257:
3171:
3140:
3126:Discrete signal
3109:
3104:
3052:
3026:
3024:Further reading
3021:
3014:
2998:
2994:
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2982:
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2964:
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2815:
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2810:
2798:
2796:
2787:
2786:
2782:
2773:
2772:
2768:
2756:10.1.1.501.6731
2743:
2739:
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2724:
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2710:
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2695:
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2681:
2666:
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2592:
2590:
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2585:
2581:
2574:
2558:
2554:
2545:
2543:
2533:
2529:
2524:
2520:
2515:Wayback Machine
2494:
2490:
2483:
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2397:
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2294:
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2256:
2252:
2247:
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2234:
2230:
2225:
2197:Sample and hold
2154:
2124:
2121:
2120:
2101:
2096:
2093:
2092:
2058:
2045:
2041:
2022:
2018:
2016:
2013:
2012:
1981:
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1934:
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1873:
1860:
1856:
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1834:
1832:
1829:
1828:
1805:
1802:
1801:
1786:analytic signal
1784:, is called an
1754:
1753:
1714:
1710:
1708:
1705:
1704:
1679:
1676:
1675:
1640:
1639:
1637:
1634:
1633:
1630:complex numbers
1619:
1607:zero-order hold
1599:
1593:
1550:
1544:
1505:The process of
1503:
1394:(progressive),
1363:
1352:
1346:
1343:
1332:
1320:
1309:
1285:
1283:Speech sampling
1253:
1251:Audio bit depth
1247:
1157:Super Audio CDs
1091:96,000 Hz
1082:88,200 Hz
1074:64,000 Hz
1067:Mitsubishi X-80
1062:50,400 Hz
1046:50,000 Hz
1035:mixing consoles
1008:Nippon Columbia
999:47,250 Hz
935:44,056 Hz
925:37,800 Hz
886:32,000 Hz
870:22,050 Hz
844:16,000 Hz
836:11,025 Hz
719:Nyquist theorem
697:
692:
680:linear function
625:sample and hold
585:
573:low-pass filter
547:
544:
543:
538:, known as the
520:
514:
510:
508:
505:
504:
487:
483:
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478:
477:
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418:
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341:low-pass filter
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193:
190:
189:
183:sampling period
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3128:
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3117:
3115:
3111:
3110:
3103:
3102:
3095:
3088:
3080:
3074:
3073:
3067:
3058:
3051:
3050:External links
3048:
3047:
3046:
3039:978-0128006450
3025:
3022:
3020:
3019:
3012:
2992:
2978:
2958:
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2679:
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2579:
2573:978-0240812731
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1618:
1615:
1595:Main article:
1592:
1589:
1546:Main article:
1543:
1540:
1502:
1499:
1472:
1471:
1438:
1437:
1430:
1365:
1364:
1323:
1321:
1314:
1308:
1307:Video sampling
1305:
1284:
1281:
1246:
1243:
1240:
1239:
1232:
1228:
1227:
1220:
1216:
1215:
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1018:
1016:48,000 Hz
1012:
1011:
1000:
996:
995:
957:
955:44,100 Hz
951:
950:
936:
932:
931:
926:
922:
921:
892:digital video
887:
883:
882:
871:
867:
866:
845:
841:
840:
837:
833:
832:
791:and encrypted
786:
785:8,000 Hz
782:
781:
778:
777:Sampling rate
696:
695:Audio sampling
693:
691:
688:
664:
663:
656:
650:
644:
641:analog circuit
634:
628:
617:Aperture error
614:
584:
581:
560:
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551:
527:
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431:
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26:
9:
6:
4:
3:
2:
3353:
3342:
3339:
3337:
3334:
3333:
3331:
3316:
3313:
3311:
3310:Undersampling
3308:
3306:
3305:Sampling rate
3303:
3301:
3298:
3296:
3293:
3291:
3287:
3284:
3282:
3279:
3277:
3274:
3272:
3269:
3268:
3266:
3264:
3260:
3254:
3253:Zak transform
3251:
3249:
3246:
3244:
3241:
3239:
3236:
3234:
3231:
3229:
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3223:
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3108:
3101:
3096:
3094:
3089:
3087:
3082:
3081:
3078:
3071:
3068:
3066:
3065:Why I/Q Data?
3062:
3059:
3057:
3054:
3053:
3044:
3040:
3036:
3032:
3028:
3027:
3015:
3009:
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2912:
2902:
2898:
2891:
2884:
2874:
2870:
2864:
2857:
2847:
2843:
2837:
2823:on 2011-02-09
2822:
2818:
2812:
2805:
2795:on 2009-09-14
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2507:
2501:
2497:
2496:C. E. Shannon
2492:
2484:
2482:9788120338593
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2455:9783030769475
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1654:
1642:
1631:
1627:
1623:
1614:
1612:
1608:
1604:
1598:
1588:
1587:
1583:
1579:
1575:
1571:
1570:undersampling
1567:
1563:
1559:
1555:
1549:
1548:Undersampling
1542:Undersampling
1534:
1530:
1528:
1524:
1520:
1516:
1512:
1508:
1498:
1496:
1495:moiré pattern
1492:
1488:
1484:
1479:
1477:
1470:
1466:
1462:
1461:
1460:
1458:
1454:
1450:
1449:digital video
1445:
1443:
1435:
1431:
1428:
1424:
1423:
1422:
1420:
1416:
1412:
1408:
1407:digital video
1403:
1401:
1397:
1393:
1389:
1385:
1383:
1379:
1375:
1371:
1361:
1358:
1350:
1340:
1336:
1330:
1329:
1324:This section
1322:
1318:
1313:
1312:
1304:
1302:
1298:
1294:
1290:
1280:
1278:
1274:
1270:
1269:Thermal noise
1266:
1262:
1258:
1252:
1237:
1233:
1230:
1229:
1225:
1221:
1218:
1217:
1213:
1209:
1206:
1205:
1201:
1197:
1194:
1193:
1189:
1185:
1181:
1177:
1173:
1170:
1167:
1166:
1162:
1158:
1154:
1151:
1148:
1147:
1143:
1139:
1135:
1131:
1128:
1125:
1124:
1120:
1116:
1113:
1112:
1108:
1104:
1100:
1096:
1093:
1090:
1089:
1084:
1081:
1080:
1076:
1073:
1072:
1068:
1064:
1061:
1060:
1056:
1052:
1048:
1045:
1044:
1040:
1036:
1032:
1028:
1024:
1019:
1017:
1014:
1013:
1009:
1005:
1001:
998:
997:
993:
989:
985:
981:
977:
973:
969:
965:
961:
958:
956:
953:
952:
948:
944:
941:
937:
934:
933:
930:
927:
924:
923:
919:
915:
911:
907:
903:
899:
895:
891:
888:
885:
884:
880:
876:
872:
869:
868:
864:
860:
856:
853:
849:
846:
843:
842:
838:
835:
834:
828:
820:
814:
810:
806:
802:
798:
794:
793:walkie-talkie
790:
787:
784:
783:
779:
776:
775:
772:
769:
767:
762:
757:
755:
751:
747:
743:
739:
735:
731:
726:
724:
720:
716:
712:
711:human hearing
707:
705:
701:
700:Digital audio
687:
685:
681:
677:
672:
669:
661:
657:
654:
651:
648:
645:
642:
638:
635:
632:
629:
626:
622:
618:
615:
612:
608:
604:
601:
600:
599:
596:
594:
590:
580:
578:
574:
555:
549:
541:
525:
521:
515:
511:
488:
484:
463:
455:
451:
447:
446:
426:
420:
411:
409:
390:
384:
376:
357:
346:
342:
338:
333:
331:
327:
323:
307:
303:
299:
296:
291:
287:
264:
260:
251:
250:sampling rate
247:
227:
204:
201:
195:
188:
187:
186:
184:
180:
164:
141:
135:
126:
122:
112:
110:
106:
105:Nyquist limit
101:
99:
98:ideal sampler
95:
91:
86:
84:
80:
76:
72:
68:
64:
60:
56:
48:
44:
39:
33:
19:
3300:Quantization
3295:Oversampling
3286:Nyquist rate
3281:Downsampling
3262:
3064:
3030:
3006:. Springer.
3002:
2995:
2983:. Retrieved
2968:
2961:
2944:
2937:
2931:. Retrieved
2927:
2918:
2910:
2904:. Retrieved
2900:
2890:
2882:
2876:. Retrieved
2872:
2863:
2855:
2849:. Retrieved
2845:
2836:
2825:. Retrieved
2821:the original
2811:
2803:
2797:. Retrieved
2793:the original
2783:
2769:
2760:
2746:
2740:
2731:
2725:. Retrieved
2721:
2716:Lavry, Dan.
2711:
2702:
2696:. Retrieved
2692:
2687:Lavry, Dan.
2682:
2674:
2670:
2657:
2647:, retrieved
2641:
2624:
2617:. Retrieved
2613:
2603:
2591:. Retrieved
2582:
2562:
2555:
2544:. Retrieved
2540:
2530:
2521:
2505:
2491:
2471:
2464:
2436:
2429:
2413:. Springer.
2409:
2402:
2382:
2308:
2304:
2300:
2296:
2291:
2279:
2275:
2271:
2266:
2253:
2244:
2231:
2202:Beta encoder
2163:Downsampling
1971:
1797:
1793:
1790:Nyquist rate
1626:I/Q sampling
1625:
1621:
1620:
1605:, such as a
1600:
1597:Oversampling
1591:Oversampling
1585:
1581:
1577:
1573:
1558:Nyquist rate
1551:
1504:
1480:
1473:
1446:
1439:
1404:
1390:(HDTV) uses
1386:
1368:
1353:
1344:
1333:Please help
1328:verification
1325:
1286:
1254:
1136:DVD tracks,
1101:DVD tracks,
983:
942:
812:
811:sounds like
808:
770:
758:
741:
727:
708:
698:
690:Applications
673:
668:oversampling
665:
653:Quantization
643:noise, etc..
597:
586:
576:
449:
443:
412:
407:
334:
329:
321:
249:
245:
243:
182:
178:
127:
124:
102:
97:
89:
87:
74:
58:
52:
46:
42:
3183:Z-transform
2733:accurately.
2619:February 6,
2237:sample size
2207:Kell factor
1582:IF sampling
1501:3D sampling
1455:. A common
1419:pixel clock
1159:, as 1-bit
1055:Soundstream
988:PCM adaptor
929:CD-XA audio
609:by using a
3330:Categories
3315:Upsampling
3176:Techniques
3145:Sub-fields
3013:1563962837
2933:2018-12-18
2906:2018-12-18
2878:2018-12-18
2851:2018-12-18
2827:2011-01-18
2799:2011-01-18
2727:2018-11-10
2698:2018-11-10
2649:2010-01-18
2546:2022-01-22
2506:Proc. IEEE
2420:0412083914
2395:References
2192:Digitizing
2168:Upsampling
1517:(CT/CAT),
1453:scan lines
1415:field rate
1411:frame rate
1249:See also:
1023:digital TV
984:monochrome
855:narrowband
730:ultrasonic
660:non-linear
593:distortion
375:Dirac comb
119:See also:
71:sound wave
3290:frequency
2985:8 January
2751:CiteSeerX
2722:Gearslutz
2693:Gearslutz
2593:8 January
2345:−
2339:⋅
2056:π
2047:−
2039:⋅
1987:^
1929:−
1871:π
1862:−
1854:⋅
1760:^
1751:⋅
1730:≜
1670:, is the
1646:^
1347:June 2007
1297:telephony
1261:sine wave
1245:Bit depth
1130:DVD-Audio
1095:DVD-Audio
1041:devices.
894:camcorder
852:telephone
805:sibilance
789:Telephone
742:degrading
647:Slew rate
621:capacitor
3271:Aliasing
3263:Sampling
2511:Archived
2387:outputs.
2212:Bit rate
2182:I/Q data
2152:See also
1554:bandpass
1483:aliasing
1481:Spatial
1469:D1 video
1465:CCIR 601
1293:phonemes
1174:, 1-bit
1010:(Denon)
960:Audio CD
918:FM radio
879:AM Radio
848:Wideband
603:Aliasing
445:Aliasing
59:sampling
2928:M-Audio
2704:margin.
1552:When a
1521:(MRI),
1188:Philips
1132:, some
1097:, some
966:audio (
623:-based
90:sampler
3224:(DTFT)
3114:Theory
3037:
3010:
2976:
2753:
2570:
2479:
2452:
2417:
1584:, and
1511:voxels
1491:chroma
1476:raster
1440:Video
1374:pixels
1289:speech
1142:HD DVD
1138:BD-ROM
1107:HD DVD
1103:BD-ROM
1037:, and
964:MPEG-1
890:miniDV
631:Jitter
456:), is
115:Theory
79:signal
75:sample
3218:(DFT)
3212:(DCT)
2953:(PDF)
2667:(PDF)
2295:When
2223:Notes
1562:alias
1457:pixel
1436:video
1429:video
1400:1080p
1396:1080i
1301:G.711
943:color
910:NICAM
898:DVCAM
863:VVoIP
702:uses
637:Noise
454:hertz
326:hertz
65:to a
3035:ISBN
3008:ISBN
2987:2014
2974:ISBN
2621:2013
2595:2014
2568:ISBN
2477:ISBN
2450:ISBN
2415:ISBN
2180:and
1624:(or
1487:luma
1434:NTSC
1392:720p
1378:NTSC
1376:(US
1186:and
1184:Sony
1172:SACD
1134:LPCM
1119:HDCD
1099:LPCM
1053:and
980:Sony
972:SVCD
940:NTSC
877:and
861:and
859:VoIP
831:)).
799:and
780:Use
759:The
750:DACs
748:and
746:ADCs
244:The
2442:doi
2307:= 2
1489:or
1427:PAL
1405:In
1382:PAL
1337:by
1027:DVD
1004:PCM
992:PAL
976:MP3
968:VCD
949:).
902:DAT
875:78s
813:eff
809:ess
740:),
464:0.5
248:or
181:or
53:In
3332::
3288:/
2936:.
2926:.
2909:.
2899:.
2881:.
2871:.
2854:.
2844:.
2802:.
2759:.
2749:.
2730:.
2720:.
2701:.
2691:.
2673:.
2669:.
2632:^
2623:.
2612:.
2539:.
2448:.
1969:.
1827:,
1613:.
1580:,
1576:,
1497:.
1467:,
1265:dB
1190:.
1057:.
1051:3M
1025:,
974:,
970:,
920:.
908:,
881:.
823:,
795:,
715:CD
686:.
595:.
410:.
332:.
252:,
111:.
88:A
57:,
3099:e
3092:t
3085:v
3016:.
2989:.
2955:.
2830:.
2777:.
2597:.
2576:.
2549:.
2485:.
2458:.
2444::
2423:.
2366:.
2362:]
2356:n
2352:)
2348:i
2342:(
2336:)
2333:T
2330:n
2327:(
2324:s
2320:[
2309:B
2305:T
2301:t
2299:(
2297:s
2286:.
2280:B
2276:B
2272:B
2261:.
2136:)
2133:t
2130:(
2127:s
2107:2
2103:/
2099:B
2078:]
2072:n
2069:T
2064:2
2061:B
2053:2
2050:i
2043:e
2036:)
2033:T
2030:n
2027:(
2024:s
2020:[
1999:)
1996:t
1993:(
1984:s
1957:]
1954:2
1950:/
1946:B
1943:,
1940:2
1936:/
1932:B
1926:[
1906:B
1884:t
1879:2
1876:B
1868:2
1865:i
1858:e
1851:)
1848:t
1845:(
1840:a
1836:s
1811:B
1808:2
1798:B
1794:B
1772:)
1769:t
1766:(
1757:s
1748:i
1745:+
1742:)
1739:t
1736:(
1733:s
1727:)
1724:t
1721:(
1716:a
1712:s
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1354:(
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1345:(
1331:.
829:/
827:f
825:/
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817:/
815:(
807:(
559:)
556:t
553:(
550:s
526:2
522:/
516:s
512:f
489:s
485:f
452:(
430:)
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424:(
421:s
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391:t
388:(
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355:(
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304:/
300:1
297:=
292:s
288:f
265:s
261:f
240:.
228:n
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205:T
202:n
199:(
196:s
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145:)
142:t
139:(
136:s
47:t
45:(
43:S
34:.
20:)
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