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Summary

Description
English: Plot of μ-Law and A-Law companding on a Decibel scale
Date
Source Own work
Author Ozhiker
Other versions Non vector version at File:Ulaw_alaw.png
SVG development
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The SVG code is valid.
 
This chart was created with Gnuplot.
 
This chart uses translateable embedded text.
Source code
InfoField

Gnuplot code

# Plot of u-Law and A-Law companding on a Decibel scale
# Works with GNUPlot 4.2 PatchLevel 6

# Open SVG file
set terminal svg noenhanced size 800 600 fname "DejaVu Sans" fsize 16
set output 'Ulaw_alaw_db.svg' 

#Set background colour
set obj 1 rectangle behind from graph 0,0 to graph 1,1
set obj 1 fillstyle solid 1.0 fillcolor rgb "#C0C0C0"

#Set plot style
set border
set key left bottom
set style line 1 linewidth 2 linecolor rgb "#0F0"
set style line 2 linewidth 2 linecolor rgb "#00F"
set style line 3 linewidth 2 linecolor rgb "#7F7FFF"
set style line 4 linewidth 2 linecolor rgb "#F00"
set style line 5 linewidth 2 linecolor rgb "#FF7F7F"
set xrange [10:-80]
set yrange [-60:0]
set xlabel "Linear  Signal (dBm0)" 
set ylabel "Encoded Signal (dBFS)" 
set pointsize 0.001
set bars 0.5
set grid


# Define functions
decibel(x) = 20*log10(x)
alaw(x) = (abs(x)<1/87.7)? sgn(x)*87.7*abs(x)/(1+log(87.7)) : (abs(x)<1)? sgn(x)*(1+log(87.7*abs(x)))/(1+log(87.7)) : 1/0
ulaw(x) = sgn( x )*( log(1 + 255 * abs( x ) ) / log(256) )
decibel_inv(x) = 10**(x/20)

# Do the Plot
plot  x title "No Companding"  ls 1, \
      decibel( alaw( decibel_inv(x - 3.17) ) ) title "A-Law"  ls 2, \
      '-' using (decibel(abs($4)/4096)) + 3.14: (decibel(abs((($6) >128)? 127-($6):($6))/128)) : (decibel(abs($3)/4096)) + 3.14 : (decibel(abs($5)/4096)) + 3.14 with xerrorbars title "A-Law Quantized"  ls 3, \
      decibel( ulaw( decibel_inv(x - 3.17) ) ) title "μ-Law" ls 4, \
      '-' using (decibel(abs($4)/8192)) + 3.17: (decibel(abs((($7) >128)? 255-($7):($7)-128)/128)) : (decibel(abs($3)/8192)) + 3.17 : (decibel(abs($5)/8192)) + 3.17 with xerrorbars title "μ-Law Quantized"  ls 5

Data

# A-Law Plot Data
#
#"Interval Num"	"Interval Size"	"Interval Top"	"Interval Centre"	"Interval Bottom"	"Encoder Output"
15	128	4095	4031.5	3968	127
14	128	3967	3903.5	3840	126
13	128	3839	3775.5	3712	125
12	128	3711	3647.5	3584	124
11	128	3583	3519.5	3456	123
10	128	3455	3391.5	3328	122
9	128	3327	3263.5	3200	121
8	128	3199	3135.5	3072	120
7	128	3071	3007.5	2944	119
6	128	2943	2879.5	2816	118
5	128	2815	2751.5	2688	117
4	128	2687	2623.5	2560	116
3	128	2559	2495.5	2432	115
2	128	2431	2367.5	2304	114
1	128	2303	2239.5	2176	113
0	128	2175	2111.5	2048	112
15	64	2047	2015.5	1984	111
14	64	1983	1951.5	1920	110
13	64	1919	1887.5	1856	109
12	64	1855	1823.5	1792	108
11	64	1791	1759.5	1728	107
10	64	1727	1695.5	1664	106
9	64	1663	1631.5	1600	105
8	64	1599	1567.5	1536	104
7	64	1535	1503.5	1472	103
6	64	1471	1439.5	1408	102
5	64	1407	1375.5	1344	101
4	64	1343	1311.5	1280	100
3	64	1279	1247.5	1216	99
2	64	1215	1183.5	1152	98
1	64	1151	1119.5	1088	97
0	64	1087	1055.5	1024	96
15	32	1023	1007.5	992	95
14	32	991	975.5	960	94
13	32	959	943.5	928	93
12	32	927	911.5	896	92
11	32	895	879.5	864	91
10	32	863	847.5	832	90
9	32	831	815.5	800	89
8	32	799	783.5	768	88
7	32	767	751.5	736	87
6	32	735	719.5	704	86
5	32	703	687.5	672	85
4	32	671	655.5	640	84
3	32	639	623.5	608	83
2	32	607	591.5	576	82
1	32	575	559.5	544	81
0	32	543	527.5	512	80
15	16	511	503.5	496	79
14	16	495	487.5	480	78
13	16	479	471.5	464	77
12	16	463	455.5	448	76
11	16	447	439.5	432	75
10	16	431	423.5	416	74
9	16	415	407.5	400	73
8	16	399	391.5	384	72
7	16	383	375.5	368	71
6	16	367	359.5	352	70
5	16	351	343.5	336	69
4	16	335	327.5	320	68
3	16	319	311.5	304	67
2	16	303	295.5	288	66
1	16	287	279.5	272	65
0	16	271	263.5	256	64
15	8	255	251.5	248	63
14	8	247	243.5	240	62
13	8	239	235.5	232	61
12	8	231	227.5	224	60
11	8	223	219.5	216	59
10	8	215	211.5	208	58
9	8	207	203.5	200	57
8	8	199	195.5	192	56
7	8	191	187.5	184	55
6	8	183	179.5	176	54
5	8	175	171.5	168	53
4	8	167	163.5	160	52
3	8	159	155.5	152	51
2	8	151	147.5	144	50
1	8	143	139.5	136	49
0	8	135	131.5	128	48
15	4	127	125.5	124	47
14	4	123	121.5	120	46
13	4	119	117.5	116	45
12	4	115	113.5	112	44
11	4	111	109.5	108	43
10	4	107	105.5	104	42
9	4	103	101.5	100	41
8	4	99	97.5	96	40
7	4	95	93.5	92	39
6	4	91	89.5	88	38
5	4	87	85.5	84	37
4	4	83	81.5	80	36
3	4	79	77.5	76	35
2	4	75	73.5	72	34
1	4	71	69.5	68	33
0	4	67	65.5	64	32
15	2	63	62.5	62	31
14	2	61	60.5	60	30
13	2	59	58.5	58	29
12	2	57	56.5	56	28
11	2	55	54.5	54	27
10	2	53	52.5	52	26
9	2	51	50.5	50	25
8	2	49	48.5	48	24
7	2	47	46.5	46	23
6	2	45	44.5	44	22
5	2	43	42.5	42	21
4	2	41	40.5	40	20
3	2	39	38.5	38	19
2	2	37	36.5	36	18
1	2	35	34.5	34	17
0	2	33	32.5	32	16
15	2	31	30.5	30	15
14	2	29	28.5	28	14
13	2	27	26.5	26	13
12	2	25	24.5	24	12
11	2	23	22.5	22	11
10	2	21	20.5	20	10
9	2	19	18.5	18	9
8	2	17	16.5	16	8
7	2	15	14.5	14	7
6	2	13	12.5	12	6
5	2	11	10.5	10	5
4	2	9	8.5	8	4
3	2	7	6.5	6	3
2	2	5	4.5	4	2
1	2	3	2.5	2	1
0	2	1	0.5	0	0
e

# u-Law Plot Data
#
#Interval Num	Interval Size	Interval Top	Interval Centre	Interval Bottom	Base Code	Output Code
0	256	8158	8030.5	7903	128	128
1	256	7902	7774.5	7647	128	129
2	256	7646	7518.5	7391	128	130
3	256	7390	7262.5	7135	128	131
4	256	7134	7006.5	6879	128	132
5	256	6878	6750.5	6623	128	133
6	256	6622	6494.5	6367	128	134
7	256	6366	6238.5	6111	128	135
8	256	6110	5982.5	5855	128	136
9	256	5854	5726.5	5599	128	137
10	256	5598	5470.5	5343	128	138
11	256	5342	5214.5	5087	128	139
12	256	5086	4958.5	4831	128	140
13	256	4830	4702.5	4575	128	141
14	256	4574	4446.5	4319	128	142
15	256	4318	4190.5	4063	128	143
0	128	4062	3998.5	3935	144	144
1	128	3934	3870.5	3807	144	145
2	128	3806	3742.5	3679	144	146
3	128	3678	3614.5	3551	144	147
4	128	3550	3486.5	3423	144	148
5	128	3422	3358.5	3295	144	149
6	128	3294	3230.5	3167	144	150
7	128	3166	3102.5	3039	144	151
8	128	3038	2974.5	2911	144	152
9	128	2910	2846.5	2783	144	153
10	128	2782	2718.5	2655	144	154
11	128	2654	2590.5	2527	144	155
12	128	2526	2462.5	2399	144	156
13	128	2398	2334.5	2271	144	157
14	128	2270	2206.5	2143	144	158
15	128	2142	2078.5	2015	144	159
0	64	2014	1982.5	1951	160	160
1	64	1950	1918.5	1887	160	161
2	64	1886	1854.5	1823	160	162
3	64	1822	1790.5	1759	160	163
4	64	1758	1726.5	1695	160	164
5	64	1694	1662.5	1631	160	165
6	64	1630	1598.5	1567	160	166
7	64	1566	1534.5	1503	160	167
8	64	1502	1470.5	1439	160	168
9	64	1438	1406.5	1375	160	169
10	64	1374	1342.5	1311	160	170
11	64	1310	1278.5	1247	160	171
12	64	1246	1214.5	1183	160	172
13	64	1182	1150.5	1119	160	173
14	64	1118	1086.5	1055	160	174
15	64	1054	1022.5	991	160	175
0	32	990	974.5	959	176	176
1	32	958	942.5	927	176	177
2	32	926	910.5	895	176	178
3	32	894	878.5	863	176	179
4	32	862	846.5	831	176	180
5	32	830	814.5	799	176	181
6	32	798	782.5	767	176	182
7	32	766	750.5	735	176	183
8	32	734	718.5	703	176	184
9	32	702	686.5	671	176	185
10	32	670	654.5	639	176	186
11	32	638	622.5	607	176	187
12	32	606	590.5	575	176	188
13	32	574	558.5	543	176	189
14	32	542	526.5	511	176	190
15	32	510	494.5	479	176	191
0	16	478	470.5	463	192	192
1	16	462	454.5	447	192	193
2	16	446	438.5	431	192	194
3	16	430	422.5	415	192	195
4	16	414	406.5	399	192	196
5	16	398	390.5	383	192	197
6	16	382	374.5	367	192	198
7	16	366	358.5	351	192	199
8	16	350	342.5	335	192	200
9	16	334	326.5	319	192	201
10	16	318	310.5	303	192	202
11	16	302	294.5	287	192	203
12	16	286	278.5	271	192	204
13	16	270	262.5	255	192	205
14	16	254	246.5	239	192	206
15	16	238	230.5	223	192	207
0	8	222	218.5	215	208	208
1	8	214	210.5	207	208	209
2	8	206	202.5	199	208	210
3	8	198	194.5	191	208	211
4	8	190	186.5	183	208	212
5	8	182	178.5	175	208	213
6	8	174	170.5	167	208	214
7	8	166	162.5	159	208	215
8	8	158	154.5	151	208	216
9	8	150	146.5	143	208	217
10	8	142	138.5	135	208	218
11	8	134	130.5	127	208	219
12	8	126	122.5	119	208	220
13	8	118	114.5	111	208	221
14	8	110	106.5	103	208	222
15	8	102	98.5	95	208	223
0	4	94	92.5	91	224	224
1	4	90	88.5	87	224	225
2	4	86	84.5	83	224	226
3	4	82	80.5	79	224	227
4	4	78	76.5	75	224	228
5	4	74	72.5	71	224	229
6	4	70	68.5	67	224	230
7	4	66	64.5	63	224	231
8	4	62	60.5	59	224	232
9	4	58	56.5	55	224	233
10	4	54	52.5	51	224	234
11	4	50	48.5	47	224	235
12	4	46	44.5	43	224	236
13	4	42	40.5	39	224	237
14	4	38	36.5	35	224	238
15	4	34	32.5	31	224	239
0	2	30	29.5	29	240	240
1	2	28	27.5	27	240	241
2	2	26	25.5	25	240	242
3	2	24	23.5	23	240	243
4	2	22	21.5	21	240	244
5	2	20	19.5	19	240	245
6	2	18	17.5	17	240	246
7	2	16	15.5	15	240	247
8	2	14	13.5	13	240	248
9	2	12	11.5	11	240	249
10	2	10	9.5	9	240	250
11	2	8	7.5	7	240	251
12	2	6	5.5	5	240	252
13	2	4	3.5	3	240	253
14	2	2	1.5	1	240	254
15	1	0	0	0	240	255
e

# Close SVG File
unset output

Explanation

Generated entirely with [[:w:Gnuplot|Gnuplot]] using the following script (tables of data were calculated from scratch using [[:w:G.711|G.711]] standard)

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
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23 October 2009

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Date/TimeThumbnailDimensionsUserComment
current00:09, 9 January 2022Thumbnail for version as of 00:09, 9 January 2022800 × 600 (63 KB)Sollyuckoimprove key label order and color choice
12:22, 24 October 2009Thumbnail for version as of 12:22, 24 October 2009800 × 600 (55 KB)OzhikerTry with DejaVu Sans font
06:40, 24 October 2009Thumbnail for version as of 06:40, 24 October 2009800 × 600 (55 KB)OzhikerTry version without specific font to try to fix mediawiki rendering problem
21:28, 23 October 2009Thumbnail for version as of 21:28, 23 October 2009800 × 600 (55 KB)Ozhiker{{Information |Description={{en|1=Plot of μ-Law and A-Law companding on a Decibel scale}} |Source={{own}} {{gnuplot}} |Author=Ozhiker |Date=2009-10-23 |Permission= |other_versions=Non vector version at en:File:Ulaw_alaw.png }} {{en

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