# Dynamic range

For other uses, see Dynamic range (disambiguation).

Dynamic range, abbreviated DR or DNR,[1] is the ratio between the largest and smallest possible values of a changeable quantity, such as in signals like sound and light. It is measured as a ratio, or as a base-10 (decibel) or base-2 (doublings, bits or stops) logarithmic value.

## Dynamic range and human perception

Factor (power) Decibels Stops
1 0 0
2 3.01 1
3.16 5 1.66
4 6.02 2
5 6.99 2.32
8 9.03 3
10 10 3.32
16 12.0 4
20 13.0 4.32
31.6 15 4.98
32 15.1 5
50 17.0 5.64
100 20 6.64
1 000 30 9.97
1 024 30.1 10
10 000 40 13.3
100 000 50 16.6
1 000 000 60 19.9
1 048 576 60.2 20
100 000 000 80 26.6
1 073 741 824 90.3 30
10 000 000 000 100 33.2

The human senses of sight and hearing have a very high dynamic range. A human is capable of hearing (and usefully discerning) anything from a quiet murmur in a soundproofed room to the sound of the loudest heavy metal concert. Such a difference can exceed 100 dB which represents a factor of 100,000 in amplitude and a factor 10,000,000,000 in power.[2][3] A human can see objects in starlight (although colour differentiation is reduced at low light levels) or in bright sunlight, even though on a moonless night objects receive 1/1,000,000,000 of the illumination they would on a bright sunny day: that is a dynamic range of 90 dB.

A human cannot perform these feats of perception at both extremes of the scale at the same time. The eyes take time to adjust to different light levels and the dynamic range of the human eye in a given scene is actually quite limited due to optical glare. The instantaneous dynamic range of human audio perception is similarly subject to masking, so that, for example, a whisper cannot be heard in loud surroundings.

In practice, it is difficult to achieve the full dynamic range experienced by humans using electronic equipment. Electronically reproduced audio and video often uses some trickery to fit original material with a wide dynamic range into a narrower recorded dynamic range that can more easily be stored and reproduced: these techniques are called dynamic range compression. For example, a good quality LCD display has a dynamic range of around 1000:1 (commercially the dynamic range is often called the "contrast ratio" meaning the full-on/full-off luminance ratio), and some of the latest CMOS image sensors now have measured dynamic ranges of about 11,000:1 (reported as 13.5 stops, or doublings, equivalent to binary bits).[4] Paper reflectance can achieve a dynamic range of about 100:1.[5] Professional ENG Camcorders such as Sony Digital Betacam currently achieves dynamic ranges of greater than 90dB in audio recording.[6]

When showing a movie or a game, a display is able to show both shadowy nighttime scenes and bright outdoor sunlit scenes, but in fact the level of light coming from the display is much the same for both types of scene (perhaps different by a factor of 10). Knowing that the display does not have a huge dynamic range, the program makers do not attempt to make the nighttime scenes millions of times less bright than the daytime scenes, but instead use other cues to suggest night or day. A nighttime scene will usually contain duller colours and will often be lit with blue lighting, which reflects the way that the human eye sees colours at low light levels.

## Examples of usage

### Audio

Audio engineers often use dynamic range to describe the ratio of the amplitude of the loudest possible undistorted sine wave to the root mean square (rms) noise amplitude, say of a microphone or loudspeaker.[dubious ]

The dynamic range of human hearing is roughly 140 dB.[7][8] The dynamic range of music as normally perceived in a concert hall doesn't exceed 80 dB, and human speech is normally perceived over a range of about 40 dB.[9]

The dynamic range differs from the ratio of the maximum to minimum amplitude a given device can record, as a properly dithered recording device can record signals well below the rms noise amplitude (noise floor).

For example, if the ceiling of a device is 5V (rms) and the noise floor is 10µV (rms) then the dynamic range is 500000:1, or 114 dB:

$20 \times \log_{10} \left(\frac{5V}{10 \mu V}\right) = 20 \times \log_{10}(500000) = 20 \times 5.7 = 114 \,\mathrm{dB}$

In digital audio theory the dynamic range is limited by quantization error. The maximum achievable dynamic range for a digital audio system with Q-bit uniform quantization is calculated as the ratio of the largest sine-wave rms to rms noise is:[10]

$\mathrm{DR_{ADC}} = 20 \times \log_{10} \left(\frac{2^Q}{1}\right) = \left ( 6.02 \cdot Q \right )\ \mathrm{dB} \,\!$

The maximum achievable signal-to-noise ratio (SNR) for a digital audio system with Q-bit uniform quantization is

$\mathrm{SNR_{ADC}} = \left (1.76 + 6.02 \cdot Q \right )\ \mathrm{dB} \,\!$

The 16-bit compact disc has a theoretical dynamic range of about 96 dB[11] for a triangle wave or 98 dB for sinusoidal signals[10] (see Quantization noise model). The perceived dynamic range of 16-bit audio can be as high as 120 dB with noise-shaped dither, taking advantage of the frequency response of the human ear.[12] Digital audio with undithered 20-bit digitization is also theoretically capable of 120 dB dynamic range. Similarly, 24-bit digital audio calculates to 144 dB dynamic range.[7] All digital audio recording and playback chains include input and output converters and associated analog circuitry, significantly limiting practical dynamic range. Observed 16-bit digital audio dynamic range is about 90 dB.[11]

Dynamic range in analog audio is the difference between low-level thermal noise in the electronic circuitry and high-level signal saturation resulting in increased distortion and, if pushed higher, clipping.[13] Multiple noise processes determine the noise floor of a system. Noise can be picked up from microphone self-noise, preamp noise, wiring and interconnection noise, media noise, etc.

Early 78 rpm phonograph discs had a dynamic range of up to 40 dB,[14] soon reduced to 30 dB and worse due to wear from repeated play. Vinyl microgroove phonograph records typically yield 55-65 dB, though the first play of the higher-fidelity outer rings can achieve a dynamic range of 70 dB.[15]

German magnetic tape in 1941 was reported to have had a dynamic range of 60 dB,[16] though modern day restoration experts of such tapes note 45-50 dB as the observed dynamic range.[17] Ampex tape recorders in the 1950s achieved 60 dB in practical usage,[16] though tape formulations such as Scotch 111 boasted 68 dB dynamic range.[18] In the 1960s, improvements in tape formulation processes resulted in 7 dB greater range,[18] and Ray Dolby developed the Dolby A-Type noise reduction system that increased low- and mid-frequency dynamic range on magnetic tape by 10 dB, and high-frequency by 15 dB, using companding (compression and expansion) of four frequency bands.[19] The peak of professional analog magnetic recording tape technology reached 90 dB dynamic range in the midband frequencies at 3% distortion, or about 80 dB in practical broadband applications.[18] The Dolby SR noise reduction system gave a 20 dB further increased range resulting in 110 dB in the midband frequencies at 3% distortion.[20] Compact Cassette tape performance ranges from 50 to 56 dB depending on tape formulation, with Metal Type IV tapes giving the greatest dynamic range, and systems such as XDR, dbx and Dolby noise reduction system increasing it further. Specialized bias and record head improvements by Nakamichi and Tandberg combined with Dolby C noise reduction yielded 72 dB dynamic range for the cassette.

The rugged elements of moving-coil microphones can have a dynamic range of up to 140 dB (at increased distortion), while condenser microphones are limited by the overloading of their associated electronic circuitry.[21] Practical considerations of acceptable distortion levels in microphones combined with typical practices in a recording studio result in a useful operating range of 125 dB.[22]

In 1981, researchers at Ampex determined that a dynamic range of 118 dB on a dithered digital audio stream was necessary for subjective noise-free playback of music in quiet listening environments.[23]

Since the early 1990s, it has been recommended by several authorities, including the Audio Engineering Society, that measurements of dynamic range be made with an audio signal present, which is then filtered out to get the noise floor.[24] This avoids questionable measurements based on the use of blank media, or muting circuits.

### Electronics

Electronics engineers apply the term to:

• the ratio of a specified maximum level of a parameter, such as power, current, voltage or frequency, to the minimum detectable value of that parameter. (See Audio system measurements.)
• In a transmission system, the ratio of the overload level (the maximum signal power that the system can tolerate without distortion of the signal) to the noise level of the system.
• In digital systems or devices, the ratio of maximum and minimum signal levels required to maintain a specified bit error ratio.
• Optimization of bit width of digital data path (according to the dynamic ranges of signal) can reduce the area, cost, and power consumption of digital circuits and systems while improving their performance. Optimal bit width of digital data path is the smallest bit width that can satisfy the required signal-to-noise ratio and avoid overflow at the same time.[25][26][27][28][29][verification needed]
• In audio and electronics applications, the ratio involved is often so huge that it is converted to a logarithm and specified in decibels.

### Metrology

In metrology, such as when performed in support of science, engineering or manufacturing objectives, dynamic range refers to the range of values that can be measured by a sensor or metrology instrument. Often this dynamic range of measurement is limited at one end of the range by saturation of a sensing signal sensor or by physical limits that exist on the motion or other response capability of a mechanical indicator. The other end of the dynamic range of measurement is often limited by one or more sources of random noise or uncertainty in signal levels that may be described as the defining the sensitivity of the sensor or metrology device. When digital sensors or sensor signal converters are a component of the sensor or metrology device, the dynamic range of measurement will be also related to the number of binary digits (bits) used in a digital numeric representation in which the measured value is linearly related to the digital number. For example, a 12-bit digital sensor or converter can provide a dynamic range in which the ratio of the maximum measured value to the minimum measured value is up to 212 = 4096. With gamma correction, this limitation can be relaxed somewhat; for example, the 8-bit encoding used in sRGB image encoding represents a maximum to minimum ratio of about 3000.

Metrology systems and devices may use several basic methods to increase their basic dynamic range. These methods include averaging and other forms of filtering, repetition of measurements, nonlinear transformations to avoid saturation, etc. In more advance forms of metrology, such as multiwavelength digital holography, interferometry measurements made at different scales (different wavelengths) can be combined to retain the same low-end resolution while extending the upper end of the dynamic range of measurement by orders of magnitude.

### Music

In music, dynamic range is the difference between the quietest and loudest volume of an instrument, part or piece of music. In modern recording, this range is often limited through audio level compression, which allows for louder volume, but can make the recording sound less exciting or live.[30] Popular music typically has a dynamic range of 6 to 10 dB, with some forms of music having as little as 1 dB or as much as 15 dB.[31]

### Photography

A scene demanding high dynamic range.

Photographers use "dynamic range" for the luminance range of a scene being photographed, or the limits of luminance range that a given digital camera or film can capture, [32] or the opacity range of developed film images, or the reflectance range of images on photographic papers.

Graduated neutral density filters are used to decrease the dynamic range of scene luminance that can be captured on photographic film (or on the image sensor of a digital camera): The filter is positioned in front of the lens at the time the exposure is made; the top half is dark and the bottom half is clear. The dark area is placed over a scene's high-intensity region, such as the sky. The result is more even exposure in the focal plane, with increased detail in the shadows and low-light areas. Though this doesn't increase the fixed dynamic range available at the film or sensor, it stretches usable dynamic range in practice.[33]

The dynamic range of sensors used in digital photography is many times less than that of the human eye and generally not as wide as that of chemical photographic media. In the domain of digital imaging, algorithms have been developed to map the image differently in shadow and in highlight in order to better distribute the lighting range across the image. These techniques are known as local tone mapping, and usually involves overcoming the limited dynamic range of the sensor array by selectively combining multiple exposures of the same scene in order to retain detail in light and dark areas. The same approach has been used in chemical photography to capture an extremely wide dynamic range: A three-layer film with each underlying layer at 1/100 the sensitivity of the next higher one has, for example, been used to record nuclear-weapons tests.[34]

The most severe dynamic-range limitation in photography may not involve encoding, but rather reproduction to, say, a paper print or computer screen. In that case, not only local tone mapping, but also dynamic range adjustment can be effective in revealing detail throughout light and dark areas: The principle is the same as that of dodging and burning (using different lengths of exposures in different areas when making a photographic print) in the chemical darkroom. The principle is also similar to gain riding or automatic level control in audio work, which serves to keep a signal audible in a noisy listening environment and to avoid peak levels which overload the reproducing equipment, or which are unnaturally or uncomfortably loud.

## References

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2. ^ D. R. Campbell. "Aspects of Human Hearing". Retrieved 2011-04-21. "The dynamic range of human hearing is [approximately] 120 dB"
3. ^ "Sensitivity of Human Ear". Retrieved 2011-04-21. "The practical dynamic range could be said to be from the threshold of hearing to the threshold of pain [130 dB]"
4. ^
5. ^ "Dynamic Range in Digital Photography". Retrieved 2011-07-11.
6. ^ "Sony Product Detail Page MSWM2100/1". Sony Pro. Retrieved 2011-12-30.
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12. ^ Montgomery, Chris (March 25, 2012). "24/192 Music Downloads ...and why they make no sense". xiph.org. Retrieved 26 May 2013. "With use of shaped dither, which moves quantization noise energy into frequencies where it's harder to hear, the effective dynamic range of 16 bit audio reaches 120dB in practice, more than fifteen times deeper than the 96dB claim. 120dB is greater than the difference between a mosquito somewhere in the same room and a jackhammer a foot away.... or the difference between a deserted 'soundproof' room and a sound loud enough to cause hearing damage in seconds. 16 bits is enough to store all we can hear, and will be enough forever."
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