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The analogy between optical frequencies and RFs leads to a novel technique for RF photonic signal processing using a femtosecond laser comb modulated by a traveling-wave tunable filter, such as an acoustooptic tunable filter (AOTF) or a novel electrooptic tunable filter (EOTF). In this new scheme, the recent history of an applied RF waveform to-be-processed slides into the tunable filter and a femtosecond pulse train diffracts off the moving acoustooptically or electrooptically induced dielectric grating, producing a shaped optical pulse train with each shaped pulse as a compressed replica of the RF waveform contained within the device aperture that is sped up by the ratio between the center optical and RF frequency. For a CW RF tone input, only a narrowband group of the frequency comb lines in the incoming laser comb is spectrally filtered and modulated due to the phase-matching condition in the filter and is simultaneously Doppler shifted by that RF due to the traveling-wave grating obeying the conservation of energy. This allows us to use the traveling-wave tunable filter as a spectrally mapped Doppler-shifted modulator that encodes different RF components onto the corresponding optical frequency comb lines. RF signal processing can then be performed by using optical techniques to manipulate the spectrally modulated laser comb. To reconstruct the processed RF signal, the Doppler-shifted and optically processed pulse train is heterodyne detected by beating with a reference femtosecond pulse train from the same laser source. A high repetition rate femtosecond laser comb is modulated by an AOTF to experimentally demonstrate this novel RF photonic signal processing technique. We demonstrate an RF tunable bandpass/notch filter, an RF down-converter, and an RF jammer er as novel applications of ultrafast lasers.