1. 用双线性变换法设计一个巴特沃斯低通IIR数字滤波器。设计指标参数为：在通带内频率低于0.2π时，最大衰减小于1dB；在阻带内[0.3π, π]频率区间上，最小衰减大于15dB.

2.0.02π为采样间隔，打印出数字滤波器在频率区间[0, π/2]上的频率响应特性曲线。

3. 用所设计的滤波器对实际心电图信号采样序列进行仿真滤波处理，观察总结滤波作用与效果

附：心电图采样序列x(n)

人体心电图信号在测量过程中往往受到工业高频干扰，所以必须经过低通滤波处理后，才能作为判断心脏功能的有用信息。下面给出一实际心电图信号采样序列样本x(n),其中存在高频干扰。在实验中以x(n)作为输入序列，滤除其中的干扰成分。

{x(n)}={-4,-2,0,-4,-6,-4,-2,-4,-6,-6,-4,-4,-6,-6,-2,6,12,8,0,-16,-38,-60,-84,-90,-66,-32,-4,-2,-4,8,12,12,10,6,6,6,4,0,0,0,0,0,-2,-4,0,0,0,-2,-2,0,0,-2,-2,-2,-2,0}

-1. With the bilinear transformation to design a Butterworth low-pass IIR digital filter. Design target parameters: the passband frequencies below 0.2π, the maximum attenuation is less than 1dB　in the stopband [0.3π, π] frequency range, the minimum attenuation greater than 15dB.

2.0.02π for the sampling interval, print out the digital filter in the frequency interval [0, π/2] on the frequency response curve.

3. With the designed filter on the actual ECG signal sample sequence to simulate filtering, observation summed up the role and effect of filtering

Attachment: ECG sampling sequence x (n)

Human ECG signal in the measurement process is often subject to industrial high-frequency interference, it must be low-pass filtering before they can determine cardiac function as a useful information. Here are a sample of the actual ECG signal sampling sequence x (n), where there is high frequency noise. In the experiment with x (n) as the input sequence, in which the interference filter e