Spectral kurtosis statistics of quantized signals

Abstract

We investigate the bias of the Spectral Kurtosis Estimator induced by the quantization and bit truncation of the accumulated spectral power, which are standard signal manipulation operations performed by radio astronomy instruments that produce Power Spectral Density (PSD) estimates by means of sequential Discret Fourier Transform (DFT) operations. We demonstrate that these bias may be properly accounted for by adjusting the shape parameter of the Gamma distribution according to which the accumulated PSD estimates are expected to be distributed without quantization. To demonstrate the validity of this approach, we test the performance of an empirically tuned SK estimator using 2-bit auto-correlation data produced by the Parkes telescope.