A nonparametric method to estimate Toeplitz covariance matrices from a sample of n independently and identically distributed p-dimensional vectors with mean zero. The data is preprocessed with the discrete cosine matrix and a variance stabilization transformation to obtain an approximate Gaussian regression setting for the log-spectral density function. Estimates of the spectral density function and the inverse of the covariance matrix are provided as well. Functions for simulating data and a protein data example are included. For details see (Klockmann, Krivobokova; 2023),