1、武汉大学数学与统计学院数学实验七MATLAB中的数学变换与特殊函数的积分 v Fourier变换与 Fourier逆变换v Laplace变换与 Laplace逆变换v Z变换与 Z逆变换v 特殊函数的积分一、 Fourier变换和逆 Fourier变换武汉大学数学与统计学院FOURIER(f,v) F(v) = int(f(x)*exp(-i*v*x),x,-inf,inf).FOURIER(f,u,v) F(v) = int(f(u)*exp(-i*v*u),u,-inf,inf).IFOURIER(F,u) f(u) = 1/(2*pi) * int(F(w)*exp(i*w*u,w,-
2、inf,inf)IFOURIER(F,v,u) f(u) = 1/(2*pi) * int(F(v)*exp(i*v*u,v,-inf,inf), vsyms t v w xvfourier(1/t) returns i*pi*(Heaviside(-w)-Heaviside(w)v fourier(exp(-x2),x,t) returns pi(1/2)*exp(-1/4*t2)v fourier(exp(-t)*sym(Heaviside(t),v) returns 1/(1+i*v)v fourier(diff(sym(F(x),x,w) returns i*w*fourier(F(x
3、),x,w) syms t u w xifourier(w*exp(-3*w)*sym(Heaviside(w) returns 1/2/pi/(3-i*t)2 ifourier(1/(1 + w2),u) returns1/2*exp(-u)*Heaviside(u)+1/2*exp(u)*Heaviside(-u) ifourier(v/(1 + w2),v,u) returns i/(1+w2)*Dirac(1,-u) ifourier(sym(fourier(f(x),x,w),w,x) returns f(x)二、 Laplace变换和逆 Laplace变换 syms a s t w
4、 x laplace(x5) returns 120/s6 laplace(exp(a*s) returns 1/(t-a) laplace(sin(w*x),t) returns w/(t2+w2) laplace(cos(x*w),w,t) returns t/(t2+x2) laplace(xsym(3/2),t) returns3/4*pi(1/2)/t(5/2)q syms s t w x yq ilaplace(1/(s-1) returns exp(t)q ilaplace(1/(t2+1) returns sin(x)q ilaplace(t(-sym(5/2),x) returns 4/3/pi(1/2)*x(3/2)q ilaplace(y/(y2 + w2),y,x) returns cos(w*x)qilaplace(sym(laplace(F(x),x,s),s,x) returns F(x)三 Z变换与逆 Z变换武汉大学数学与统计学院F = ZTRANS(f) F(z) = symsum(f(n)/zn, n, 0, inf)F = ZTRANS(f,w)F(w) = symsum(f(n)/wn, n, 0, inf).F = ZTRANS(f,k,w)F(w) = symsum(f(k)/wk, k, 0, inf).
