A mechanism is provided for constructing an oversampled waveform for a set of incoming signals received by a receiver. In one implementation, the oversampled waveform is constructed by way of cooperation between the receiver and a waveform construction mechanism (WCM). The receiver receives the incoming signals, samples a subset of the incoming signals at a time, stores the subsets of sample values into a set of registers, and subsequently provides the subsets of sample values to the WCM. The WCM in turn sorts through the subsets of sample values, organizes them into proper orders, and “stitches” them together to construct the oversampled waveform for the set of incoming signals. With proper cooperation between the receiver and the WCM, and with proper processing logic on the WCM, it is possible to construct the oversampled waveform for the incoming signals without requiring large amounts of resources on the receiver.