Mathematical Methods and Algorithms for Signal Processing Authors: Todd K. Moon, Wynn C. Stirling Context: This text is a graduate-level staple in Electrical Engineering and Applied Mathematics, known for its rigorous approach to the linear algebra and optimization theory underpinning modern signal processing.
Therefore, the Fourier transform of the signal $x(t) = e^-2$ is:
$$X(\omega) = \int_-\infty^\infty x(t) e^-j\omega t dt$$
Using the definition of the absolute value function, we can split the integral into two parts: