The log of a Gaussian is a parabola, which makes finding where exactly a peak in the spectrum lies a question of solving a quadratic equation.

My plan was to detect the frequency of the speaker by counting (with weights) which distance between peaks is the most common. I wanted to avoid calculating the power cepstrum as I felt that I was running out of computing power on the devices already[0] - a mistaken belief in the long run, but I was too proud of my little algorithm and how stable it was to let go.

[0] Sending raw sample data to a more powerful machine was out of the question as I wanted to remain within the bandwidth offered by Bluetooth at the time due to power consumption considerations.