A generalization to the Teager-Kaiser energy function and application to resolving two closely-spaced tones

Based on physical considerations, Kaiser (1990) proposed a new energy function for discrete time signals, known as the Teager-Kaiser energy function (TKEF). An interesting property of the TKEF is that if the input signal consists of two closely-spaced tones (amplitude modulated signal), the TKEF produces the difference frequency tone (envelope signal). However, a drawback is that the TKEF is highly sensitive to additive noise. We propose a generalized TKEF (GTKEF) to reduce the noise sensitivity. Fortunately, it turns out that the generalization can be used to enhance the sum frequency tone as well. This enables us to apply the GTKEF to resolve of two closely-spaced tones. The result can be viewed as an interesting nonlinear preprocessing scheme that can be used to transform a signal consisting of two closeby frequencies at f₁ and f₂ into a signal consisting of frequencies at (f₁-f₂) and (f ₁+f₂). Clearly, it is much easier to resolve the latter frequencies, whichever spectral analysis method is used