Let $f(t)$ be an even function, i.e., $f(-t)=f(t)$ for all $t$. Let the Fourier transform of $f(t)$ be defined as

$F(\omega)=\int_{-\infty}^{\infty} f(t) e^{-j \omega t} d t$. Suppose $\frac{d F(\omega)}{d \omega}=-\omega F(\omega)$ for all $\omega$ and $F(0)=1$. Then

Consider a continuous time signal $x(t)$ defined by $x(t)=0$ for $|t|>1$ and $x(t)=1-|t|$ for $|t| \leq 1$ Let the Fourier transform of $x(t)$ be defined as $X(\omega)=\int_{-\infty}^{\infty} x(t) e^{-j \omega t} d t$. The maximum magnitude of $X(\omega)$ is $\_\_\_\_$ .

Suppose x₁(t) and x₂(t) have the Fourier transforms as shown below. Which one of the following statements is TRUE?

Consider a signal defined by $$$x\left(t\right)=\left\{\begin{array}{l}e^{j10t}\;\;\;for\;\left|t\right|\leq1\\0\;\;\;\;\;\;\;for\;\;\left|t\right|>1\end{array}\right.$$$ Its Fourier Transform is