1.确定参数：

Wp 通带截止频率

Ws  阻带截止频率

As  衰减dB

Rp   纹波dB

2.根据参数确定理想 频率响应 （M     (Wp + Ws )/2  ）

双边响应

3.选窗

过滤带宽

阻带衰减

4.得出最终响应

时域相乘 频域卷积

5.观察各项参数是否达标（采用归一化后的数据）

衰减

幅频特性

相频

群延时 ？？

···

Ps：观察频率响应的函数

这里a = 1 因为FIR可由差分方程描述

故分母为1

代码：

wp =0.2*pi;

ws = 0.3*pi;

tr_width = ws -wp;

M = ceil(6.6*pi/tr_width)+1;

n = [0:1:M-1];

wc = ((ws + wp)/2) %ideal LPF cutoff frequency

hd = ideal_lp(wc,M);

w_ham = (hamming(M))';

h = hd .* w_ham;

[db,mag,pha,grd,w] = freqz_m(h,[1]);

delta_w = 2*pi/1000;

Rp = -(min(db(1:1:wp/delta_w+1)));

As = -round(max(db(ws/delta_w+1:1:501)));

%plot

subplot(2,2,1);

stem(n,hd);

title('Ideal Impulse Response');

axis([0 M-1 -0.1 0.3]);

xlabel('n');

ylabel('hd(n)');

subplot(2,2,2);

stem(n,w_ham);

title(' Hamming Window');

axis([0 M-1 0 1.1]);

xlabel('n');

ylabel('w(n)');

subplot(2,2,3);

stem(n,h);

title('Actual Impluse Response');

axis([0 M-1 -0.1 0.3]);

xlabel('n');

ylabel('h(n)');

subplot(2,2,4);

plot(w/pi,db);

title('Magnitude Response in dB');grid

axis([0 1 -100 10]);

xlabel('frequency in pi units');

ylabel('Decibels');

带通：

wp1 =0.35*pi;

ws1 = 0.2*pi;

wp2 =0.65*pi;

ws2 = 0.8*pi;

tr_width = min((wp1 -ws1),(ws2 - wp2));

M = ceil(11*pi/tr_width)+1;

M

n = [0:1:M-1];

wc1 = ((ws1 + wp1)/2);

wc2 = ((ws2 + wp2)/2);

hd = ideal_lp(wc2,M)-ideal_lp(wc1,M);

w_ham = (blackman(M))';

h = hd .* w_ham;

[db,mag,pha,grd,w] = freqz_m(h,[1]);

delta_w = 2*pi/1000;

Rp = -(min(db(wp1/delta_w+1:1:wp2/delta_w+1)));

Rp

As = -round(max(db(ws2/delta_w+1:1:501)));

As

%plot

subplot(2,2,1);

stem(n,hd);

title('Ideal Impulse Response');

axis([0 M-1 -0.5 0.5]);

xlabel('n');

ylabel('hd(n)');

subplot(2,2,2);

stem(n,w_ham);

title(' blackman Window');

axis([0 M-1 0 1.1]);

xlabel('n');

ylabel('w(n)');

subplot(2,2,3);

stem(n,h);

title('Actual Impluse Response');

axis([0 M-1 -0.5 0.5]);

xlabel('n');

ylabel('h(n)');

subplot(2,2,4);

plot(w/pi,db);

title('Magnitude Response in dB');grid

axis([0 1 -150 10]);

xlabel('frequency in pi units');

ylabel('Decibels');