极坐标图象
2 U; Y5 P9 o5 b1 X1 L ?6 B" w 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: d& M; V0 {/ E' i" D6 @
polar(theta,r) 5 \! u: g& i" y! M
) S% E# ^5 q* q+ k' J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。 2 [! ^3 U5 u& Y' |: [ s+ r3 d
例3.5* a- `2 P8 k6 u( P
心形麦克风 ) [. Z6 @6 P6 l5 o2 f
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
* i7 y& m) |& m/ W- S9 lGain=2g(1+cosθ) (3.3) p* M8 e& ^+ b+ }1 r3 d
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。 3 b$ Y1 K- ^3 }9 k
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
8 h8 ~ h! @ A9 {代码如下:
# }% z, g" q. ~. V- <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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