----- Forwarded Message: Date: 25 Oct 1996 10:48:12 To: Recipients of conference <fastnet@igc.apc.org> From: james@bovik.org (James Salsman) Subject: speech subterfuge I have some indirect evidence that patent-related activities of the U.S. Air Force may have intentionally obscured the mathematical definition of "cepstrum" from the mid-1970s, with literally tremendous implecations for the computer speech processing industry (perhaps billions of dollars in real economic damage by now), and also harming current war reduction projects such as automatic language translation systems. The correct definition was published in 1963 by Cooley and Tukey (who also coined the term "bit".) For those who care, the Cooley-Tukey cepstrum is: FFT( ln( | FFT( sample .* window ) | ) ) And for speech processing, the definition is: FFT( ln( melScale( | FFT( sample .* window ) | ) ) ) (The "melody scale" atenuates frequencies atenuated by the human ear. N.B.: Both the resulting cepstral magnitude and phase are significant, e.g., the result is a vector of complex numbers. Furthermore, only the first few elements of the cepstral vector are necessary for the formant envelope, while the exitation (i.e., the harmonics) are encoded as a peak towards the end of the vector.) The error has been to use the inverse Fourier transform instead of the second (outside) FFT, which seems to be why researchers have been experimenting with the (slightly) better Discrete Cosine Transform, from video signal processing. Sincerely, :James Salsman ----- End Forward