Fourier Transform - Prerequisites

 $a+jb$  

 $R\angle\theta$  

 $Re^{j\theta}$  

 $R\left(\cos\theta+j\sin\theta\right)$  

ALL OPTIONS are TRUE

 $\left(A_c\right)^2$  

 $\frac{\left(A_c\right)^2}{2}$  

 $\int_{-\infty}^{\infty}x\left(t\right)e^{-j2\pi ft}dt$  

 $\int_{-\infty}^{\infty}x\left(t\right)e^{-j2\pi ft}df$  

 $\int_{-\infty}^{\infty}x\left(t\right)e^{j2\pi ft}dt$  

 $\int_{-\infty}^{\infty}x\left(t\right)e^{j2\pi ft}df$  

 $\int_{-\infty}^{\infty}X\left(f\right)e^{-j2\pi ft}dt$  

 $\int_{-\infty}^{\infty}X\left(f\right)e^{-j2\pi ft}df$  

 $\int_{-\infty}^{\infty}X\left(f\right)e^{j2\pi ft}dt$  

 $\int_{-\infty}^{\infty}X\left(f\right)e^{j2\pi ft}df$  

$\delta\left(f\right)$

$\frac{\sin\left(\pi f\right)}{\left(\pi f\right)}$

$1$

$\delta\left(1\right)$

 $\delta\left(f\right)=0\ \forall\ f\ne0\ and\ \int_{-\infty}^{\infty}\delta\left(f\right)df=1$  

 $\delta\left(f\right)=1\ when\ f=0,\ and\ \delta\left(f\right)\ =\ 0\ \forall\ f\ne0$  

 $\cos\left(j\theta\right)+\sin\left(j\theta\right)$  

 $\cos\left(\theta\right)+j\sin\left(\theta\right)$  

 $\frac{e^{j\theta}+e^{-j\theta}}{2}$  

 $\frac{e^{j\theta}-e^{-j\theta}}{2j}$  

 $\frac{1}{2}\left[\cos\left(A+B\right)+\cos\left(A-B\right)\right]$  

 $\frac{1}{2}\left[\cos\left(A-B\right)-\cos\left(A+B\right)\right]$  

$F\left\{x\left(t\right)e^{j2\pi f_ct}\right\}=X\left(f-f_c\right)$

$F\left\{x\left(t\right)e^{-j2\pi f_ct}\right\}=X\left(f+f_c\right)$

Both

None

 $M\left(f+f_c\right)+M\left(f-f_c\right)$  

 $\frac{1}{2}\left[M\left(f+f_c\right)+M\left(f-f_c\right)\right]$  

 $\frac{1}{2}\left[M\left(f+f_c\right)-M\left(f-f_c\right)\right]$  

 $M\left(f_c\right)$