In this case there a couple of bridge rectifiers converting the AC to DC.
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Yes, you need rectifiers to get from AC to DC after the transformer steps down (in this case) the AC to a lower voltage. Depending on if the transformer has a center tap or not and if you want full wave or half wave rectification then you either need a bridge (4 diodes) or two discrete diodes. At that point you have (depending on what source you read) either rectified AC or unfiltered DC which is very noisy and does not develop full DC voltage potential. You add large filter capacitors after the bridge and then you have higher DC voltage with minimal ripple. Some electronics can operate with unfilterd DC/rectified AC but many circuits, especially in the modern era may not function correctly.
George