Topic: Signals and Systems
Let $F(w)$ be the Fourier Transform of a function $f(t)$. The $F(0)$ is
- A. $\int_{-\infty}^{\infty}f(t)dt$
- B. $\int_{-\infty}^{\infty}|f(t)|^{2}dt$
- C. $\int_{-\infty}^{\infty}|t\cdot f(t)|^{2}dt$
- D. $\int_{-\infty}^{\infty}t\cdot f(t)dt$
Answer: A. $\int_{-\infty}^{\infty}f(t)dt$
Explanation: $F(\omega)=\int_{-\infty}^{\infty}f(t)e^{-j\omega t}dt$. Putting $\omega=0$, we get $F(0)=\int_{-\infty}^{\infty}f(t)e^{0}dt = \int_{-\infty}^{\infty}f(t)dt$.