Multisine excitation design to increase the efficiency of system identification analysis through undersampling and DFT optimization

Multisine excitations are commonly employed to measure the frequency response of a nonlinear system. A typical pseudo-logarithmically-spaced frequency distribution may be oversampled at a rate significantly greater than the Nyquist rate to ensure accurate signal reconstruction without aliasing. In this paper, two algorithms are presented for optimizing the frequency distribution of a multisine excitation signal such that the system output can be undersampled without corruption, resulting in compact DFT bin utilization. In addition, the optimized excitation signal is designed to approximate a user-defined frequency distribution and make allowances for harmonic frequencies generated by system nonlinearities. Results show that at least an eleven-fold improvement in DFT bin utilization is possible for an example two-decade logarithmically-spaced 25-tone excitation signal applied to a nonlinear system exhibiting both second and third order harmonics. The use of optimized excitation signals in power constrained applications, such as structural health monitoring, can help to increase adoption rates by reducing system complexity and power source requirements.