Q8Advanced Engineering Mathematics I

1. Complex Fourier Transform: $F\{f(x)\}=F(s)={\int }_{-\infty }^{\infty }f(x)e^{-isx}dx$ Inverse: $f(x)=\frac{1}{2\pi }{\int }_{-\infty }^{\infty }F(s)e^{isx}ds$

2. Fourier Cosine Transform: $F_c\{f(x)\}=F_c(s)=\sqrt{\frac{2}{\pi }}{\int }_0^{\infty }f(x)\cos (sx)dx$ Inverse: $f(x)=\sqrt{\frac{2}{\pi }}{\int }_0^{\infty }{F}_c(s)\cos (sx)ds$