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:

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

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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

1. 
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2. %; P8 r5 b; j; {$ S$ t$ D
   
3. % Purpose:
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4. % This program plots the gain pattern of a cardioid
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5. % microphone.
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6. %
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7. % Record of revisions:9 ~8 }& o( m! ]0 o
   
8. % Date Programmer Description of change* `# p$ l! ?* D0 c. m
   
9. % ==== ========== =====================\" \1 X# S9 g7 S. i5 z\" _\" t
   
10. % 12/10/97 S. J. Chapman Original code
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11. %
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12. % Define variables:
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13. % g -- Microphone gain constant
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14. % gain -- Gain as a function of angle( w7 E0 P) _0 A
    
15. % theta -- Angle from microphone axis (radians)
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16. % Calculate gain versus angle- S6 Y6 y. D0 ?/ |- V6 K\" ]+ o4 }0 K
    
17. g = 0.5;\" f9 u+ j  k( R% N
    
18. theta = 0:pi/20:2*pi;
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19. gain = 2*g*(1+cos(theta));2 V. S; }. T. \# c; q( p4 Y
    
20. % Plot gain
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21. polar (theta,gain,'r-');* N0 y* k) O! \5 G* V
    
22. title ('Gain versus angle \it\theta');
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