连续时间傅里叶变换创新.pptVIP

heaviside：单位阶跃函数 help heaviside HEAVISIDE Unit Step function f=Heaviside(t) returns a vector f the same size as the input vector, where each element of f is 1 if the corresponding element of t is greater than zero. 举例： syms t; y=cos(t)*(heaviside(t+0.5*pi)-heaviside(t-0.5*pi)); ezplot(y); 解： 主要代码 % exe4_7_a.m clear; x1=sym((1/2)*exp(-2*t)*heaviside(t)); x2=sym(exp(-4*t)*heaviside(t)); subplot(2,1,1); ezplot(x1,[0,2]); legend(x1); axis([0 2 0 1]); subplot(2,1,2); ezplot(x2,[0,2]); legend(x2); axis([0 2 0 1]); fourier函数 FOURIER Fourier integral transform. F = FOURIER(f) is the Fourier transform of the sym scalar f with default independent variable x. F(w) = int(f(x)*exp(-i*w*x),x,-inf,inf) See also sym/ifourier, sym/laplace, sym/ztrans. 主要代码 % exe4_7_a.m x1=sym((1/2)*exp(-2*t)*heaviside(t)); x2=sym(exp(-4*t)*heaviside(t)); X1=fourier(x1); X2=fourier(x2); subplot(2,1,1); ezplot(abs(X1),[-20,20]);legend(|X1|) axis([-20 20 0 0.3]); subplot(2,1,2); ezplot(abs(X2),[-20,20]);legend(|X2|) axis([-20 20 0 0.3]); 练习1 close all;clear all; syms t a u % exersice 1: Fourier transform of exp(-abs(t)) x1=exp(-abs(t)); X1=fourier(x1) ezplot(X1,[-10,10]);axis([-10,10 0 2.1]); x11=ifourier(X1,w) figure; x111=simple(x11) ezplot(x111,[-10,10]);axis([-10,10 0 1.1]); 运行结果1 X1 = 2/(w^2 + 1) x11 = (2*pi*exp(-w)*heaviside(w) + 2*pi*heaviside(-w)*exp(w))/(2*pi) x111 = exp(-w)*heaviside(w) + heaviside(-w)*exp(w) 练习2 % exersice 2: Fourier transform of % exp(-a*t)*heaviside(t) x2=exp(-a*t)*heaviside(t); X2=fourier(x2); a=2; X22=subs(X2) x22=ifourier(X22) figure; subplot(2,1,1);ezplot(abs(X22),[-10 10]); subplot(2,1,2);ezplot(angle(X22),[-10 10]); 运行结果2 X22 = 1/(w*i + 2) x22 = exp(-2*x)*heaviside(x) H31 = 2/5 - i/5 练习3 % exersice 3: sinusoidal signals pass the RC low pass filter x3=sin(t)+sin(3*t); H31=subs(X22,w,1) H33=subs(X22,w,3) x33=abs(H31)*sin(t+angle(H31))+abs(H33)*sin(3*t+angle(H33)); figure; subplot(2,1,1);ezplot(x3,[-10 10]); subplot(2,1,2);ezplot(x33,[-10 10]