现有一个信号：x(n)=1+cos(π*n/4)+ cos(2*π*n/3)设计及各种数字滤波器以达下列目的：

低通滤波器，滤除cos(2*π*n/3) 的成分，即想保留的成分为1+cos(π*n/4)

高通滤波器，滤除1+cos(π*n/4) 的成分，即想保留的成分为cos(2*π*n/3)

带通滤波器，滤除1+cos(2*π*n/3) 的成分，即想保留的成分为cos(π*n/4)

带阻滤波器，滤除cos(π*n/4) 的成分，即想保留的成分为1+cos(2*π*n/3)

1. 用MATLAB命令butterord求除滤波器的阶数,用命令butter设计各滤波器；画出滤波器幅度和相频相应 取各滤波器的系统函数H(z)。

-an existing signal : x (n) = a cos ( * n / 4) cos (2 * * n / 3) design and digital filter to achieve the following objectives : low-pass filter, filter cos (2 * * n / 3) the ingredients that want to retain an element of a cos ( * n / 4) high-pass filter, a filter cos ( * n / 4) components, namely to retain the element of cos (2 * * n / 3) band-pass filter , a filter cos (2 * * n / 3) components, namely to retain the element of cos ( * n / 4) band stop filter, the filter cos ( * n / 4) components, namely to retain the ingredients for a cos ( 2 * * n / 3) 1. MATLAB order butterord except for the band Filter, using the order of the filter design butter; paint Filter magnitude and phase frequency of the corresponding filter system function H (z).