During operation, the system uses N sensors to sample an electromagnetic interference (EMI) signal emitted by a target asset while the target asset is running a periodic workload, wherein each of the N sensors has a sensor sampling frequency f, and wherein the N sensors perform sampling operations in a round-robin ordering with phase offsets between successive samples. During the sampling operations, the system performs phase adjustments among the N sensors to maximize phase offsets between successive sensors in the round-robin ordering. Next, the system combines samples obtained through the N sensors to produce a target EMI signal having an EMI signal sampling frequency F=f×N. The system then generates a target EMI fingerprint from the target EMI signal. Finally, the system compares the target EMI fingerprint against a reference EMI fingerprint for the target asset to determine whether the target asset contains any unwanted electronic components.