积分变换 一、Fourier变换1.fourier:正变换2.ifourier:逆变换 二、Laplace变换三、Z变换
一、Fourier变换 1.fourier:正变换
fourier(f,trans_var,eval_point)
f为原函数,trans_var为交换变量,eval_point为频率变量。
命令行:
输出:
>> TestF1 =pi^(1/2)*exp(-y^2/4) F2 =pi^(1/2)*exp(-w^2/4) F2y =pi^(1/2)*exp(-y^2/4) 2.ifourier:逆变换ifourier(F,trans_var,eval_point)
命令行:
输出:
>> Test f1t =exp(-x^2) f2t =exp(-x^2) f2ty =exp(-x^2) 二、Laplace变换fzdfh变换是一个线性变换,可将一个有参数实数t(t≥ 0)的函数转换为一个参数为复数s的函数。
laplace(f,trans_var,eval_var)Laplace正变换ilaplace(f,trans_var,eval_var)Laplace逆变换命令行:
clear;syms x a t sf1 = 1/sqrt(x);f2 = exp(-a*t);L1 = laplace(f1,x,s)L2 = laplace(f2)L2t = laplace(f2,s)f1t = ilaplace(L1,s,x)f2t = ilaplace(L2)f2ty = ilaplace(L2,s,x)输出:
>> Test L1 =pi^(1/2)/s^(1/2) L2 =1/(a + s) L2t =1/(a + s) f1t =1/x^(1/2) f2t =exp(-a*t) f2ty =exp(-a*x) 三、Z变换 Z变换ztrans(f,trans_var,eval_point)逆变换iztrans(F,trans_var,eval_point)命令行:
clear;syms x s tf1 = 1/sqrt(x);f2 = sin(t);z1 = ztrans(f1,x,s) %求f1的Z变换,用s代替频率变量z2 = ztrans(f2)z2y = ztrans(f2,s)f1t = iztrans(z1,s,x)f2t = iztrans(z2)f2yt = iztrans(z2y,s,x)输出:
>> Test z1 =ztrans(1/x^(1/2), x, s) z2 =(z*sin(1))/(z^2 - 2*cos(1)*z + 1) z2y =(s*sin(1))/(s^2 - 2*cos(1)*s + 1) f1t =1/x^(1/2) f2t =sin(n) f2yt =sin(x)