The problems of identifying the frequency and parameters of multi-sinusoidal signals with constant parameters are considered in finite time. The signal is represented as the output of a linear generator, where the parameters of the sinusoidal signal (amplitude, phase, and frequency) are unknown. The main idea is to apply the Jordan waveform and lag to parameterize the signal and obtain a linear regression model. Unknown parameters are estimated using DREM method. The performance of algorithms considered in the article is illustrated by computer modeling. Our main contribution is to propose a new approach for parameterization of multisinusoidal signals and finite time parameter estimation.