Approximate optimal periodogram smoothing for cepstrum estimation using a penalty term

The cepstrum of a random process is useful in many applications. The cepstrum is usually estimated from the periodogram. To reduce the mean square error (MSE) of the estimator, the periodogram may be smoothed with a kernel function. We present an explicit expression for a kernel function which is approximatively MSE optimal for cepstrum estimation. A penalty term has to be added to the minimization problem, but we demonstrate how the weighting of the penalty term can be chosen. The performance of the estimator is evaluated on simulated processes. Since the MSE optimal smoothing kernel depends on the true covariance function, we give an example of a simple data driven method.