The objective of this work is to extend the linear analysis of PulsedDigitalOscillators to those topologies having a Finite Impulse Response (FIR) in the feedback loop of the circuit. It will be shown with two specific examples how the overall response of the oscillator can be adjusted to some point by changing the feedback filter, when the resonator presents heavy damping losses. Extensive discrete-time simulations and experimental results obtained with a MEMS cantilever with thermoelectric actuation and piezoresistive position sensing are presented. It will be experimentally shown that the performance of the oscillator is good even below the Nyquist limit.