Frequency domain linear prediction based on temporal analysis

Frequency-domain linear prediction (FDLP) is widely used in speech coding for modeling envelopes of transients signals, such as voiced and unvoiced stops, plosives, etc. FDLP fits an auto regressive model to the discrete cosine transform (DCT) coefficients of a sequence. The spectral prediction coefficients provide a parametric model of the temporal envelope. The prediction coefficients are obtained by solving the set of Yule-Walker equations expressing the relationship between lagged spectral autocorrelation values. A limitation of the direct approach of computing the spectral autocorrelation values is that the sequence has to be padded with a large number of zeros for the autocorrelation estimates to be reasonably accurate. This comes at the cost of increased computational complexity. We present an efficient and accurate method for computing the spectral autocorrelation samples. We show that the spectral autocorrelation can be computed as cosine-weighted temporal centroids, where the weighting function is dependent on time-index of the samples.