Psychoacoustic equivalence of frequency modulation and quasi-frequency modulation

Frequency modulation (FM) is known to be reasonably approximated by quasi-frequency modulation (QFM) for small modulation indices, beta, but the range of beta for which this approximation is appropriate is unclear. Thresholds for discrimination between FM and QFM with equal beta's are obtained in order to estimate an upper bound on beta for determining when this approximation is valid psychoacoustically, i.e., when FM and QFM are indiscriminable. At low modulation frequencies (fm < or = 4 Hz), QFM is never a valid approximation to FM at any detectable modulation level since discrimination thresholds are below FM detection thresholds. For modulation frequencies between 8 and 32 Hz, discrimination thresholds are approximately -2.5 dB (20 log beta) and can be accounted for by detection of envelope fluctuations in the QFM signal. For modulation frequencies at 64 Hz and above, discrimination thresholds improve with increasing modulation frequency in the same manner as FM and QFM detection thresholds. Discrimination in this frequency region seems to be mediated by detection of the component 2fm Hz below the carrier, i.e., by the most detectable component in the FM signal which does not occur in the QFM signal.