极坐标图象

森之张卫东

极坐标图象
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Matlab中包括一个重要的函数叫做polar，它用于在极坐标系中画图。这个函数的基本形式如下:

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polar(theta,r)

其是theta代表一个弧度角数组，r代表一个距离数组。它用来画以角度为自变量的函数的极坐标图是非常有用的。

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心形麦克风

为舞台表演设计的麦克风大多都是定向麦克风，它能够增大来自演唱者的信号，抑制后面观众的噪声信号。一个心形麦克风的增益gain是关于角度θ的函数，关系式如下

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Gain=2g(1+cosθ)                 (3.3)

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其中g是和特定的心形麦克风有关的常量。θ是声源和麦克风之间的夹角。假设一个麦克风的g是0.5，画出函数Gain的极坐标图。

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答案：我们必须计算出与角度对应的函数值，然后画出相应的极坐标图。产生的结果如图3.7所示。注意这种麦克风叫做心形麦克风，所以得出来曲线的形状像颗心。

file:///C:/Users/lx/AppData/Local/Temp/msohtmlclip1/01/clip_image003.gif

代码如下：

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1. <div align="left"><font face="Times New Roman"><font color="#000000">% Scriptfile: microphone.m</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">%</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">%Purpose:</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">% Thisprogram plots the gain pattern of a cardioid</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">% microphone.</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">%</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">% Recordof revisions:</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">% DateProgrammer Description of change</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">% ============== =====================</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">% </font></font><font face="Times New Roman"><font color="#000000">12/10/97</font></font><font face="Times New Roman"><font color="#000000">S. J. Chapman Original code</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">%</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">% Definevariables:</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">% g --Microphone gain constant</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">% gain --Gain as a function of angle</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">% theta-- Angle from microphone axis (radians)</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">%Calculate gain versus angle</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">g = 0.5;</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">theta =0:pi/20:2*pi;</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">gain =2*g*(1+cos(theta));</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">% Plotgain</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">polar(theta,gain,'r-');</font></font></div><div align="left"><font face="Times New Roman"><font color="#000000">title('Gain versus angle \it\theta');</font></font></div>

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森之张卫东

1. 
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2. %- |& y* W' s& s8 Z) x
   
3. % Purpose:
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4. % This program plots the gain pattern of a cardioid
   \" i1 `# t  J0 `4 U# x
5. % microphone.\" Q3 P6 E; c# u. }
   
6. %
   \" K# |: r/ B4 k5 K
7. % Record of revisions:
   * A/ x' C. R+ |( f5 i* C0 U! s$ ?
8. % Date Programmer Description of change
   ! P' a# w) Y+ ~\" `  k+ f. @- o
9. % ==== ========== =====================3 \8 m' ^, Z* C2 x
   
10. % 12/10/97 S. J. Chapman Original code
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11. %; o' }$ X, k0 u4 G& a5 G; S
    
12. % Define variables:
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13. % g -- Microphone gain constant
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14. % gain -- Gain as a function of angle5 p. U; I7 D/ h' N9 z
    
15. % theta -- Angle from microphone axis (radians)' Z3 A5 d3 m' h  }5 Z7 E+ ^7 w
    
16. % Calculate gain versus angle
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17. g = 0.5;
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18. theta = 0:pi/20:2*pi;* @' ^( F- B& I6 W; e  g0 u
    
19. gain = 2*g*(1+cos(theta));
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20. % Plot gain9 c6 O# Y: G* _8 G( @
    
21. polar (theta,gain,'r-');% T5 [- w- ]- Z  |3 p
    
22. title ('Gain versus angle \it\theta');/ N: z4 h7 D+ }# t
    

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