Multisines

Multisines are signals formed by the coherent sum of multiple sine waves, each at a distinct frequency. They are commonly used in system identification, vibration testing, and audio engineering to excite a system across a range of frequencies in a single measurement. A typical multisine has the form s(t) = sum_{k=1}^N A_k sin(2π f_k t + φ_k), where f_k are the chosen frequencies, A_k the amplitudes, and φ_k the phases.

The frequency set f_k is usually placed on a predetermined grid, and the amplitudes and phases are selected to tailor the energy distribution or to minimize undesirable time-domain peaks. Random or optimized phase choices are common; phase optimization can reduce the crest factor, resulting in a waveform that looks more like noise and fits within a given dynamic range.

Multisines offer fast spectral measurements because many frequencies are excited simultaneously, reducing test duration compared with sequential sine sweeps. They are particularly useful for identifying linear transfer functions and detecting nonlinearities: by examining responses at harmonic and intermodulation frequencies, one can separate linear from nonlinear behavior.

In practice, multisines require careful design to avoid excessive peak power, spectral leakage, and coherence loss. Windowing, gating, and synchronization with data acquisition improve measurement accuracy. Variants include deterministic multisines and randomized-phase multisines, and they can be scaled to target specific frequency bands or to stress-test components under controlled energy distributions.