例 1-1%周期信号（方波）的展开,fb_jinshi.mclose all;clear all;N=100; %取展开式的项数为 2N＋1 项 T=1;fs=1/T;N_sample=128; %为了画出波形，设置每个周期的采样点数dt = T/N_sample; t=0:dt:10*T-dt; n=-N:N;Fn = sinc(n/2).*exp(-j*n*pi/2);Fn(N+1)=0; ft = zeros(1,length(t));for m=-N:N ft = ft + Fn(m+N+1)*exp(j*2*pi*m*fs*t);end plot(t,ft)例 1-2利用 FFT 计算信号的频谱并与信号的真实频谱的抽样比较。脚本文件 T2F.m 定义了函数 T2F，计算信号的傅立叶变换。function [f,sf]= T2F(t,st)%This is a function using the FFT function to calculate a signal's Fourier%Translation%Input is the time and the signal vectors,the length of time must greater%than 2%Output is the frequency and the signal spectrumdt = t(2)-t(1);T=t(end);df = 1/T;N = length(st); f=-N/2*df:df:N/2*df-df; sf = fft(st);sf = T/N*fftshift(sf);脚本文件 F2T.m 定义了函数 F2T，计算信号的反傅立叶变换。function [t st]=F2T(f,sf)%This function calculate the time signal using ifft function for the input%signal's spectrum df = f(2)-f(1);Fmx = ( f(end)-f(1) +df);dt = 1/Fmx;N = length(sf);T = dt*N; %t=-T/2:dt:T/2-dt;t = 0:dt:T-dt; sff = fftshift(sf);st = Fmx*ifft(sff); 另写脚本文件 fb_spec.m 如下：%方波的傅氏变换, fb_spec.mclear all;close all;T=1;N_sample = 128;dt=T/N_sample; t=0:dt:T-dt;st=[ones(1,N_sample/2), -ones(1,N_sample/2)]; %方波一个周期 subplot(211);plot(t,st);axis([0 1 -2 2]);xlabel('t'); ylabel('s(t)');subplot(212);[f sf]=T2F(t,st); %方波频谱plot(f,abs(sf)); hold on;axis([-10 10 0 1]);xlabel('f');ylabel('|S(f)|'); %根据傅氏变换计算得到的信号频谱相应位置的抽样值sff= T^2*j*pi*f*0.5.*exp(-j*2*pi*f*T).*sinc(f*T*0.5).*sinc(f*T*0.5);plot(f,abs(sff),'r-')例 1-3%信号的能量计算或功率计算,sig_pow.mclear all;close all;dt = 0.01;t = 0:dt:5; s1 = exp(-5*t).*cos(20*pi*t);s2 = cos(20*pi*t);E1 = sum(s1.*s1)*dt; %s1(t)的信号能量P2 = sum(s2.*s2)*dt/(length(t)*dt); %s2(t)的信号功率 s[f1 s1f]=...
