The statistics of whitened data

Whitening data using an estimated power spectral density results in an output sequence whose power can vary due to the mismatch between the true and estimated spectrum. We derive the probability density function of the power of the whitened data for two cases: (i) using spectral estimates independent from the data to be whitened and (ii) using spectral estimates dependent upon the data to be whitened. Even though these probability density functions do not have finite means, we compute a useful measure that agrees well with simulation results.