A COMPARISON OF THE ENERGY OPERATOR AND THE HILBERT TRANSFORM APPROACH TO SIGNAL AND SPEECH DEMODULATION

The Hilbert transform together with Gabor's analytic sipal provides a standard linear integral approach to estimate the amplitude envelope a nd instantaneous frequency of signals with a combined amplitude modula tion (AM) and frequency modulation (FM) structure. A recent alternativ e approach uses a nonlinear differential 'energy' operator to track th e energy required to generate an AM-FM signal and separate it into amp litude and frequency components. In this paper, we compare these two f undamentally different approaches for demodulation of arbitrary signal s and of speech resonances modeled by AM-FM signals. The comparison is done from several viewpoints: magnitude of estimation errors, computa tional complexity, and adaptability to instantaneous signal changes. W e also propose a refinement of the energy operator approach that uses simple binomial convolutions to smooth the energy signals. This smooth ed energy operator is compared to the Hilbert transform on tracking mo dulations in speech vowel signals, band-pass filtered around their for mants. The effects of pitch periodicity and band-pass filtering on bot h demodulation approaches are examined and an application to formant t racking is presented. The results provide strong evidence that the est imation errors of the smoothed energy operator approach are similar to that of the Hilbert transform approach for speech applications, but s maller for communication applications. In addition, the smoothed energ y operator approach has smaller computational complexity and faster ad aptation due to its instantaneous nature.