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

A 10 kHz even-symmetric square wave is passed through a bandpass filter with centre frequency at 30 kHz and 3 dB passband of 6 kHz. The filter output is