Robust time-domain frequency analysis

One domain in which the ordering filters have not appeared is frequency analysis. Simultaneously one must note that the impulse rejection properties of the ordering filters could be very beneficial due to the lack of robustness of the DFT/FFT. Another problem with the DFT/FFT is the ambiguity of the estimate of frequency at a point (frequency localization). This paper introduces a transform (WMMR/MED/COUNT) that simultaneously solves both of the problems in some cases. The Gabor transform and various wavelet techniques have recently been reviewed as a substitute to FFT frequency analysis for spatial localization. While the Gabor transform optimally infers frequency content and spatial localization simultaneously, it suffers from the fact that it requires a full period within the window. This paper presents a transform based on the WMMR filters that will yield frequency analysis and spatial localization with a window width of 1/4 period or less. Experimentally, it has been shown that this technique can be used with impulsive noise of up to 40% and with random baseline shifts. The short-time Fourier, Gabor transform and the WMMR/MED/COUNT transforms (WMCT) are compared for their localization properties in noisy and noiseless situations.