Finite impulse response (FIR) models are very popular in process industries because of their simple model structure, flexibility to explain arbitrary complex stable linear dynamics and finally their ease of implementation in on-line applications. In general, identification of FIR models requires large number of parameters to be estimated. In case of systems with multiple time scales, the length of FIR model structure under conventional uniform sampling becomes arbitrarily high due to simultaneous presence of fast and slow dynamics. This results in more variability in the estimated parameters when the conventional methods such as ordinary least squares are used. In this work, the FIR model estimation problem is formulated as a sparse optimization problem, where the sparse representation of impulse response coefficients for linear-time invariant multiscale systems in the time-frequency domain is exploited in order to explain the overall FIR model effectively with fewer number of coefficients and thereby incurring less variability in the estimated parameters. The effectiveness of proposed methodology is demonstrated by means of simulation case studies. © 2018