P. Maragos et al., ENERGY SEPARATION IN SIGNAL MODULATIONS WITH APPLICATION TO SPEECH ANALYSIS, IEEE transactions on signal processing, 41(10), 1993, pp. 3024-3051
Oscillatory signals that have both an amplitude-modulation (AM) and a
frequency-modulation (FM) structure are encountered in almost all comm
unication systems. We have also used these structures recently for mod
eling speech resonances, being motivated by previous work on investiga
ting fluid dynamics phenomena during speech production that provide ev
idence for the existence of modulations in speech signals. In this pap
er, we use a nonlinear differential operator that can detect modulatio
ns in AM-FM signals by estimating the product of their time-varying am
plitude and frequency. This operator essentially tracks the energy nee
ded by a source to produce the oscillatory signal. To solve the fundam
ental problem of estimating both the amplitude envelope and instantane
ous frequency of an AM-FM signal we develop a novel approach that uses
nonlinear combinations of instantaneous signal outputs from the energ
y operator to separate its output energy product into its amplitude mo
dulation and frequency modulation components. The theoretical analysis
is done first for continuous-time signals. Then several efficient alg
orithms are developed and compared for estimating the amplitude envelo
pe and instantaneous frequency of discrete-time AM-FM signals. These e
nergy separation algorithms are then applied to search for modulations
in speech resonances, which we model using AM-FM signals to account f
or time-varying amplitude envelopes and instantaneous frequencies. Our
experimental results provide evidence that bandpass filtered speech s
ignals around speech formants contain amplitude and frequency modulati
ons within a pitch period. Overall, the energy separation algorithms,
due to their very low computational complexity and instantaneously-ada
pting nature, are very useful in detecting modulation patterns in spee
ch and other time-varying signals.