Do you recognize this low pass filter

I have a simple 1st order lag filter implementation that performs well, shown in the block diagram below. This is legacy 'code' we've been using for many years, the original developers have long since moved on. I've been asked to doc the requirements (development of the difference equation) starting from the s domain and assuming

k1 is , k2 is 0.5, τ is the time constant, in sec, and Ts is the time between samples, in sec.

My assumption was I would arrive at a bilinear transform of but it's just not happening as the topology is wrong. Any hints as to the transform used?

Thanks, Chris

Answer 1

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Answered here:

https://dsp.stackexchange.com/questions/69713/do-you-recognize-this-discrete-realization-of-a-low-pass-filter/69746#69746