Fixed-point error analysis of fast Hartley transform

Fast Hartley transform (FHT) has been proposed recently by Bracewell. This is closely related to the fast Fourier transform (FFT) However, it has two advantages over the FFT, namely, the forward and inverse transforms are the same; and the Hartley transformed outputs are real-valued, rather than complex data, Hence, the speed of computation can be increased by 50% for performing fast convolution or correlation. These properties have led to investigations to use the Hartley transform for time-efficient discrete Fourier analysis of real signals. In this paper, the error-performance of radix-2 decimation-in-time and decimation-in-frequency form of the fast Hartley transform algorithm has been studied. The analysis assumes fixed-point sign magnitude arithmetic. The analysis is carried out for decimation-in-time and decimation-in-frequency form of the fast Hartley transform algorithms, assuming all the errors to be uncorrelated. Then, the analysis is carried out, assuming the truncation errors to be correlated, in the case of decimation-in-frequency form of FHT. The predicted results are compared with computer simulation studies and those obtained in the case of fast Fourier transform. It has been observed that the expressions obtained in the analysis are similar to those obtained in the case of FFT for the corresponding cases.