Zero Order Hold with polyphase resampler
I was able to achieve this with a square pulse impulse response of length I(interpolation rate). The square impulse response in relation to an equivalent sin(x)/x and linear interpolator(triangular) response is show in the figure below. This is still not a perfect design as I see discontinuities every I samples in the resampled output. 

Edit: The discontinuities are addressed by changing the transition of high-low in the square impulse response, from two samples to three sample. So instead of the transitions being (high, low) in two samples, it will be (high, mean(high,low),low) over three sample and likewise for transition from low ot high.