An Efficient Algorithm for Segmenting Quasi-Periodic Digital Signals Into Pseudo Cycles: Application in Lossy Audio Compression

Signal segmentation is used in many areas, from audio processing to health applications, and consists of dividing a signal into segments, homogeneous according to given metrics. Those metrics, and even the methods used, vary substantially according to each application. We propose a general, lower-level algorithm that divides a quasi-periodic digital signal into its fundamental building blocks, the pseudo cycles. Features derived from this segmentation, such as the temporal envelope and the length of each pseudo cycle, can be used in further tasks, like sound compression, with direct applications in audio streaming bandwidth reduction and compression of digital musical instruments sample libraries. The method is based on the sliding discrete Fourier transform, with assumptions from the circular time-shift theory used for performance improvements. The segmentation algorithm is tested via an application to lossy audio compression. This implementation, dubbed Harmonic Compression, is compared with the MP3, AAC, and Opus codecs at similar compression rates, on a set of 8 voice and 8 instrument signals chosen to represent typical samples used in digital instruments, and is shown to perform better than those codecs in objective quality metrics and simulated subjective listening tests, exhibiting faster decoding speeds while achieving similar compression rates. A website and a GitHub repository, where results can be heard and a C++ implementation of the proposed codec can be obtained, are available. We find that the algorithm is immediately applicable to domain-specific lossy audio compression and envelope extraction, with signal classification and wavetable matching examples of other potential uses.