Find the fourier transform of the triangle function give below.f( t)=( a+ t)/a² −a< t<0,( a-t)/a² 0< t< a,0 | t|> a please ca you give me the solving to human understand method

To find the Fourier Transform of the given triangle function, we will use the definition of the Fourier Transform and exploit the symmetry of the function.

Step 1: Define the Fourier Transform
The Fourier Transform $F(\omega)$ of a function $f(t)$ is given by the integral:

$$F(\omega) = \int_{-\infty}^{\infty} f(t) e^{-j\omega t} dt$$

Step 2: Substitute the function into the integral
The function $f(t)$ is non-zero only for $-a < t < a$. Therefore, the integral limits can be restricted:

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