Understanding Reflection Calculation in Wave Digital Filters

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Hello everyone,

this implementation that I'm trying to grasp. It involves calculating the reflected wave (b1) using the reflection coefficient and the incident plus reflected waves at two ports in a series adaptor.

The code snippet from wdf serial adaptor is as follows:
const auto b1 = port1.wdf.b - port1Reflect * (x + port1.wdf.b + port2.wdf.b);

I understand that port1Reflect is the reflection coefficient already computed based on the port resistances

But what equation does this calculation of the reflection of b come from? , I've been searching for papers and I don't see anything.

https://github.com/Chowdhury-DSP/chowds ... adaptors.h

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This old paper has pretty good description of all the basic WDF constructs: https://ccrma.stanford.edu/~jingjiez/po ... actice.pdf

But.. basically the wave variables are a=v+i*R and b=v-i*R where v is voltage, i is current and R is port impedance and the reflection coefficients can be obtained by solving for Kirchoff current/voltage laws.

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The wave variables a and b in WDF reflect the waves incident and reflected at a port, and the reflection coefficients are derived by applying Kirchhoff's laws if i'm not wrong.

it makes sense thank you :)

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