In this letter, we show that the frequency estimator in the Discrete-Time Energy Separation Algorithm-1a (DESA- 1a) proposed by Maragos et al. can be derived using Prony's method when the signal is xn = A cos(ωc n + θ). In the presence of noise, the DESA-1a frequency estimator is not equivalent to the Prony estimator. Simulation results indicate that on the whole, both methods share a similar sensitivity to noise.