Signal discontinuities matter beyond music

A lot of real data repeats. A ball bearing turns once per revolution. A heart beats once per cycle on an ECG. A machine tool follows the same path again and again, and grid voltage swings up and down 50 or 60 times a second.

These cycles are only useful if the end of one can flow into the start of the next without a jump. That jump is a discontinuity. The middle of a cycle can look healthy while the fault sits at the join. In audio it is a click. In vibration data it is a false spike. In a heart recording it can look like an edge that is not really there.

Signal healing repairs only the join and keeps the rest of the cycle. It was first built for wavetable synths. The method, the score and the audio results are explained in How to remove the click in a wavetable loop.

The aiXiv preprint ran the same seam test on seven boards of non-audio cycles, with 256 cycles per board. Three boards hold bearing revolutions from the public CWRU, MFPT and Paderborn datasets. Two hold single heartbeats from the MIT-BIH and PTB-XL ECG datasets. Two are synthetic stand-ins for a machine-tool path and a power-grid voltage cycle.

The repair search ran separately on each board. Every repair got the same R_blend score from 0 to 1, where higher means the join matches a clean version and the middle stays unchanged.

On bearings the searched repair scored 0.960 (CWRU), 0.943 (MFPT) and 0.937 (Paderborn). A seam-trained Noise2Noise model scored between 0.842 and 0.866. A classic cosine crossfade scored between 0.461 and 0.483.

On heartbeats the searched repair scored 0.975 (MIT-BIH) and 0.945 (PTB-XL). Noise2Noise scored about 0.75 on both. The cosine crossfade scored 0.414 and 0.512.

On the synthetic boards the searched repair scored 0.991 for the machine-tool path and 0.992 for the voltage cycle.

Bearing revolution: one full turn of a ball bearing in a machine. Vibration sensors record a repeating pattern per turn.

ECG: an electrocardiogram, a recording of the heart's electrical activity. Each heartbeat forms one cycle.

Board: in the paper, a set of 256 cycles from one data source, all scored the same way.

Noise2Noise: a neural network trained to clean signals from noisy examples. It is the strongest learned comparison in the tests.

Cosine crossfade: a classic smooth blend between the end and the start of a cycle, used here as the simple baseline.

These are early results and not a product claim. Each board uses one search seed, so the numbers do not yet show how stable the method is across runs. The paper calls them stress tests of the seam protocol and does not claim general transfer across domains.

The score measures how well the join is repaired. It does not measure fault detection in machines or clinical quality of a heart recording. Those would need their own studies. The paper is a preprint and has not been peer reviewed.

The open question is how far clean cycle joins travel outside sound. If a signal is meant to close, the join deserves its own treatment. The wavetable article covers the music side.