DSP题库详解
1已知3阶椭圆IIR数字低通滤波器的性能指标为：通带截止频率0.4π，通带波纹为0.6dB，最小阻带衰减为32dB。设计一个6阶全通滤波器对其通带的延时进行均衡。绘制低通滤波器和级联滤波器的延时。
%Progranm 1
% Group-delay equalization of an IIR filter.
%
[n,d] = ellip(3,0.6,32,0.4);
[GdH,w] = grpdelay(n,d,512);
plot(w/pi,GdH); grid
xlabel('\omega/\pi'); ylabel('Group delay, samples');
title('Original Filter');
F = 0:0.001:0.4;
g = grpdelay(n,d,F,2);  % Equalize the passband
Gd = max(g)-g;
% Design the allpass delay equalizer
[num,den,tau] = iirgrpdelay(6, F, [0 0.4], Gd);                  %设计六阶的全通滤波器
[b,a]=iirgrpdelay(6,F,[0 0.4],Gd);
He1=dfilt.df2(b,a);
He=dfilt.df2(n,d);
He_all=dfilt.cascade(He,He1);
grpdelay(He_all)                                            %DFILT:Digital Filter Implementation.
%[GdA,w] = grpdelay(num,den,512);
%figure(2);
%plot(w/pi,GdH+GdA); grid
%xlabel('\omega/\pi');ylabel('Group delay, samples');
%title('Group Delay Equalized Filter');
2设计巴特沃兹模拟低通滤波器，其滤波器的阶数和3-dB截止频率由键盘输入，程序能根据输入的参数，绘制滤波器的增益响应。
% Program 2
% Program to Design Butterworth Analog Lowpass Filter
% Type in the filter order and passband edge frequency设计边缘频率
N = input('Type in filter order = ');
Wn = input('3-dB cutoff angular frequency = ');
% Determine the transfer function
[num,den] = butter(N,Wn,'s');                                          %计算滤波器的分子和分母
%  Compute and plot the frequency response
[h,w]=freqz(num,den);
plot (w/pi,20*log10(abs(h)));
xlabel('\omega/\pi'); ylabel('Magnitude, dB');
title('The magnitude respponse of the system')
axis([0 3 -80 5])
3%%%%%%%%%%
% To use the residue
num=[1,-0.2,0.5,0,0];
den=[1,3.2,1.5,-0.8,1.4];
[r,p,k]=residue(num,den)
4% Program 4
% Cheby1 analog highpass filter design
%
Wp=0.75;Ws=0.35;Rs=43;Rp=0.5;
[N,Wn]=cheb1ord(Wp,Ws,Rp,Rs,'s');
% Determine the coefficients of the transfer function
[num,den]=cheby1(N,Rp,Wn,'high','s');
% Compute and plot the frequency response
omega=[0:1:30*pi];                                              %w=0:0.01:pi;
h=freqs(num,den,omega);                          %plot(w/pi,20*log10(abs(h))) plot(omega/(2*pi),20*log10(abs(h)));
xlabel('\omega/\pi');ylabel('Magnitude,dB');
title('IIR Chebyshev1 Highpass Filter/digital')
5.
% Program to 绘制30点序列的实部与虚部
%
n=0:29;
x=0.2*exp((0.4+0.5*j).*n);
subplot(1,2,1)
stem(n,real(x))
title('The real part ');
xlabel('n');ylabel('magnitude')
subplot(1,2,2)
stem(n,imag(x))
title('The imagine part')
xlabel('n');ylabel('magnitude')
6.
% Program to Design Type 1 Chebyshev analog Lowpass Filter
%
% Read in the filter order, passband edge frequency
% and passband ripple in dB
N = input('Order = ');
Wc = input('type in the 3 dB cutoff frequency=');
matlab求傅里叶变换
Rp = input(' Type in the peak ripple value in passband: ');
% Determine the coefficients of the transfer function
[num,den] = cheby1(N,Rp,Wc,'s');
% Compute and plot the frequency response
[h,w]=freqs(num,den);
plot (w/pi,20*log10(abs(h)));
xlabel('Frequency, Hz'); ylabel('magnitude, dB');
title('IIR Chebyshev1 Lowpass Filter/analog')
grid on
7.
% Determination of the Factored Form
% of a Rational z-Transform
%熟悉命令[num,den]=residuez(r,p,k)；[r,p,k]=residuez(num,den) clear all
r = [1 0.6 1.8];
p =[-3.2 2.4 2.4];
k =0.2;
[num, den] = residuez(r,p,k);
disp('Numerator polynomial coefficients'); disp(num)
disp('Denominator polynomial coefficients'); disp(den)
8,  设计IIR数字带通滤波器
% Program to Design iir digital bandpass Filter
clear all
Wp = [0.4 0.6];                                                        %Wp and Ws 都是向量组，带通的性质
Ws = [0.3 0.7];
Rp = 0.6;
Rs = 35;
[N,Wn] = buttord(Wp, Ws, Rp, Rs);
[b,a] = butter(N,Wn);                                  %巴特卧兹滤波器的分子和分母
[h,w] = freqz(b,a,256);                                %求出在频域的画图点，256，即要花的点数
gain = 20*log10(abs(h));
plot (w/pi,gain);grid on
xlabel('\omega/\pi'); ylabel('magnitude, dB');
title('IIR Butterworth Bandpass Filter');
9%draw the requested sequence
clear
n=0:23;
x=2*0.9.^n;
stem(n,x)
title('x[n]')
xlabel('n');ylabel('magnitude')
grid on
10%
% Program to Design Elliptic analog Lowpass Filter                  %椭圆模拟低通滤波器设计
% Read in the filter order, passband edge frequency,
% passband ripple in dB and minimum stopband
% attenuation in dB

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