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Answer by Marcus Müller for Why is energy zero at zero bandwidth?

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The curves represent energy (or power) densities; thus, energy is what you get when you integrate them over a range. For example, you could get the power in the range 1000 Hz to 2000 Hz by integrating over the curve:

$$P_{1\,\text{kHz}\to2\,\text{kHz},\text{ woman}} = \int_{1000}^{2000} S_{\text{woman}}(f)\,\mathrm{d}f,$$

i.e. the area under the curve.

Now, since this curve is bounded at every point, the integral for a single point (so, the integral from 20 kHz to 20 kHz) is zero. That's a basic property of integrals.


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