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Substituting $t = 0$ into the inverse Fourier transform formula simplifies the exponential term $e^{i\omega t}$ to 1, removing the oscillatory component from the integrand. This transforms the inverse transform equation into a direct relationship between the value of the original function at the origin, $f(0)$, and the integral of its Fourier transform $F(\omega)$ over the entire real line.

Conditions: The inverse Fourier transform formula is $f(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} F(\omega) e^{i\omega t} d\omega$.; The function $f(t)$ is the rectangular pulse with $f(0)=1$.; $F(\omega)$ is the previously computed Fourier transform $2 \frac{\sin \omega}{\omega}$.

Substituting $t = 0$ into the inverse Fourier transform formula simplifies the exponential term $e^{i\omega t}$ to 1, removing the oscillatory component from the integrand. This transforms the inverse transform equation into a direct relationship between the value of the original function at the origin, $f(0)$, and the integral of its Fourier transform $F(\omega)$ over the entire real line.

Conditions: The inverse Fourier transform formula is $f(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} F(\omega) e^{i\omega t} d\omega$.; The function $f(t)$ is the rectangular pulse with $f(0)=1$.; $F(\omega)$ is the previously computed Fourier transform $2 \frac{\sin \omega}{\omega}$.