Where does ringing collide?

In signal processing, ringing is the spurious oscillation that appears near a step or discontinuity after a signal is band-limited or passed through a sharp filter, decaying as it moves away from the edge. It is the engineering face of the Gibbs phenomenon: truncating a Fourier series at a jump leaves a persistent overshoot of about nine percent that does not vanish as more terms are added. Gibbs described the overshoot in his 1899 Nature note on Fourier's series, Hewitt and Hewitt later traced the history as the Gibbs–Wilbraham phenomenon, and Oppenheim and Schafer's Discrete-Time Signal Processing treats the resulting ringing in filter design. The referent is an overshoot-and-oscillation artifact in a filtered signal, not the sounding of bells or a symptom in the ear.[1][2][3]

Unit

The amplitude and decay of overshoot oscillations beside a discontinuity

Recovery means

Not applicable

Measured by

Quantified by the overshoot magnitude (the Gibbs ~9% near a jump), the ripple amplitude, and how quickly the oscillation decays from the edge

In clinical medicine, ringing in the ears is the everyday description of tinnitus: the perception of sound (a ring, hiss, or buzz) in the absence of any external acoustic source. It is usually linked to changes in the auditory system and central auditory processing rather than a real tone, and can range from a minor nuisance to a disabling symptom. Baguley, McFerran, and Hall's review Tinnitus summarises its mechanisms, assessment, and management. The referent is a phantom auditory percept in a person, entirely distinct from a filter's overshoot or the ringing of bells despite sharing the word.[4]

Unit

The perceived loudness, pitch, and distress of a phantom auditory sensation

Recovery means

Tinnitus may remit or habituate over time; management (sound therapy, cognitive approaches) targets the distress and perceived loudness rather than a guaranteed cure

Measured by

Assessed by pitch and loudness matching, minimum masking level, and validated distress questionnaires