File:Butterworth_response.png
維基百科,自由的 encyclopedia
![File:Butterworth response.png](http://upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Butterworth_response.png/800px-Butterworth_response.png)
原始文件 (1,240 × 880像素,文件大小:86 KB,MIME类型:image/png)
摘要
描述Butterworth response.png |
English: The frequency response of a Butterworth filter with logarithmic axes (Bode plot) and various labels. Cutoff frequency is normalized to 1 rad/s. Gain is normalized to 0 dB in the passband.
Many orders on one plot: File:Butterworth orders.png. Version with no text available at File:Butterworth plain.png, though you should probably just modify the source code and regenerate it in your own language. See Wikipedia graph-making tips. Generated in gnuplot with the script below (save as butterworth.plt and then open in gnuplot). Then I opened the butterworth.ps file in a text editor to edit the line colors and linestyles, as per this description. This avoids needing to open in proprietary software, and really isn't that difficult (especially if you don't know the commands in the proprietary software either). ;-) Identify the lines easily by their color (the arrow is currently magenta and I want it to be black. Ah, there is the entry with 1 0 1, red + blue = magenta) or by using the gnuplot linestyle−1. (For instance, gnuplot's linestyle 3 corresponds to the ps file's /LT2.) Then you can edit the colors and dashes by hand. I changed the original: /LT0 { PL [] 1 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def into this: /LT0 { PL [] 0 0 1 DL } def /LT1 { PL [4 dl 2 dl] 0.5 0.5 0.5 DL } def /LT2 { PL [6 dl 3 dl] 0.3 0.3 1 DL } def /LT3 { PL [] 0 0 0 DL } def/LT4–/LT8 I left unchanged. (I don't know what they're used for anyway.) /LTw, /LTb, and /LTa are for the grid lines and such. To convert the PostScript file to PNG:
|
日期 | 2005年6月26日 (上传日期) |
来源 | 自己的作品 |
作者 | Omegatron |
其他版本 |
|
gnuplot source InfoField | click to expand
set samples 2001
set terminal postscript enhanced landscape color lw 2 "Times-Roman" 20
set output "butterworth.ps"
# Butterworth amplitude response and decibel calculation. n is the order, which is just 1 in this image.
G(w,n) = 1 / (sqrt(1 + w**(2*n)))
dB(x) = 20 * log10(abs(x))
# Gridlines
set grid
# Set x axis to logarithmic scale
set logscale x 10
# Set range of x and y axes
set xrange [0.001:1000]
set yrange [-60:10]
# Create x-axis tic marks once per decade (every multiple of 10)
set xtics 10
# Use 10 x-axis minor divisions per major division
set mxtics 10
# Axis labels
set xlabel "Angular frequency (rad/s)"
set ylabel "Gain (dB)"
# No need for a key
set nokey #0.1,-25
# Frequency response's line plotting style
set style line 1 lt 1 lw 2
# Draw a separator between passband and stopband and label them
set style line 2 lt 2 lw 1
set style arrow 2 nohead ls 2
set arrow 3 from 1,-60 to 1,10 as 2
# Label coordinates are relative to the graph window, not to the function, centered at the 1/4 and 3/4 width points
set label 1 "Passband" at graph 0.25, graph 0.1 c
set label 2 "Stopband" at graph 0.75, graph 0.1 c
# Asymptote lines and slope lines are the same "arrow" style
set style line 3 lt 3 lw 1
set style arrow 3 nohead ls 3
# Draw asymptote lines
set arrow 1 from 1,0 to 1000,-60 as 3
set arrow 2 from .001,0 to 1,0 as 3
# -3 dB arrow style and arrow
set style line 4 lt 4 lw 1
set style arrow 4 head filled size screen 0.02,15,45 ls 4
set arrow 4 from 2,3 to 1,0 as 4
# "Cutoff frequency" label uses same coordinates as the function
set label 3 "Cutoff frequency" at 2,4 l
# "-3 dB" label
set arrow 5 from 0.5,-6 to 1,-3 as 4
set label 4 "-3.01 dB" at 0.5,-7 r
# Draw slope lines and label
set arrow 6 from 100,-20 to 12,-20 as 3
set arrow 7 from 100,-20 to 100,-39 as 3
set label 5 "Slope: -20 dB/decade" at 100,-18 c
# Plot the filter response
plot \
dB(G(x,1)) ls 1 title "1st-order response"
|
![]() |
File:Butterworth response.svg是此文件的矢量版本。 如果此文件质量不低于原点阵图,就应该将这个PNG格式文件替换为此文件。
File:Butterworth response.png → File:Butterworth response.svg
更多信息请参阅Help:SVG/zh。
|
许可协议
![w:zh:知识共享](https://upload.wikimedia.org/wikipedia/commons/thumb/7/79/CC_some_rights_reserved.svg/90px-CC_some_rights_reserved.svg.png)
![署名](https://upload.wikimedia.org/wikipedia/commons/thumb/1/11/Cc-by_new_white.svg/24px-Cc-by_new_white.svg.png)
![相同方式共享](https://upload.wikimedia.org/wikipedia/commons/thumb/d/df/Cc-sa_white.svg/24px-Cc-sa_white.svg.png)
- 您可以自由地:
- 共享 – 复制、发行并传播本作品
- 修改 – 改编作品
- 惟须遵守下列条件:
- 署名 – 您必须对作品进行署名,提供授权条款的链接,并说明是否对原始内容进行了更改。您可以用任何合理的方式来署名,但不得以任何方式表明许可人认可您或您的使用。
- 相同方式共享 – 如果您再混合、转换或者基于本作品进行创作,您必须以与原先许可协议相同或相兼容的许可协议分发您贡献的作品。
![]() |
已授权您依据自由软件基金会发行的无固定段落及封面封底文字(Invariant Sections, Front-Cover Texts, and Back-Cover Texts)的GNU自由文件许可协议1.2版或任意后续版本的条款,复制、传播和/或修改本文件。该协议的副本请见“GNU Free Documentation License”。http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
说明
此文件中描述的项目
描繪內容
GNU自由文档许可证1.2或更高版本 简体中文(已转写)
知识共享署名-相同方式共享1.0通用 简体中文(已转写)
知识共享署名-相同方式共享2.0通用 简体中文(已转写)
知识共享署名-相同方式共享2.5通用 简体中文(已转写)
image/png
87,607 字节
880 像素
1,240 像素
文件历史
点击某个日期/时间查看对应时刻的文件。
日期/时间 | 缩略图 | 大小 | 用户 | 备注 | |
---|---|---|---|---|---|
当前 | 2005年7月23日 (六) 17:45 | ![]() | 1,240 × 880(86 KB) | Omegatron | split the cutoff frequency markers |
2005年7月23日 (六) 16:31 | ![]() | 1,250 × 880(92 KB) | Omegatron | Better butterworth filter response curve | |
2005年6月26日 (日) 19:54 | ![]() | 250 × 220(2 KB) | Omegatron | A graph or diagram made by User:Omegatron. (Uploaded with Wikimedia Commons.) Source: Created by User:Omegatron {{GFDL}}{{cc-by-sa-2.0}} Category:Diagrams\ |
文件用途
全域文件用途
以下其他wiki使用此文件:
- be-tarask.wikipedia.org上的用途
- de.wikipedia.org上的用途
- eo.wikipedia.org上的用途
- et.wikipedia.org上的用途
- fr.wikipedia.org上的用途
- hi.wikipedia.org上的用途
- it.wikipedia.org上的用途
- ja.wikipedia.org上的用途
- pl.wikipedia.org上的用途
- pt.wikipedia.org上的用途