Question:
what does this symbol mean: μ?
Asile
2007-10-18 07:19:11 UTC
is it ohms?
Nine answers:
Gaara of the Sand
2007-10-18 07:23:08 UTC
it means micro. like kilograms's kilo and centimetre's centi.



micro is 10^-6 so 1 micrometer is 1/10^6 of a meter
marcusviii_bloodfin1
2007-10-18 08:13:43 UTC
Lower Case letter of Mu

In the system of Greek numerals it has a value of 40. Mu was derived from the Egyptian hieroglyphic symbol for water



The lower-case letter mu is used as a special symbol in many academic fields. The upper case Mu isn't generally used in this way because it is normally indistinguishable from the Latin M.



In mathematics:

the Möbius function in number theory

the population mean or expected value in probability and statistics

a measure in measure theory

In measurement:

the SI prefix micro-, which represents one millionth, or 10−6.

the micron, an old unit which corresponds to the micrometre (which is now denoted "µm")

In classical physics and engineering:

the coefficient of friction

Poisson's ratio

reduced mass in the two-body problem

permeability in electromagnetism

dynamic viscosity in fluid mechanics

In inorganic chemistry:

the prefix given in IUPAC nomenclature for a bridging ligand.

In particle physics:

the elementary particle called the muon

In Pharmacology:

an important opiate receptor

In thermodynamics:

the chemical potential of a system or component of a system.

Letters that arose from the Greek Μ include the Latin M and Cyrillic М.



That’s what I could find on a google. Warning this data is from Wikipedia so how correct it is questionable but I find Wikipedia most of the time to be a good source of info.
munoz
2017-02-17 21:45:57 UTC
1
2016-03-13 06:19:31 UTC
The Greek letter mu, the equivalent of M, in lower case.
oyyo
2007-10-18 07:52:05 UTC
no...ohm is just like a road bumper.....

This is called.... micro = 1*10^-6
-TeRenCe- -
2007-10-18 08:15:43 UTC
No.it is not ohm.

it is an unit of measurement just like kilogram(K), mega(M).

its value is 1^-6
Neo
2007-10-18 08:32:16 UTC
it's micro....0.000001.
Blondie131
2007-10-18 07:34:21 UTC
i think its mu...
The Answer Man
2007-10-18 13:21:45 UTC
Here you go read on.





μ-law algorithm

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Graph of μ-law & A-law algorithms

Graph of μ-law & A-law algorithms



The µ-law algorithm is a companding algorithm, primarily used in the digital telecommunication systems of North America, Japan and Australia. As with other companding algorithms, its purpose is to reduce the dynamic range of an audio signal. In the analog domain, this can increase the signal-to-noise ratio (SNR) achieved during transmission, and in the digital domain, it can reduce the quantization error (hence increasing signal to quantization noise ratio). These SNR increases can be traded instead for reduced bandwidth for equivalent SNR.



It is similar to the A-law algorithm used in Europe.

Contents

[hide]



* 1 Algorithm Types

o 1.1 Continuous

o 1.2 Discrete

* 2 Implementation

* 3 Usage Justification

* 4 Comparison with A-law

* 5 See also

* 6 References

* 7 External links



[edit] Algorithm Types



There are two forms of this algorithm - an analog version, and a quantized digital version.



[edit] Continuous



For a given input x, the equation for μ-law encoding is[1]



F(x) = \sgn(x) \frac{\ln(1+ \mu |x|)}{\ln(1+\mu)}~~~~-1 \leq x \leq 1,



where μ = 255 (8 bits) in the North American and Japanese standards.



μ-law expansion is then given by the inverse equation:



F^{-1}(y) = \sgn(y) (1 / \mu ) [(1 + \mu)^{|y|}- 1]~~~~-1 \leq y \leq 1



The equations are culled from Cisco's Waveform Coding Techniques.



[edit] Discrete



This is defined in ITU-T Recommendation G.711



G.711 is rather unclear about what the values at the limit of a range code up as. (e.g. whether +31 codes to 0xEF or 0xF0). However G.191 provides example C code for a u-law encoder which gives the following encoding. Note the difference between the positive and negative ranges. e.g. the negative range corresponding to +30 to +1 is -31 to -2. This is accounted for by the use of a 1's complement (simple bit inversion) rather than 2's complement to convert a negative value to a positive value during encoding.

Quantized μ-law algorithm 13 bit Binary Linear input code 8 bit Compressed code

+8158 to +4063 in 16 intervals of 256 0x80 + interval number

+4062 to +2015 in 16 intervals of 128 0x90 + interval number

+2014 to +991 in 16 intervals of 64 0xA0 + interval number

+990 to +479 in 16 intervals of 32 0xB0 + interval number

+478 to +223 in 16 intervals of 16 0xC0 + interval number

+222 to +95 in 16 intervals of 8 0xD0 + interval number

+94 to +31 in 16 intervals of 4 0xE0 + interval number

+30 to +1 in 15 intervals of 2 0xF0 + interval number

0 0xFF

-1 0x7F

-31 to -2 in 15 intervals of 2 0x70 + interval number

-95 to -32 in 16 intervals of 4 0x60 + interval number

-223 to -96 in 16 intervals of 8 0x50 + interval number

-479 to -224 in 16 intervals of 16 0x40 + interval number

-991 to -480 in 16 intervals of 32 0x30 + interval number

-2015 to -992 in 16 intervals of 64 0x20 + interval number

-4063 to -2016 in 16 intervals of 128 0x10 + interval number

-8159 to -4064 in 16 intervals of 256 0x00 + interval number



The above table is for the much more obscure 14 bit u-law encoding. The graph is identical to the standard 16 bit version, it's just scaled differently. The above 14 bit numbers can be generated by the following Java snippet.



int j = 512;

int linear = -8159;

for (int ulaw = 0; ulaw <= 127; ulaw++) {

System.out.println("ulaw " + Integer.toHexString(ulaw) + " becomes " + linear);

if ((ulaw & 0xf) == 0) j >>= 1;

linear += j;

}

j = -256;

linear = 7903;

for (int ulaw = 128; ulaw < 255; ulaw++) {

System.out.println("ulaw " + Integer.toHexString(ulaw) + " becomes " + linear);

if ((ulaw & 0xf) == 0xf) j >>= 1;

linear += j;

}

System.out.println("ulaw ff becomes 0");





Which can be used to generate a simple Java lookup array to convert from a u-law byte to 14 bit linear.



private static final int[] ULAW_TO_LINEAR_14_BIT = new int[]{

-8159, -7903, -7647, -7391, -7135, -6879, -6623, -6367, -6111, -5855, -5599, -5343, -5087, -4831, -4575, -4319,

-4063, -3935, -3807, -3679, -3551, -3423, -3295, -3167, -3039, -2911, -2783, -2655, -2527, -2399, -2271, -2143,

-2015, -1951, -1887, -1823, -1759, -1695, -1631, -1567, -1503, -1439, -1375, -1311, -1247, -1183, -1119, -1055,

-991, -959, -927, -895, -863, -831, -799, -767, -735, -703, -671, -639, -607, -575, -543, -511, -479, -463, -447,

-431, -415, -399, -383, -367, -351, -335, -319, -303, -287, -271, -255, -239, -223, -215, -207, -199, -191, -183,

-175, -167, -159, -151, -143, -135, -127, -119, -111, -103, -95, -91, -87, -83, -79, -75, -71, -67, -63, -59, -55,

-51, -47, -43, -39, -35, -31, -29, -27, -25, -23, -21, -19, -17, -15, -13, -11, -9, -7, -5, -3, -1, 7903, 7647,

7391, 7135, 6879, 6623, 6367, 6111, 5855, 5599, 5343, 5087, 4831, 4575, 4319, 4063, 3935, 3807, 3679, 3551, 3423,

3295, 3167, 3039, 2911, 2783, 2655, 2527, 2399, 2271, 2143, 2015, 1951, 1887, 1823, 1759, 1695, 1631, 1567, 1503,

1439, 1375, 1311, 1247, 1183, 1119, 1055, 991, 959, 927, 895, 863, 831, 799, 767, 735, 703, 671, 639, 607, 575,

543, 511, 479, 463, 447, 431, 415, 399, 383, 367, 351, 335, 319, 303, 287, 271, 255, 239, 223, 215, 207, 199, 191,

183, 175, 167, 159, 151, 143, 135, 127, 119, 111, 103, 95, 91, 87, 83, 79, 75, 71, 67, 63, 59, 55, 51, 47, 43, 39,

35, 31, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1, 0};



But the values generated with the Sun Microsystems c routine g711.c commonly available on the Internet generate the much more common 16 bit series:



private static final int[] ULAW_TO_LINEAR_16_BIT = new int[]{

-32124, -31100, -30076, -29052, -28028, -27004, -25980, -24956, -23932, -22908, -21884, -20860, -19836, -18812,

-17788, -16764, -15996, -15484, -14972, -14460, -13948, -13436, -12924, -12412, -11900, -11388, -10876, -10364,

-9852, -9340, -8828, -8316, -7932, -7676, -7420, -7164, -6908, -6652, -6396, -6140, -5884, -5628, -5372, -5116,

-4860, -4604, -4348, -4092, -3900, -3772, -3644, -3516, -3388, -3260, -3132, -3004, -2876, -2748, -2620, -2492,

-2364, -2236, -2108, -1980, -1884, -1820, -1756, -1692, -1628, -1564, -1500, -1436, -1372, -1308, -1244, -1180,

-1116, -1052, -988, -924, -876, -844, -812, -780, -748, -716, -684, -652, -620, -588, -556, -524, -492, -460,

-428, -396, -372, -356, -340, -324, -308, -292, -276, -260, -244, -228, -212, -196, -180, -164, -148, -132, -120,

-112, -104, -96, -88, -80, -72, -64, -56, -48, -40, -32, -24, -16, -8, 0, 32124, 31100, 30076, 29052, 28028,

27004, 25980, 24956, 23932, 22908, 21884, 20860, 19836, 18812, 17788, 16764, 15996, 15484, 14972, 14460, 13948,

13436, 12924, 12412, 11900, 11388, 10876, 10364, 9852, 9340, 8828, 8316, 7932, 7676, 7420, 7164, 6908, 6652, 6396,

6140, 5884, 5628, 5372, 5116, 4860, 4604, 4348, 4092, 3900, 3772, 3644, 3516, 3388, 3260, 3132, 3004, 2876, 2748,

2620, 2492, 2364, 2236, 2108, 1980, 1884, 1820, 1756, 1692, 1628, 1564, 1500, 1436, 1372, 1308, 1244, 1180, 1116,

1052, 988, 924, 876, 844, 812, 780, 748, 716, 684, 652, 620, 588, 556, 524, 492, 460, 428, 396, 372, 356, 340,

324, 308, 292, 276, 260, 244, 228, 212, 196, 180, 164, 148, 132, 120, 112, 104, 96, 88, 80, 72, 64, 56, 48, 40,

32, 24, 16, 8, 0};



Searching the Internet for a short subset of the 16 bit sequence, such as "32124, 31100, 30076" will quickly demonstrate the industry dominance of the 16 bit format vs a search for the obscure 14 bit sequence "8159, 7903, 7647"



[edit] Implementation



There are three ways of implementing a μ-law algorithm :



Analog

Use an amplifier with non-linear gain to achieve companding entirely in the analog domain.

Non-linear ADC

Use an Analog to Digital Converter with quantization levels which are unequally spaced to match the μ-law algorithm.

Digital

Use the quantized digital version of the μ-law algorithm to convert data once it is in the digital domain.



[edit] Usage Justification



This encoding is used because speech has a wide dynamic range. In the analog world, when mixed with a relatively constant background noise source, the finer detail is lost. Given that the precision of the detail is compromised anyway, and assuming that the signal is to be perceived as audio by a human, one can take advantage of the fact that perceived intensity (loudness) is logarithmic[2] by compressing the signal using a logarithmic-response op-amp. In telco circuits, most of the noise is injected on the lines, thus after the compressor, the intended signal will be perceived as significantly louder than the static, compared to an un-compressed source. This became a common telco solution, and thus, prior to common digital usage, the mu-law specification was developed to define an inter-compatible standard.



As the digital age dawned, it was noted that this pre-existing algorithm had the effect of significantly reducing the number of bits needed to encode recognizable human voice. Using mu-law, a sample could be effectively encoded in as few as 8 bits, a sample size that conveniently matched the symbol size of most standard computers.



Mu-law encoding effectively reduced the dynamic range of the signal, thereby increasing the coding efficiency while biasing the signal in a way that results in a signal-to-distortion ratio that is greater than that obtained by linear encoding for a given number of bits. This is an early form of perceptual audio encoding.



The mu-law algorithm is also used in the .au format, which dates back at least to the SPARCstation 1 as the native method used by Sun's /dev/audio interface, widely used as a de facto standard for Unix sound. The .au format is also used in various common audio API's such as the classes in the sun.audio Java package in Java 1.1 and in some C# methods.



This graph illustrates how u-law concentrates sampling in the smaller (softer) values. The values of a u-law byte 0-255 are the horizontal axis, the vertical axis is the 16 bit linear decoded value. This image was generated with the Sun Microsystems c routine g711.c commonly available on the Internet.



Image:Ulaw.JPG



[edit] Comparison with A-law



The A-law algorithm provides a slightly larger dynamic range than the mu-law at the cost of worse proportional distortion for small signals. By convention, A-law is used for an international connection if at least one country uses it.



This article contains material from the Federal Standard 1037C, which, as a work of the United States Government, is in the public domain.



[edit] See also



* ITU-T Recommendation G.711

* Au file format

* A-law algorithm

* Audio level compression

* Signal compression

* Companding



[edit] References



1. ^ Cisco - Waveform Coding Techniques. Retrieved on 2007-02-23.

2. ^ Wikipedia on sound.



[edit] External links



* Waveform Coding Techniques - Has details of implementation

* A-Law and mu-Law Companding Implementations Using the TMS320C54x (PDF)

* A-law and μ-law realisation (on C)





[show]

v • d • e

Data compression methods

Lossless compression methods

Theory Entropy · Complexity · Redundancy

Entropy encoding Huffman · Adaptive Huffman · Arithmetic (Shannon-Fano · Range) · Golomb · Exp-Golomb · Universal (Elias · Fibonacci)

Dictionary RLE · LZ77/78 · LZW · LZWL · LZO · DEFLATE · LZMA · LZX

Others BWT · PPM · DMC

Audio compression methods

Theory Convolution · Sampling · Nyquist–Shannon theorem

Audio codec parts LPC (LAR · LSP) · WLPC · CELP · ACELP · A-law · μ-law · MDCT · Fourier transform · Psychoacoustic model

Others Dynamic range compression · Speech compression · Sub-band coding

Image compression methods

Terms Color space · Pixel · Chroma subsampling · Compression artifact

Methods RLE · Fractal · Wavelet · SPIHT · DCT · KLT

Others Bit rate · Test images · PSNR quality measure · Quantization

Video compression

Terms Video Characteristics · Frame · Frame types · Video quality

Video codec parts Motion compensation · DCT · Quantization

Others Video codecs · Rate distortion theory (CBR · ABR · VBR)

Timeline of information theory, data compression, and error-correcting codes

See Compression Formats and Standards for formats and Compression Software Implementations for codecs





[show]

v • d • e

Multimedia compression formats

Video compression

ISO/IEC MJPEG · MPEG-1 · MPEG-2 · MPEG-4 ASP · MPEG-4/AVC

ITU-T H.261 · H.262 · H.263 · H.264

Others AVS · Bink · Dirac · Indeo · MJPEG · Pixlet · RealVideo · Smacker · Theora · VC-1 · VP6 · VP7 · WMV

Audio compression

ISO/IEC MPEG-1 Layer III (MP3) · MPEG-1 Layer II · MPEG-1 Layer I · AAC · HE-AAC · HE-AAC v2

ITU-T G.711 · G.722 · G.722.1 · G.722.2 · G.723 · G.723.1 · G.726 · G.728 · G.729 · G.729.1 · G.729a

Others AC3 · Apple Lossless · ATRAC · FLAC · iLBC · Monkey's Audio · μ-law · Musepack · Nellymoser · OptimFROG · RealAudio · SHN · Speex · Vorbis · WavPack · WMA · TAK

Image compression

ISO/IEC/ITU-T JPEG · JPEG 2000 · lossless JPEG · JBIG · JBIG2 · PNG · WBMP

Others BMP · GIF · ILBM · PCX · PGF · TGA · TIFF · HD Photo

Media containers

General 3GP · ASF · AVI · Bink · DMF · DPX · FLV · Matroska · MP4 · MXF · NUT · Ogg · Ogg Media · QuickTime · RealMedia · Smacker · VOB

Audio only AIFF · AU · WAV

See Compression Methods for methods and Compression Software Implementations for codecs

Retrieved from "http://en.wikipedia.org/wiki/%CE%9C-law_algorithm"



Categories: Audio codecs | ITU-T recommendations

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