qq_37278781的博客

卷积与相关函数卷积若已知函数f1(t)f_1(t)f1​(t)，f2(t)f_2(t)f2​(t)，则积分∫−∞+∞f1(τ)f2(t−τ)dτ\int_{-\infty}^{+\infty}f_1(\tau)f_2(t-\tau)d\tau∫−∞+∞​f1​(τ)f2​(t−τ)dτ称为函数f1(t)f_1(t)f1​(t)，f2(t)f_2(t)f2​(t)的卷积，记为f1(t)∗f2(t)f_1(t)*f_2(t)f1​(t)∗f2​(t)，即∫−∞+∞f1(τ)f2(t−τ)dτ=f1(t

Fourier变换的性质线性性质设F1(ω)=F[f1(t)]F_1(\omega)=\mathscr{F}[f_1(t)]F1​(ω)=F[f1​(t)]，F2(ω)=F[f2(t)]F_2(\omega)=\mathscr{F}[f_2(t)]F2​(ω)=F[f2​(t)]，α\alphaα，β\betaβ是常数，则F[αf1(t)+βf2(t)]=αF[f1(t)]+βF[f2(t)]=αF1(ω)+βF2(ω)\mathscr{F}[\alpha f_1(t)+\beta f_2(t)]=\

Fourier 变换Fourier 变换的概念定义  若函数f(t)f(t)f(t)在(−∞,+∞)(-\infty,+\infty)(−∞,+∞)上满足 Fourier 积分定理的条件则称函数F(ω)=∫−∞+∞f(t)e−jωt dtF(\omega)=\int_{-\infty}^{+\infty}f(t)e^{-j\omega t}\,dtF(ω)=∫−∞+∞​f(t)e−jωtdt为f(t)f(t)f(t)的Fourier 变换。称函数f(t)=12π∫−∞+∞F(ω)ejωt dωf

Fourier 变换Fourier 积分Fourier 积分公式Fourier 积分定理若f(t)f(t)f(t)在(−∞,+∞)(-\infty,+\infty)(−∞,+∞)上满足下列条件：f(t)f(t)f(t)在任一有限区间上满足DirichletDirichletDirichlet条件f(t)f(t)f(t)在无限区间(−∞,+∞)(-\infty,+\infty)(−∞,+∞)上绝对可积（即积分∫−∞+∞∣f(t)∣dt\displaystyle\int_{-\infty}^{+\