Showing papers on "Inverse trigonometric functions published in 1980"

Implementation and comparison of two transformed reflection coefficient scalar quantization methods

Abstract: Based upon the theoretical development of a recent paper on scalar parameter quantization of speech reflection coefficients, an experimental comparison study of two quantization methods was undertaken. The first method, called uniform sensitivity quantization, makes use of measured sensitivity data from speech parameters to obtain quantization tables. Log area and inverse sine transformation followed by uniform quantization are examples of approaches which are considered in this category (with the inverse sine approach theoretically resulting in the uniform sensitivity solution). The second method is called minimum expected spectral deviation or minimum deviation quantization. This approach theoretically makes use of the probability density of each parameter in addition to the parameter sensitivity. A practical implementation of this method is presented here along with computer programs and then a comparison with the uniform sensitivity method is given. Quantitative results and subjective evaluation by an experienced listener indicate that moderate to substantial bit savings can be obtained by using the minimum deviation method which embeds parameter probability density information into the quantization process.

Very high accuracy Chebyshev expansions for the basic trigonometric functions

Abstract: Chebyshev expansion coefficients, accurate to forty decimal places, for the functions sine, cosine, and tangent, are tabulated. The methods used to generate the expansions are outlined and the ways in which accuracy of the tabulated coefficients were checked are noted.