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The integral

$$\int_{-\infty}^{\infty}|X(f)|^2df$$

of the absolute Fourier spectrum squared is the energy in the signal, but what about the integral of the 'simple' absolute Fourier spectrum?

$$\int_{-\infty}^{\infty}|X(f)|df$$

Does it represent anything? I couldn't find any information on that point. Any hint would be appreciated!

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If $x(t)$ and $X(f)$ are Fourier transform pairs then the value

$$\int_{-\infty}^{\infty}|X(f)|df$$

can serve as an upper bound on the magnitude of $x(t)$:

$$|x(t)|=\left|\int_{-\infty}^{\infty}X(f)e^{j2\pi f t}df\right|\le \int_{-\infty}^{\infty}|X(f)|df$$

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