Topic: Continuous-time Signals
Value of the integral $\int_{-\infty}^{\infty}\delta(t)sin(\frac{t}{\sqrt{2}})dt$ is:
- A. 0.707
- B. 1.414
- C. 0
- D. 1
Answer: C. 0
Explanation: By the sifting property of the Dirac delta function, $\int_{-\infty}^{\infty} f(t)\delta(t)dt = f(0)$. Here, $f(t) = \sin(\frac{t}{\sqrt{2}})$. Evaluating at $t = 0$ gives $f(0) = \sin(0) = 0$.