Fixed-point error analysis of rectangular transform

The fixed-point error analysis of long length RT's is presented assuming sign-magnitude or 1's complement arithmetic. The errors introduced by the input-addltion, multiplication and the output-addition stages are separately considered in each dimension and are suitably combined to give the average output noise variance. The various error components signifying the characteristics error parameters of a module are obtained for each short length RT. Filters of different transform lengths are chosen for illustration. The theoretical noise variance obtained in each case is found to have excellent agreement with the corresponding simulated results. The noise performance of RT and FFT filters is also compared. It is seen that the input noise has worsened by a factor of 3.8 bits in passing through an RT filter compared to 6.15 bits as in case of FFT filter.