Impulse response of LTI Systems I am trying to solve the attached question. Please I would appreciate if some one can check my approach and tell me if I am correct and how can I proceed to find h0(t)




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$h_0(t)$ is inverse Fourier transform of $H(jw)$. Your formula is OK, you can continue your calculation to practice your math manipulation, why not.
To check the result, you can remark that $H(jw)$ is rotated $sinc$ function. And $sinc$ must be the Fourier transform of a rectangular box function.