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 and instantaneous frequency of signals with a combined amplitude modulation (AM) and frequency modulation (FM) structure. A recent alternative approach uses a nonlinear differential 'energy' operator to track the energy required to generate an AM-FM signal and separate it into amplitude and frequency components. In this paper, we compare these two fundamentally different approaches for demodulation of arbitrary signals and of speech resonances modeled by AM-FM signals. The comparison is done from several viewpoints: magnitude of estimation errors, computational complexity, and adaptability to instantaneous signal changes. We also propose a refinement of the energy operator approach that uses simple binomial convolutions to smooth the energy signals. This smoothed energy operator is compared to the Hilbert transform on tracking modulations in speech vowel signals, band-pass filtered around their formants. The effects of pitch periodicity and band-pass filtering on both demodulation approaches are examined and an application to formant tracking is presented. The results provide strong evidence that the estimation errors of the smoothed energy operator approach are similar to that of the Hilbert transform approach for speech applications, but smaller for communication applications. In addition, the smoothed energy operator approach has smaller computational complexity and faster adaptation due to its instantaneous nature.