Reciprocal index lookup for BTSC compatible coefficients

A method of calculating a variable spectral expansion filter coefficient in a BTSC compatible stereo decoder from a feed-forward variable, comprising:

• a. calculating a reciprocal value that is proportional to the feed-forward variable;
• b. indexing a lookup table using a pre-selected set of high order bits of the reciprocal value so as to generate at least one parameter of a filter coefficient function, wherein a first portion of the lookup table stores a plurality of discrete values at index points of a line segment corresponding to a filter coefficient function approximation, so as to generate an initial discrete value corresponding to the filter coefficient function at a value of the high order bits, and wherein a second portion of the lookup table stores a plurality of slope values, each slope value indicating a slope of a line segment of the filter coefficient function, so as to generate a slope value of a line segment corresponding to the filter coefficient function at the value of the high order bits;
• and
• c. linearly interpolating an approximation of the expansion filter coefficient based on the slope value, the initial discrete value and a preselected set of low order bits of the reciprocal value.

An apparatus for calculating a variable spectral expansion filter coefficient in a BTSC compatible stereo decoder from a feed-forward variable, comprising:

• a. a reciprocal value component configured and arranged so as to calculate a reciprocal value proportional to the feed-forward variable;
• b. a lookup table is indexed by a pre-selected set of high order bits of the reciprocal value, wherein a first portion of the lookup table stores a plurality of discrete values at index points of a line segment corresponding to a filter coefficient function approximation, so as to generate an initial discrete value corresponding to the filter coefficient function at a value of the high order bits, and wherein a second portion of the lookup table stores a plurality of slope values, each slope value indicating a slope of a line segment of the filter coefficient function, so as to generate a slope value of a line segment corresponding to the filter coefficient function at the value of the high order bits;
• and
• c. a linear interpolation component configured and arranged so as to interpolate an approximation of the expansion filter coefficient based on the slope value, the initial discrete value and a pre-selected set of low order bits of the reciprocal value.

A method of calculating a variable spectral expansion filter coefficient in a BTSC compatible stereo decoder from a feed-forward variable, comprising:

• a. calculating a reciprocal value that is proportional to a reciprocal of the feed-forward variable;
• b. indexing a lookup table using a preselected set of bits of the reciprocal value to generate at least one parameter of a filter coefficient function;
• and
• c. linearly interpolating an approximation of the expansion filter coefficient based upon the at least one parameter of the filter coefficient function.

A method of calculating a variable spectral expansion filter coefficient in a BTSC compatible stereo decoder from a feed-forward variable, comprising:

• a. calculating a reciprocal value that is proportional to a reciprocal of the feed-forward variable;
• b. indexing a lookup table using a preselected set of high order bits of the reciprocal value, wherein a first portion of the lookup table stores a plurality of discrete values at index points of a line segment corresponding to a filter coefficient function approximation, so as to generate an initial discrete value corresponding to the filter coefficient function at a value of the high order bits, and wherein a second portion of the lookup table stores a plurality of slope values, each slope value indicating a slope of a line segment of the filter coefficient function, so as to generate a slope value of a line segment corresponding to the filter coefficient function at the value of the high order bits;
• and
• c. linearly interpolating an approximation of the expansion filter coefficient based on the slope value, the initial discrete value and a preselected set of low order bits of the reciprocal value.

An apparatus for calculating a variable spectral expansion filter coefficient in a BTSC compatible stereo encoder from a feed-forward variable, comprising:

• a. a reciprocal value circuit that calculates a reciprocal value that is proportional to a reciprocal of the feed-forward variable;
• b. a lookup table that is indexed by a preselected set of high order bits of the reciprocal value, wherein a first portion of the lookup table stores a plurality of discrete values at index points of a line segment corresponding to a filter coefficient function approximation, so as to generate an initial discrete value corresponding to the filter coefficient function at a value of the high order bits, and wherein a second portion of the lookup table stores a plurality of slope values, each slope value indicating a slope of a line segment of the filter coefficient function, so as to generate a slope value of a line segment corresponding to the filter coefficient function at the value of die high order bits;
• and
• c. a linear interpolation circuit that interpolates an approximation of the expansion filter coefficient based on die slope value, the initial discrete value and a preselected set of low order bits of the reciprocal value.