A data processing system is disclosed. The system includes a processor, a transformer, a first memory buffer, a second memory buffer, a first filter, and a second filter. An obtained transmission signal symbol is first transformed to first data. The first memory buffer stores the first data. The processor obtains peak data based on the first data according to a predetermined threshold. The transformer transforms the peak data to second data and stores the second data in the second memory buffer. The first filter filters the second data to determine reserved data of the second data and removes the reserved data from the second data to generate third data. The transformer transforms the third data to fourth data and stores the fourth data in the second memory buffer. The processor merges the first and fourth data to generate fifth data. The second filter filters the fifth data based on the transmission signal symbol and a previously obtained transmission signal symbol.