Fourier Transform Definition The problem assumes a specific normalization for the Fourier Transform, likely $F(s) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{\infty} f(x) e^{-isx} dx$. 2. Triangular Pulse The function is likely a triangular pulse defined as $f(x) = \max(0, 1 - |x|/a)$. 3. FT of Triangular Pulse The Fourier Transform of $f(x) = \max(0, 1 - |x|/a)$ is $\frac{4 \sin^2(as/2)}{s^2}$ (using the definition $\int f(x)e^{-isx}dx$). 4. Matching the Option Applying the normalization $F(s) = \frac{1}{\sqrt{2\pi}} \int f(x) e^{-isx} dx$ to the triangular pulse yields $F(s) = \frac{1} {\sqrt{2\pi}} \frac{4 \sin^2(as/2)}{s^2} = \frac{2\sqrt{2}}{\sqrt{\pi}} \frac{\sin^2(as/2)} {s^2}$. This matches option C: $ \frac{2\sqrt{2}\sin^2\left(\frac{\text{as}} {2}\right)}{\sqrt{\pi}\text{as}^2} = \frac{2\sqrt{2}}{\sqrt{\pi}} \frac{\sin^2(as/2)}{a^2 s^2} a = \frac{2\sqrt{2}}{\sqrt{\pi}} \frac{\sin^2(as/2)}{as^2}$. 408. If two roots of the equation 4x³ + 20x² - 23x + 6 = 0 are equal, then roots of the equation are – - Question not attempted
Asked in Asst. Statistical Officer (Agri. Deptt.) 2024 · Topic: Mechanics (Newton's Laws of Motion and their applications)
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