数字信号处理—matlab实现.doc

题目一 : A sinusoid正弦曲线 of frequency频率 ω0=0.1πand duration持续 of 300 samples样本, that is ,0≤n300, is input to a (causal) filter滤波器 with transfer 转移function功能 ,where a=0.97。Adjust调整 the scale factor因子 b such that the filter’s gain增益 at ω0 is unity唯一的。 Determine确定 and plot画出 the input x(n) and the output y(n) of the filter over the interval间隔 0≤n450, by iterating重复 the difference equation相等的 of the filter. At the same time, plot the filter’s magnitude response.响应 程序代码： w0=0.1*pi;%输入x(n)序列 n=0:299; x=sin(w0*n); subplot(3,1,1); stem(n,x,.); xlabel(n); ylabel(x(n)); a=[1 -0.97]; %求出滤波器的系数a,b (|h(z)|==1) b=abs(1+a(2)*exp(-j*0.1*pi)); y1=filter(b,a,x);%利用给定的系数a,b对x中的数据滤波，结果放在y1中 N=450; y=zeros(1,N); for m=1:300 y(m)=y1(m); end; n=[0:length(y)-1]; subplot(3,1,2); stem(n,y,.); axis([0,450,-2,2]); xlabel(n); ylabel(y); w=0:0.02*pi:2*pi; Hw=abs(freqz(b,a,w));%求出频率响应 subplot(3,1,3); plot(w,Hw); grid on; axis([0,0.5*pi,0,15]); xlabel(w);ylabel(Hw); 程序图： 题目二: It is desired to extract a constant signal x (n)=s(n)+ ν(n)=s+ ν (n),where ν(n) is zero-mean white Caussian noise of varianceбv2 . (1) First-order IIR smoother; To this end, the following IIR lowpass filter is used:, where the parameter a is restrict to the range 0a1.This can be achieve in two ways. (2) FIR averaging filters: Consider ,for example, the third-order filter H(z)=h0+h1z-1+h2z-2+h3z-3.(提示:当h0,h1,h2,h3四个系数相等时,其噪声抑制效果最佳)． 程序代码： （1）s=3;%常数序列 v=randn(1,100);%噪声序列 x=v+s;%加噪序列 N=0:99; subplot(311); plot(N,x) xlabel(N);ylabel(x); axis([0 100 0 5]); a=0.5; b=1-a; m=b; n=[1,-a]; y1=filter(m,n,x);%滤波后的序列 subplot(312); plot(y1) xlabel(n);ylabel(y1); axis([0 100 0 5]); title(a=0.5); s=3; v=randn(1,100); x=v+s; a=0.99; b=1-a; m=b; n=[1,-a]; y2=filter(m,n,x); subplot(313); plot(y2) xlabel(n);ylabel(y2); title(a=0.99); 程序图： （2） s=3;%常数序列 v=randn(1,100);%噪声序列 x=v+s;%加噪序列 N=0:99; subplot(411); plot(N,x) xlabel(N);ylabel(x); axis([0 100 0 5]); a=0.1; b=1-a; m=[0.1,0.2,0.3,0.4]; %滤波器系数不同 n=1; y1=filter(m,n,x); su