MATLAB 傅里叶变换

fourier函数

进行傅里叶变换。

语法


fourier(f)
fourier(f,transVar)
fourier(f,var,transVar)

描述

表达式描述
fourier(f)返回f的傅里叶变换。默认情况下，函数symvar决定自变量，w是变换变量。
fourier(f,transVar)使用转换变量transVar而不是w。
fourier(f,var,transVar)分别用自变量var和转换变量transVar代替symvar和w。

常用的傅里叶变换输入

函数 输入/输出 语法
矩形脉冲 输入

syms a b t
f = rectangularPulse(a,b,t);

f_FT = fourier(f)
输出 f_FT =- (sin(a*w) + cos(a*w)*1i)/w + (sin(b*w) + cos(b*w)*1i)/w
单位脉冲(狄拉克) 输入

f = dirac(t);

f_FT = fourier(f)
输出 f_FT =1
绝对值 输入 f = a*abs(t);
f_FT = fourier(f)
输出 f_FT =
-(2*a)/w^2
Step(Heaviside) 输入 f = heaviside(t);
f_FT = fourier(f)
输出 f_FT =
pi*dirac(w) – 1i/w
常数 输入 f = a;
f_FT = fourier(a)
输出 f_FT =pi*dirac(1, w)*2i
余弦cos 输入 f = a*cos(b*t);
f_FT = fourier(f)
输出 f_FT =pi*a*(dirac(b + w) + dirac(b – w))
正弦Sin 输入 f = a*sin(b*t);
f_FT = fourier(f)
输出 f_FT =pi*a*(dirac(b + w) – dirac(b – w))*1i
Sign 输入 f = sign(t);
f_FT = fourier(f)
输出 f_FT =-2i/w
三角Triangle 输入 syms c
f = triangularPulse(a,b,c,t);
f_FT = fourier(f)
输出 f_FT =-(a*exp(-b*w*1i) – b*exp(-a*w*1i) – a*exp(-c*w*1i) + …
c*exp(-a*w*1i) + b*exp(-c*w*1i) – c*exp(-b*w*1i))/ …
(w^2*(a – b)*(b – c))
右侧指数 输入 f = exp(-t*abs(a))*heaviside(t);
f_FT = fourier(f)

assume(a > 0)
f_FT_condition = fourier(f)
assume(a,’clear’)
输出 f_FT =1/(abs(a) + w*1i) – (sign(abs(a))/2 – 1/2)*fourier(exp(-t*abs(a)),t,w)

f_FT_condition =1/(a + w*1i)
两侧指数 输入 assume(a > 0)
f = exp(-a*t^2);
f_FT = fourier(f)
assume(a,’clear’)
输出 f_FT =(pi^(1/2)*exp(-w^2/(4*a)))/a^(1/2)
高斯 输入 assume([b c],’real’)
f = a*exp(-(t-b)^2/(2*c^2));
f_FT = fourier(f)

f_FT_simplify = simplify(f_FT)
assume([b c],’clear’)
输出 f_FT =(a*pi^(1/2)*exp(- (c^2*(w + (b*1i)/c^2)^2)/2 – b^2/(2*c^2)))/ …
    (1/(2*c^2))^(1/2)

f_FT_simplify =2^(1/2)*a*pi^(1/2)*exp(-(w*(w*c^2 + b*2i))/2)*abs©
第一类贝塞尔函数，nu = 1 输入 syms x
f = besselj(1,x);
f_FT = fourier(f);
f_FT = simplify(f_FT)
输出 f_FT =(2*w*(heaviside(w – 1)*1i – heaviside(w + 1)*1i))/(1 – w^2)^(1/2)