Microwave photonic filters with arbitrary phase response can be achieved by merging high-repetition-rate electro-optic frequency comb technology with line-by-line pulse shaping. When arranged in an interferometric configuration, the filter features a number of programmable complex-coefficient taps equal to the number of available comb lines. In this work, we use an ultrabroadband comb generator resulting in a microwave photonic phase filter with >100 complex-coefficient taps. We demonstrate the potential of this filter by performing programmable chirp control of ultrawideband waveforms that extend over long (>10 ns) temporal apertures. This work opens new possibilities for compensating realistic linear distortion impairments on ultrabroadband wireless signals spanning over dozens of nanosecond temporal apertures.