Digital Signal Processing of the Inharmonic Complex Tone

In this paper, a set of digital signal processing (DSP) procedures tailored for the analysis of complex musical tones with prominent inharmonicity is presented. These procedures are implemented within a MATLAB-based application and organized into three submodules. The application follows a structured DSP chain: basic signal manipulation; spectral content analysis; estimation of the inharmonicity coefficient and the number of prominent partials; design of a dedicated filter bank; signal decomposition into subchannels; subchannel analysis and envelope extraction; and, finally, recombination of the subchannels into a wideband signal. Each stage in the chain is described in detail, and the overall process is demonstrated through representative examples. The concept and the accompanying application are initially intended for rapid post-processing of recorded signals, offering a tool for enhanced signal annotation. Additionally, the built-in features for subchannel manipulation and recombination enable the preparation of stimuli for perceptual listening tests. The procedures have been tested on a set of recorded tones from various string instruments, including those with pronounced inharmonicity, such as the piano, harp, and harpsichord.