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_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) |
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