GATE EC 2023 Question Paper (05-Feb-2023) (Shift 2)

Consider a system with input 𝑥(𝑡) and output 𝑦(𝑡) = 𝑥(𝑒${}^{\text{t}}$). The system is

Let 𝑚(𝑡) be a strictly band-limited signal with bandwidth 𝐵 and energy 𝐸. Assuming 𝜔₀ = 10𝐵, the energy in the signal 𝑚(𝑡) cos 𝜔₀𝑡 is

The Fourier transform 𝑋(𝜔) of $\mathrm{x}(\mathrm{t})={\mathrm{e}}^{-{\mathrm{t}}^2}$ is

Note: ${\int }_{-\infty }^{\infty }{\mathrm{e}}^{-{\mathrm{y}}^2}\mathrm{dy}=\sqrt{\pi }$

In the table shown below, match the signal type with its spectral characteristics.

For a real signal, which of the following is/are valid power spectral density/densities?