11、离散信号变换：z变换与离散傅里叶变换详解

离散信号变换：z变换与离散傅里叶变换详解

1. z变换基础与MATLAB应用

z变换为离散信号提供了广义频域（z）表示，适用于任意序列。下面通过具体示例和代码展示其应用。

1.1 MATLAB脚本示例

>> n = [0:7]; x = cos(pi*n/3);
y = filter(b,a,x,xic)
y =
Columns 1 through 4
1.80750000000000
4.35545833333333
2.83975000000000
-1.56637197916667
Columns 5 through 8
-4.71759442187500
-3.40139732291667
1.35963484230469
5.02808085078841
% Matlab Verification
>> A=real(2*R(1)); B=imag(2*R(1)); C=real(2*R(3)); D=imag(2*R(4));
>> y=A*cos(pi*n/3)+B*sin(pi*n/3)+((0.95).^n).*(C*cos(pi*n/3)+D*sin(pi*n/3))
y =
Columns 1 through 4
1.80750000000048
4.35545833333359
2.83974999999978
-1.56637197916714
Columns 5 through 8
-4.71759442187528
-3.40139732291648
1.35963484230515
5.02808085078871

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