We demonstrate a novel microwave photonic filter based on a non-coherent broadband optical source and the variable optical carrier time shift (VOCTS) method. Optical slicing which is essential conventionally is not employed in our scheme. Nevertheless, equivalent "electrical slicing" is performed by VOCTS, generating a passband free from the carrier-suppression effect. The baseband response is eliminated by using carrier-suppression or phase modulation. Single bandpass is also achieved due to the continuous-time sinusoidal impulse response. Detailed theoretical analyses are presented and agree with the experiments quite well.