E = @(r) V*log(b/a)/(2*pi*epsilon0*L)*r;
时间: 2023-10-06 20:04:08 浏览: 27
This is a MATLAB anonymous function that defines the electric field (E) at a distance (r) from a long straight wire carrying a voltage (V) and having a length (L) and a radius (a) placed at a distance (b) from the wire. The function uses the formula for the electric field of a straight wire, which is given by:
E = V/(2*pi*epsilon0*L)*ln(b/a)*r
where epsilon0 is the electric constant or vacuum permittivity. The anonymous function uses the @ symbol to define the function handle, and the input variable (r) is enclosed in parentheses. The function calculates the electric field at any distance (r) from the wire, given the input parameters (V, L, a, b).
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//生成高斯噪声 double generateGaussianNoise(double mu, double sigma) { //定义小值 const double epsilon = numeric_limits<double>::min(); static double z0, z1; static bool flag = false; flag = !flag; //flag为假构造高斯随机变量X if (!flag) return z1 * sigma + mu; double u1, u2; //构造随机变量 do { u1 = rand() * (1.0 / RAND_MAX); u2 = rand() * (1.0 / RAND_MAX); } while (u1 <= epsilon); //flag为真构造高斯随机变量 z0 = sqrt(-2.0*log(u1))*cos(2 * CV_PI*u2); z1 = sqrt(-2.0*log(u1))*sin(2 * CV_PI*u2); return z0*sigma + mu; }
这是一段C++代码,用于生成一个均值为`mu`,标准差为`sigma`的高斯噪声。该代码使用了Box-Muller转换算法来生成高斯分布的随机数。
具体实现步骤如下:
1. 定义一个非常小的常量`epsilon`,用于防止分母为0的情况。
2. 定义两个静态变量`z0`和`z1`,并将`flag`设为`false`。
3. 如果`flag`为假,则生成高斯分布的随机数`z1`。如果`flag`为真,则生成高斯分布的随机数`z0`。
4. 通过使用随机数生成器`rand()`生成两个随机变量`u1`和`u2`。
5. 如果`u1`小于等于`epsilon`,则重新生成随机变量`u1`和`u2`。
6. 如果`flag`为假,则使用如下公式计算高斯随机变量`z1`:
```
z1 = u2 * sigma + mu;
```
7. 如果`flag`为真,则使用如下公式计算高斯随机变量`z0`:
```
z0 = sqrt(-2.0*log(u1))*cos(2 * CV_PI*u2);
z1 = sqrt(-2.0*log(u1))*sin(2 * CV_PI*u2);
```
8. 返回高斯随机变量`z0`或`z1`。
需要注意的是,该代码使用了静态变量和标志位来交替生成高斯随机变量。这种实现方式可以避免重复计算,提高了代码的效率。但是,该代码只能生成一个随机数,如果需要生成多个随机数,则需要在外部循环中多次调用该函数。
此外,也可以使用OpenCV中的`randn()`函数来生成高斯噪声,它是一个内置的高斯随机数生成器。
matlab编写程序设计带通滤波器,参数要求为ws1=0.2*pi;wp1=0.35*pi; ws2=0.8*pi;wp2=0.65*pi;Ap=-3dB, As=-65dB;N=40,给定T1,T2
好的,根据您的要求,我为您编写了一个MATLAB程序,实现了40阶带通滤波器的设计。以下是代码:
```
% 定义参数
ws1 = 0.2 * pi;
wp1 = 0.35 * pi;
ws2 = 0.8 * pi;
wp2 = 0.65 * pi;
Ap = 3;
As = 65;
N = 40;
T1 = 0.1;
T2 = 0.2;
% 计算通带截止频率和阻带截止频率
wp = [wp1, wp2];
ws = [ws1, ws2];
% 计算折中频率
wc = sqrt(wp1*wp2);
% 选择滤波器类型
delta_p = (10^(0.05*Ap)-1)/(10^(0.05*Ap)+1);
delta_s = 10^(-0.05*As);
epsilon = sqrt(delta_p);
if delta_p < delta_s
type = 'elliptic';
else
type = 'chebyshev2';
end
% 计算滤波器参数
if strcmp(type, 'elliptic')
[N, Wn] = ellipord(wp, ws, delta_p, delta_s);
[b, a] = ellip(N, epsilon, As, Wn);
elseif strcmp(type, 'chebyshev2')
[N, Wn] = cheb2ord(wp, ws, delta_p, delta_s);
[b, a] = cheby2(N, As, Wn);
end
% 绘制幅频特性图
[H, w] = freqz(b, a);
figure;
plot(w/pi, 20*log10(abs(H)));
title('Magnitude Response');
xlabel('Normalized Frequency (\times\pi rad/sample)');
ylabel('Magnitude (dB)');
grid on;
% 计算单位抽样响应
n = 0:N-1;
imp = (wc/pi)*sinc((wc/pi)*(n-(N-1)/2));
h = b(1)*imp;
for i = 2:length(b)
imp = [0 imp(1:end-1)];
h = h + b(i)*imp;
end
for i = 2:length(a)
imp = [0 imp(1:end-1)];
h = h - a(i)*h;
end
% 绘制单位抽样响应图
figure;
stem(n, h);
title('Impulse Response');
xlabel('n');
ylabel('Amplitude');
grid on;
% 计算单位阶跃响应
step = ones(1, N);
y = filter(b, a, step);
% 绘制单位阶跃响应图
figure;
stem(n, y);
title('Step Response');
xlabel('n');
ylabel('Amplitude');
grid on;
% 计算T1和T2时的输出响应
t = 0:N-1;
x = cos(wc*t);
y1 = filter(b, a, x);
y2 = filter(b, a, x.*(t>=T1));
y3 = filter(b, a, x.*(t>=T2));
% 绘制输出响应图
figure;
subplot(3, 1, 1);
plot(t, x);
title('Input Signal');
xlabel('n');
ylabel('Amplitude');
grid on;
subplot(3, 1, 2);
plot(t, y1);
title('Output Signal (All)');
xlabel('n');
ylabel('Amplitude');
grid on;
subplot(3, 1, 3);
plot(t, y2, 'r', t, y3, 'g');
title(['Output Signal (T1=', num2str(T1), ', T2=', num2str(T2), ')']);
xlabel('n');
ylabel('Amplitude');
legend(['T1=', num2str(T1)], ['T2=', num2str(T2)]);
grid on;
```
您可以将代码复制到MATLAB代码编辑器中运行,得到滤波器的单位抽样响应、单位阶跃响应和输出响应。同时,程序还绘制了滤波器的幅频特性图和输出响应图。