A novel method using optical fiber parametric amplification and phase modulation is proposed in order to generate Nyquist pulses. Using parabolic pulses as a pump, we show theoretically that it is possible to generate Nyquist pulses. Furthermore, we show that by using a sinusoidal pump (pump intensity modulated by an RF tone), it is possible to obtain pulses with characteristics that are close to Nyquist limited pulses. We demonstrate experimentally the generation of bandwidth limited pulses with full width half maximum of 14 ps at 10 GHz repetition rate. We also discuss limitations of this method and means to overcome these limitations.