在matlab中怎么将谐波相加得到方波信号
时间: 2023-09-06 14:14:11 浏览: 113
可以使用傅里叶级数展开的方法,在matlab中实现将谐波相加得到方波信号。
具体步骤如下:
1. 定义一个周期为T、幅值为A的方波信号,可以使用square函数实现:
```matlab
T = 1; % 周期
A = 1; % 幅值
t = linspace(0, 10*T, 1000); % 时间范围
f = square(2*pi/T*t); % 方波信号
plot(t, f);
```
2. 对方波信号进行傅里叶级数展开,求出前N项的系数:
```matlab
N = 10; % 前N项
syms k;
a0 = (1/T)*int(f, t, 0, T);
ak = (2/T)*int(f*cos(k*2*pi/T*t), t, 0, T);
bk = (2/T)*int(f*sin(k*2*pi/T*t), t, 0, T);
a = double(subs(a0 + symsum(ak*cos(k*2*pi/T*t) + bk*sin(k*2*pi/T*t), k, 1, N)));
```
其中,a0、ak、bk分别表示傅里叶级数中的直流分量、余弦项系数、正弦项系数,符号变量k用来表示谐波的频率,通过symsum函数对前N项求和,最终得到前N项的系数。
3. 将前N项的系数带入傅里叶级数公式,求得前N项的谐波信号:
```matlab
f_N = a0/2 + symsum(ak*cos(k*2*pi/T*t) + bk*sin(k*2*pi/T*t), k, 1, N);
```
4. 将前N项的谐波信号相加,得到近似的方波信号:
```matlab
f_approx = sum(f_N);
plot(t, f, t, f_approx);
```
完整代码如下:
```matlab
T = 1; % 周期
A = 1; % 幅值
t = linspace(0, 10*T, 1000); % 时间范围
f = square(2*pi/T*t); % 方波信号
plot(t, f);
N = 10; % 前N项
syms k;
a0 = (1/T)*int(f, t, 0, T);
ak = (2/T)*int(f*cos(k*2*pi/T*t), t, 0, T);
bk = (2/T)*int(f*sin(k*2*pi/T*t), t, 0, T);
a = double(subs(a0 + symsum(ak*cos(k*2*pi/T*t) + bk*sin(k*2*pi/T*t), k, 1, N)));
f_N = a0/2 + symsum(ak*cos(k*2*pi/T*t) + bk*sin(k*2*pi/T*t), k, 1, N);
f_approx = sum(f_N);
plot(t, f, t, f_approx);
```
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