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Multiplying $g(t)$ by $e^{-2\pi i ft}$ rotates the signal's amplitude around the complex plane at a rate determined by $f$. When averaged over time, contributions from frequencies matching $f$ accumulate constructively (moving away from the origin), while mismatched frequencies tend to cancel out due to symmetric distribution around the circle.

Conditions: $g(t)$ is a real-valued time-domain signal.; $f$ represents cycles per unit time.; The averaging is performed over a finite or infinite time window.

Multiplying $g(t)$ by $e^{-2\pi i ft}$ rotates the signal's amplitude around the complex plane at a rate determined by $f$. When averaged over time, contributions from frequencies matching $f$ accumulate constructively (moving away from the origin), while mismatched frequencies tend to cancel out due to symmetric distribution around the circle.

Conditions: $g(t)$ is a real-valued time-domain signal.; $f$ represents cycles per unit time.; The averaging is performed over a finite or infinite time window.