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Transforming real linear prediction coefficients to line spectral representations with a real FFT

This paper describes a novel algorithm for transforming linear prediction coefficients (LPCs) to line spectral frequencies (LSFs) and line spectral pairs (LSPs) used by most of the speech processing applications. The symmetric and antisymmetric polynomials (SAPS) for LSP/LSFs, corresponding to the LPC polynomial, are first multiplexed into a single real sequence. The required samples of SAPS correspond to the DFT of the obtained real sequence. The proposed algorithm is referred as PMLS as it is based on the Plus Minus (PM) algorithm an FFT which efficiently computes the DFT of a real sequence for the positive frequency interval only. The samples of the SAPS are efficiently utilized for the computation of a single parameter which is used for computation of LSF and LSP independently with some interpolation principles. This interpolation exploits the available samples of SAPS and does not require their samples at finer resolution. The efficiency of the PMLS is illustrated with the help of some examples. Some guidelines for an optimal implementation of PMLS on fixed point digital signal processors (DSPs) are also presented.