It is well established that a Chebyshev correlation function of the length 2K can be calculated from a K-step Chebyshev propagation. Here, we propose an ansatz that such a doubling scheme can also be utilized to calculate positions and widths of narrow resonances using the low-storage filter diagonalization (LSFD) based on the damped Chebyshev propagation. This ansatz, which is shown to be numerically valid in two real molecular systems (HCO((X) over tilde) and SO2((C) over tilde)), reduces the computational cost by half.