The disclosed system produces synthetic signals for testing machine-learning systems. During operation, the system generates a set of N composite sinusoidal signals, wherein each of the N composite sinusoidal signals is a combination of multiple constituent sinusoidal signals with different periodicities. Next, the system adds time-varying random noise values to each of the N composite sinusoidal signals, wherein a standard deviation of the time-varying random noise values varies over successive time periods. The system also multiplies each of the N composite sinusoidal signals by time-varying amplitude values, wherein the time-varying amplitude values vary over successive time periods. Finally, the system adds time-varying mean values to each of the N composite sinusoidal signals, wherein the time-varying mean values vary over successive time periods. The time-varying random noise values, amplitude values and mean values can be selected through a roll-of-the-die process from a library of values, which are learned from industry-specific signals.