ENERGY SEPARATION IN SIGNAL MODULATIONS WITH APPLICATION TO SPEECH ANALYSIS

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.