REAL DISCRETE FOURIER-TRANSFORM

The author shows that the real discrete Fourier transform (RDFT) corresponds to a Fourier series for sampled periodic signals with sampled periodic frequency responses, just as a discrete Fourier transform (DFT) corresponds to a complex Fourier series (or Fourier transform) for the same type of signals. It is found that the RDFT has better performance than DFT in data compression and filtering for all signals in the sense that Pearl's measure for RDFT is less than Pearl's measure for DFT by an amount DELTA W. The RDFT also has better performance than DFT in the computation of real convolution because of the reduced number of operations, and the fact that forward and inverse transforms can be implemented with the same signal flowgraph, thereby facilitating hardware and software design.