It has been demonstrated that microcalorimeter spectrometers based on superconducting transition-edge-sensor can readily achieve sub-100 eV energy resolution near 100 keV. However, the active volume of a single microcalorimeter has to be small to maintain good energy resolution, and pulse decay times are normally in the order of milliseconds due to slow thermal relaxation. Consequently, spectrometers are typically built with an array of microcalorimeters to increase detection efficiency and count rate. Large arrays, however, require as much pulse processing as possible to be performed at the front end of the readout electronics to avoid transferring large amounts of waveform data to a host computer for processing. In this paper, they present digital filtering algorithms for processing microcalorimeter pulses in real time at high count rates. The goal for these algorithms, which are being implemented in the readout electronics that they are also currently developing, is to achieve sufficiently good energy resolution for most applications while being (a) simple enough to be implemented in the readout electronics and (b) capable of processing overlapping pulses and thus achieving much higher output count rates than the rates that existing algorithms are currently achieving. Details of these algorithms are presented, and their performance was compared to that of the 'optimal filter' that is the dominant pulse processing algorithm in the cryogenic-detector community.