We investigate an all-fibered frequency-shifting loop (FSL) which includes an electro-optic amplitude modulator (EOM) and an optical amplifier, and is seeded by a continuous-wave laser. We demonstrate an original double-pulse regime when the loop length is a multiple of the RF modulation wavelength applied to the modulator (integer Talbot condition). The inter-pulse interval is governed by both the bias voltage and modulation depth of the EOM. The system is modeled by an interference model that takes the amplitude modulation function and loop delay into account. Above threshold the FSL generates mode-locked picosecond pulse doublets with a continuously adjustable delay.