GATE ECE 2025 | Question: 8

Question

Consider a continuous-time, real-valued signal $f(t)$ whose Fourier transform $F(\omega)=\int_{-\infty}^{\infty} f(t) \exp (-j \: \omega t) d t$ exists.

Which one of the following statements is always TRUE?

• A. $\mid F(\omega) \mid  \leq \int_{-\infty}^{\infty}\mid f(t)\mid  d t$
• B. $\mid F(\omega)\mid >\int_{-\infty}^{\infty}\mid f(t)\mid  d t$
• C. $\mid F(\omega)\mid  \leq \int_{-\infty}^{\infty} f(t) d t$
• D. $\mid F(\omega)\mid  \geq \int_{-\infty}^{\infty} f(t) d t$

Answer 1

|e^-jwt|=1, since for a integral the magnitude of integral will be greater..... So option A