The Hartley transform applied to speech coding

Homomorphic deconvolution has some appealing properties for speech coding applications, yet has failed to achieve any significant popularity. This is due, in part, to the mathematical complexity of the deconvolution process and the difficulty in handling the spectral phase information in the formation of the cepstrum. The paper introduces the application of the Hartley transform as a substitute for the Fourier transform in the computation of the cepstrum. This real transform avoids the need to handle the phase explicitly and thus removes the need for phase unwrapping. The Hartley transform has similar deconvolution properties as the Fourier transform and also has a fast implementation. It has the additional advantage that its forward and inverse forms are identical, thus simplifying implementation. The difficulties with the complex Fourier cepstrum are discussed, the alternative form, the Hartley cepstrum is introduced and some of its useful properties are examined. The use of the Hartley cepstrum in a homomorphic coder is also discussed and some preliminary results are given