Nonlinear median transform domain denoising of frequency response functions

ABSTRACT Frequency response functions (FRF) are the primary means of experimentally evaluating the structural characteristics of vibrating systems. Vibration analyzers estimate the FRF through the ratio of the output/input power spectral densities (PSD); which in turn are estimated using periodograms. However, periodograms are inconsistent estimators. In addition, noise in the input and output data further degrade the performance of the periodogram. Therefore, practical estimation of FRFs from noisy measurements is achieved through time averaged periodograms. In the last decade, the discrete wavelet transform (DWT) has emerged as a powerful tool for denoising functions. Recently, wavelet domain post processing methods have been suggested to eliminate noise contamination in FRFs, as an alternative to time averaging. The Median Interpolating Pyramid transform (MIPT) based denoising algorithm is inherently similar to DWT algorithms. However, it is more capable of eliminating impulsive noise and is an alternate method for improving FRF estimates. In this work, a MIPT based denoising algorithm is implemented to eliminate impulsive and Gaussian noise contamination of FRF estimates. Preliminary results obtained using simple 2 degree-of-freedom (DOF) systems demonstrate that an average improvement of 5 dB can be achieved using the MIPT algorithm as a post processor to the traditional periodogram based estimate.