ROC curve measurements using euro-rack modules (and some DIY)

Acoustic signal processing projects encourage DIY electronics as well as hardware designed to expose principles found either in nature or from man-made sources. Searching within the Eurorack format of the modular synthesis community, functional equivalents to more common DIY units are identified. Some signal generators and measurements are still underrepresented commercially and require DIY Eurorack modules to be built. One goal is to use existing Eurorack components where DIY modules are designed as necessary in this format. A Receiver Operating Characteristic curve (ROC) is calculated for three cases using analog energy detection and probability density function (pdf) circuitry. The hypothesis for noise (N) is a fixed Gaussian noise distribution. The three hypotheses for the signal plus noise (S+N) have signals characterized as; a constant sinusoid with random phase, a broadband unknown Gaussian signal, and an unknown narrow band Gaussian signal utilizing a narrow band carrier frequency. Our classroom demonstration involves two loudspeakers, one for noise, the other for signal. The detected microphone’s voltage is bandpass filtered, amplified, squared, integrated and then fed into the pdf circuitry where pulses are counted for 4 seconds in each voltage window. Increasing the signal amplitude will increase the detection index.