Higher order statistics based IIR notch filtering scheme for enhancing sinusoids in coloured noise

It is known that sinusoids generate lines in their spectra, but false lines may appear when the sinusoids are corrupted by coloured additive noise. In the paper, a higher-order statistics-based IIR filtering scheme is suggested to suppress additive coloured noise, thus enhancing the desired spectral peaks due to the sinusoids. The filter used is an unknown pole-zero constrained IIR notch filter. The filter coefficients are estimated by applying the linear prediction (LP) method to a block of a fourth-order mixed cumulant slice (FOMCS) of the input noisy signal. Therefore, the presented scheme automatically handles Gaussian noise (white or coloured). In the non-Gaussian noise case, a novel analysis is presented to show that, associated with the FOMCS, there is a new signal-to-noise ratio called the `signal-to-noise kurtosis ratio´ (SNKR). This SNKR is a multiple of the conventional SNR if the additive noise is coloured non-Gaussian. Thus, the presented scheme is capable of handling additive coloured noise (Gaussian or non-Gaussian). The performance of the proposed scheme, compared with a correlation-based counterpart, is demonstrated through computer simulations