Page  361 ï~~Real-time spectrum/cepstrum games Peter Pabon Royal Conservatory Institute for sonology Juliana van Stolberglaan 12595 CA Den Haag Holland sun4nl Ikoncon1pabon@nluug.nl Abstract The overlap-add (OLA) or overlap-save method proves to be an efficient method for frquency domain processing of sound signals. The method opens up a series of musical interesting applications like: phase-vocoding, linear pitch shifting, filtering, morphing, pitch tracking, stretching, formant tracking etc. The OLA technique allows us to move "wave fragments" or "spectral fragments" around in both time and frequency domain in almost any fashion. The only restriction is that we have to stick to one golden rule: "never mess-up the (derivatives of) window structure". The method allows special games to be played with wave portions in the time/frequency plane. For instance, a kind of musical-chairs game that swaps wave portions, or an algorithm that dynamically shuffles and again unravels the time/spectrum fragments all belong to the possibilities. An interesting group of options/applications evolves when the spectral features are used as design criterion for the processing of the signal itself. For example: the estimated pitch can be used to split up a periodic signal in its odd and even spectral components, or to edit the spectral envelope in a pitch synchronous manner. Modern DSP's give us the option to run most of the above methods in real-time. For a Motorola 96000 processor an OLA-backbone structure is setup, an operating system that already implements all processing steps to and from the frequency domain. Next, a high level programming environment is used to control a special DSP toolkit, a series of low level processing units to manipulate the intermediate spectra in various ways. All units are specially designed to process spectral features on a way that ensures preservation of the window structure. The DSP's overpower in calculation force even allows spectral derivatives as the cepstrum to be edited in real-time. The cepstrum, defined here as the Fourier transform of the (real) log-amplitude spectrum, forms a powerful condensation of spectral features. The first "quefrency" samples of the cepstrum outline the spectral slope (A), while the remaining low-'quefrency portion models the hills and valleys in the spectral envelope (B). Furthermore, the cepstrum can exhibit so called "rahmonic peaks" transcribing the periodic portion of the spectrum (C). Instead of manipulations on the level of the spectrum, we can go one step higher and process cepstrum features. In general, cepstral amplitude modification can be interpreted as a filtering of the related time signal feature. Cepstral coefficients can be combined easily between multiple sound sources. For instance, spectral envelope features of one source can be merged with the flattened (spectral white) periodic series of another source. Typical time/frequency tricks like phase shifting can be applied to cepstral group (B) so as to shift around in a periodic fashion, or to invert, the peaks in the spectral envelope. A very dramatic effect, especially with speech input, is the possibility to increase or decrease the sharpening of the spectral envelope peaks (the resonance), just by a simple weighting of the low-quefrency rahmonics (B). Maybe the most stunning application is that of pitch linked spectral comb-filtering by simply removing or inverting cepstral rahmonics (C). Any periodicity that shows up in the spectrum is leveled out by flattening the cepstrum. The method even allows the definition of a pitch zone for which all periodic features are to be removed, a so called pitch-band filter. This method can be used for pitch dependant removal of the instrumental contributions from a orchestral mixed signal having a very concealed spectral structure. The result is the total mix without the targeted pitches. It should be noted that the quality of such a filtering method will never be a 100%. Within the Fourier concept periodicity is a very strictly defined, "pure" mathematical entity. This pure character is seldom matched/found with natural (real-life) signals. Only the pure periodic components are removed, leaving only the quasi periodic noise contributions as a remainder. In this paper the DSP-OLA system will be discussed, and sound examples of several of the above mentioned applications like the pitch-band filtering will be demonstrated/played. (This paper will be provided as addenda upon receipt. (editor)) ICMC Proceedings 1994 361 Audio Analysis and Re-Synthesis