VLSI implementation of an efficient method for the computation of line spectral frequencies

In speech coding applications using linear predictive techniques, the computation of line spectral frequencies (LSFs) from the predictor coefficients is an extremely computationally intensive task. The unique properties of the symmetric and antisymmetric polynomial roots limit the region which must be searched, however it is still necessary to perform a root-finding algorithm on a high-order polynomial. Certain algorithms have been developed to reduce the complexity of the root finding exercise. One such algorithm, developed by Ramachandran and Kabal, takes advantage of certain properties of the symmetric and antisymmetric polynomials to map the upper portion of the unit circle onto the real interval [-1,1] by converting the polynomials into a Chebyshev polynomial series representation. Because Chebyshev polynomials may be evaluated efficiently using the Clenshaw recurrence formula, far fewer computations are necessary to search the linear region for zero crossings. This work investigates the implementation of the Ramachandran-Kabal algorithm in a VLSI design suitable for integration into larger speech processing systems. An implementation exclusively in VHDL is developed. Simulation of the VHDL design is performed and the post-synthesis results evaluated