A New Signal Processing Method Based on Intrinsic Frequency

This paper proposes a new signal processing method for non-stationary signals based on a new concept called intrinsic frequency. Intrinsic frequency, as derived in this paper, is an inherent characteristic of a signal, which has clear physical meanings and describes the local waveform of the data. This new method actually corresponds to a completely adaptive local fitting of the signal data into harmonic functions. Compared with short-time Fourier transform, it allows for non-integer numbers of complete sinusoidal waves, thus is not subjected to uncertainty principle. Unlike wavelet transform, it does not use any preset functional forms, thus is very adaptive to data. It does not have the problems of HHT due to Bedrosan and Nuttul theorem. This paper gives the mathematic derivation of intrinsic frequency, followed by five examples of continuous signals. The results are compared with theoretical frequencies, Fourier transform, instantaneous frequencies based on Hilbert transform, and instantaneous frequencies based on Hilbert Huang Transform. The advantages and physical meanings are clearly shown. Numerical algorithm for discrete signals and the difficulties of the method are also discussed. This new analysis method can be applied to a wide spectrum of challenging engineering problems. In structural engineering, the applications include analysis of ground motion characteristics, nonlinear structural responses, structural health monitoring, and damage detection.