用MATLAB软件已知一个信号序列的主值为 x(n)=[0,1,2,3,2,1,0],显示两个周期的信号序列波形。 求傅里叶级数逆变换的图形,与原信号图形进行比较。
时间: 2024-02-24 18:57:38 浏览: 205
可以按照以下步骤显示两个周期的信号序列波形,并求傅里叶级数逆变换的图形:
1. 定义信号序列x(n)及其周期N:
```
x = [0, 1, 2, 3, 2, 1, 0];
N = length(x);
```
2. 复制x(n)得到两个周期的信号序列:
```
x2 = [x, x];
```
3. 绘制两个周期的信号序列波形:
```
n = 0:N-1;
n2 = 0:2*N-1;
subplot(2, 1, 1);
stem(n2, x2);
xlabel('n');
ylabel('x(n)');
title('Two Periods of Signal x(n)');
```
4. 计算傅里叶级数系数并进行逆变换:
```
k = 0:N-1;
Xk = fft(x)/N;
x_reconstruct = zeros(1, 2*N);
for i = 1:2*N
for j = 1:N
x_reconstruct(i) = x_reconstruct(i) + Xk(j)*exp(1j*2*pi*k(j)*(i-1)/(2*N));
end
end
```
5. 绘制傅里叶级数逆变换的图形,并与原信号图形进行比较:
```
subplot(2, 1, 2);
stem(n2, real(x_reconstruct));
xlabel('n');
ylabel('x(n)');
title('Reconstructed Signal x(n)');
```
完整的Matlab代码如下:
```
x = [0, 1, 2, 3, 2, 1, 0];
N = length(x);
x2 = [x, x];
n = 0:N-1;
n2 = 0:2*N-1;
subplot(2, 1, 1);
stem(n2, x2);
xlabel('n');
ylabel('x(n)');
title('Two Periods of Signal x(n)');
k = 0:N-1;
Xk = fft(x)/N;
x_reconstruct = zeros(1, 2*N);
for i = 1:2*N
for j = 1:N
x_reconstruct(i) = x_reconstruct(i) + Xk(j)*exp(1j*2*pi*k(j)*(i-1)/(2*N));
end
end
subplot(2, 1, 2);
stem(n2, real(x_reconstruct));
xlabel('n');
ylabel('x(n)');
title('Reconstructed Signal x(n)');
```
运行上述代码,即可得到两个周期的信号序列波形和傅里叶级数逆变换的图形,并且两者进行比较。
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