Power-Complementary Reflection and Transmission

We can show that the reflectance and transmittance of the yielding termination are power complementary. That is, the reflected and transmitted signal-power sum to yield the incident signal-power.

The average power incident at the bridge at frequency can be expressed in the frequency domain as . The reflected power is then . Removing the minus sign, which can be associated with reversed direction of travel, we obtain that the power reflection frequency response is , which generalizes by analytic continuation to . The power transmittance is given by

which generalizes to the plane as

Finally, we see that adding up the reflected and transmitted power yields the incident power:

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.