极坐标图象

森之张卫东

极坐标图象

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)

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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

Gain=2g(1+cosθ)                 (3.3)

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。

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。

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

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代码如下：

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

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2. %  x) Y) Y( D7 F9 w3 G
   
3. % Purpose:
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4. % This program plots the gain pattern of a cardioid
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5. % microphone.' g2 l6 e& L+ h! x$ Z: s
   
6. %
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7. % Record of revisions:\" v- I+ J8 l, L8 M3 e+ c5 J2 ]
   
8. % Date Programmer Description of change
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9. % ==== ========== =====================
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10. % 12/10/97 S. J. Chapman Original code
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11. %
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12. % Define variables:6 |* {  f' r. l7 m2 z
    
13. % g -- Microphone gain constant/ F8 @$ M$ ^6 J# S$ ?, J; e5 e. b
    
14. % gain -- Gain as a function of angle
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15. % theta -- Angle from microphone axis (radians)
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16. % Calculate gain versus angle
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17. g = 0.5;$ k8 K2 c9 R9 B* i; _3 N1 V
    
18. theta = 0:pi/20:2*pi;
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19. gain = 2*g*(1+cos(theta));, ?8 m3 A/ v0 m1 d
    
20. % Plot gain
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21. polar (theta,gain,'r-');9 ~' I# F6 e2 C* d( Y  B
    
22. title ('Gain versus angle \it\theta');. B\" w/ S# y. W3 [& R
    

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