An improved speech production model for voiced speech utilising seasonal AR-AR model and Markov chain Monte Carlo simulation
Summaryofreconstruction andestimationresultsunderavarietyofcorrupt-ing noise conditions when running the sampling algorithm on the data of Figure 11.All the SNR values are given in dB.It should be pointed out that even though, from an algorithmic point of view, thesignal reconstruction step is very efﬁciently implemented, it is still computationallyintensive, especially for large values of the effective order of the state-space system p+q  , which commonly occur when processing speech signals. There are a numberof ways in which the computational efﬁciency can be increased, and a couple of obvi-ous suggestions are presented below. Due to the nature of the model, the state vector,and resulting matrices, are sparse, allowing for efﬁcient sparse matrix operations tobe employed. Furthermore, approximately 85% of the computational time is spent inupdating the state covariance matrices in the Kalman ﬁlter and smoother. If the sys-tem is known to be time-invariant and stationary (as would be the case over a singleframe of speech), these matrices converge within the ﬁrst few iterations, eliminatingthe need for the recursive updates. In some special cases the steady-state values forthese matrices can be obtained by an analytic solution of the Riccati equation, elimi-nating the updating step completely.