Rectification is a process which can change a.c to d.c. Half wave rectification is only half the job done. Full wave rectification will be perfect which requires the use of 4 diodes connected appropriately. To improve the fluctuating dc to non fluctuating d.c , a capacitor can be added in parallel to the load (which has been taken out of syllabus). The important waveform is that across the load and not the diode. Since V of load is shown the waveform can be drawn in any direction positive or negative (but of course looks better in the positive sense)
pic taken:http://www.osha.gov
