1、离散时间信号处理课程设计 设计要求:某雷达系统接收机框架如图1所示。接收机输入信号,其中,中心频率=40MHz,为相位调制函数(调制带宽B=2MHz),信号谱如图2所示。输出基带信号In、Qn数据率(采样率)为2.5MHz。LPFADCNCOLPF采样率变换采样率变换数字信号处理单元Xc(t)cosw0nsinw0nfsXnS_InS_Qn图1 接收机原理框架BfXc(f)f0-f0B图2 接收信号参数 1. 请设计ADC的采样率fs,画出xn的频谱X(ejw)2. 请推导正交解调器的输出S_In和S_Qn的表达式,画出频谱示意图;若要将信号谱搬移到零中频,请确定NCO的频率W03. 请设计一
2、个FIR线性相位数字LPF对正交解调的输出进行处理,要求杂散抑制比超过50dBc,确定滤波器设计指标、给出设计过程和结果。4. 请确定采样率变换模块的参数(抽取或内插系数),画出输出信号谱。设计过程1.设计ADC的采样率fs,画出xn的频谱X(ejw)Adc采样率fs=2*f0,fs取100MHZ。(t)为相位调制函数(调制带宽B=2MHz),取(t)=cos(2*1000000*t)作为单音调制信号,则,程序如下:clear;clc;clf;n0=20000;%点数sprate=100000000;%采样频率100Mt0=n0/sprate;%总时长fca=40000000;%载波频率fsi
3、=1000000;%信号频率t=linspace(0,t0,n0);Dsb=cos(2*pi*fca*t+cos(fsi*2*pi*t);subplot(3,1,1);plot(t(1:100),Dsb(1:100);title(时域);xlabel(t);ylabel(voltage);grid on;legend(modulated signal);subplot(3,1,2);w=linspace(-1,1,n0);plot(w,fftshift(abs(fft(Dsb);title(幅频);xlabel(w);ylabel(|X(ejw)|);grid on;legend(modula
4、ted signal);subplot(3,1,3);plot(w,fftshift(angle(fft(Dsb);title(相频);xlabel(w);ylabel(X(ejw);grid on;legend(modulated signal);上图中频域图0.8代表0.8*100000000/2 = 40M2.推导正交解调器的输出S_In和S_Qn的表达式,画出频谱示意图;若要将信号谱搬移到零中频,请确定NCO的频率W0W0=4/5S_In = xn* cosw0n=cos4n/5 +cosn/50*cos4n/5Sl=Dsb.*cos(2*pi*fca*t);subplot(3,1,1
5、);plot(t(1:100),Sl(1:100);title(时域);xlabel(t);ylabel(voltage);grid on;legend(modulated signal);subplot(3,1,2);plot(w,fftshift(abs(fft(Sl);title(幅频);xlabel(w);ylabel(|X(ejw)|);grid on;legend(modulated signal);subplot(3,1,3);plot(w,fftshift(angle(fft(Sl);title(相频);xlabel(w);ylabel(X(ejw);grid on;legen
6、d(modulated signal);S_Qn =xn* sinw0n=cos4n/5 +cosn/50*sin4n/5Sq=Dsb.*sin(2*pi*fca*t);subplot(3,1,1);plot(t(1:100),Sq(1:100);title(时域);xlabel(t);ylabel(voltage);grid on;legend(modulated signal);subplot(3,1,2);plot(w,fftshift(abs(fft(Sq);title(幅频);xlabel(w);ylabel(|X(ejw)|);grid on;legend(modulated si
7、gnal);subplot(3,1,3);plot(w,fftshift(angle(fft(Sq);title(相频);xlabel(w);ylabel(X(ejw);grid on;legend(modulated signal);3.设计一个FIR线性相位数字LPF对正交解调的输出进行处理,要求杂散抑制比超过50dBc,确定滤波器设计指标、给出设计过程和结果。在20Mhz左右范围内混叠产生一些频率需滤除,所以设计fir的指标为:fpass=5MHZ,fstop=15MHZ,要求杂散抑制比超过50dBc,取Astop=50db时就已足够了。窗函数采用Kaiser窗,wp=/10,ws=3/
8、10,wc=/5, w=/5,A=50= 0.5842*(A-21)0.4+0.07886*(A-21)=4.5336M=(A-8)/(2.285*pi/5) = 29.254M取30pp=linspace(0,29,30);hlp=(sin(pp-15)*pi/5)./(pp-15)*pi);hlp(16)=0.2;h=hlp.*FIRLPF;scatter(pp,h,o);subplot(3,1,2);ll=linspace(0,2*pi,20000);h3=zeros(1,20000);for k=1:20000 h3(k)=0; for i=1:30 h3(k) = h3(k) + h
9、(i)*exp(-1j*2*pi*(k-1)*(i-1)/20000); endendplot(ll,10*log(abs(h3);grid on;xlabel(w);ylabel(dB);4.确定采样率变换模块的参数(抽取或内插系数),画出输出信号谱。S_In通过低通滤波器后Sl=Dsb.*cos(2*pi*fca*t);Sl=conv(Sl,h);subplot(3,1,1);plot(t(1:1000),Sl(1:1000);title(时域);xlabel(t);ylabel(voltage);grid on;legend(modulated signal);subplot(3,1,2
10、);w=linspace(-1,1,20029);plot(w,fftshift(abs(fft(Sl);title(幅频);xlabel(w);ylabel(|X(ejw)|);grid on;legend(modulated signal);subplot(3,1,3);plot(w,fftshift(angle(fft(Sl);title(相频);xlabel(w);ylabel(X(ejw);grid on;legend(modulated signal);采样率降为2.5M,即抽取系数为40,程序如下Sll=zeros(1,500);for i=1:500 Sll(i)=Sl(i*4
11、0);endsubplot(3,1,1);plot(t(1:200),Sll(1:200);title(时域);xlabel(t);ylabel(voltage);grid on;legend(modulated signal);subplot(3,1,2);w=linspace(-1,1,500);plot(w,fftshift(abs(fft(Sll);title(幅频);xlabel(w);ylabel(|X(ejw)|);grid on;legend(modulated signal);subplot(3,1,3);plot(w,fftshift(angle(fft(Sll);titl
12、e(相频);xlabel(w);ylabel(X(ejw);grid on;legend(modulated signal);对S_Q做同样的操作Sq=Dsb.*sin(2*pi*fca*t);Sq=conv(Sq,h);subplot(3,1,1);plot(t(1:1000),Sq(1:1000);title(时域);xlabel(t);ylabel(voltage);grid on;legend(modulated signal);subplot(3,1,2);w=linspace(-1,1,20029);plot(w,fftshift(abs(fft(Sq);title(幅频);xla
13、bel(w);ylabel(|X(ejw)|);grid on;legend(modulated signal);subplot(3,1,3);plot(w,fftshift(angle(fft(Sq);title(相频);xlabel(w);ylabel(X(ejw);grid on;legend(modulated signal);降采样后Sqq=zeros(1,500);for i=1:500 Sqq(i)=Sq(i*40);endsubplot(3,1,1);plot(t(1:200),Sqq(1:200);title(时域);xlabel(t);ylabel(voltage);grid on;legend(modulated signal);subplot(3,1,2);w=linspace(-1,1,500);plot(w,fftshift(abs(fft(Sqq);title(幅频);xlabel(w);ylabel(|X(ejw)|);grid on;legend(modulated signal);subplot(3,1,3);plot(w,fftshift(angle(fft(Sqq);title(相频);xlabel(w);ylabel(X(ejw);grid on;legend(modulated signal);