Source Signature Analysis by Modulation Envelopes

A signature of sound or sound quality would be conveyed by envelopes in the time or spectral domain. Speech intelligibility that may be a representative of sound quality, is closely related to the modulation envelope in the time domain. This chapter investigates how dynamically a linear system changes the envelopes of input signals for the output responses. The phase response, defined by the poles and zeros for the linear system, may be the key to preserve the source envelopes even in the output responses. Transmission of amplitude modulation is sensitive to the fine structure of phase spectral characteristics in a local frequency range such as a group delay. A linear system preserves signal envelopes when the group delay might be well defined in a corresponding frequency interval. Envelopes represent signal dynamics that resembles instantaneous squared magnitudes in the time domain, but they are highly related to the phase spectral property. Transmission of squared sinusoidal envelopes could be estimated by the modulation indexes with delays of envelopes for a linear system. The modulation transfer function for a squared impulse response could be dealt with from a perspective of poles and zeros. Linear phase systems may be the standard for envelope transmission.