Reciprocal index lookup for BTSC compatible coefficients

A method for decoding an encoded BTSC composite audio signal comprising:

• digitally separating a L−R signal, a L+R signal and a SAP signal all being encoded in the composite signal;
• digitally applying deemphasis to the L+R signal;
• digitally processing the L−R signal;
• digitally processing the SAP signal;
• and
• combining the de-emphasized L+R signal with the digitally processed L−R signal to produce separate L and R audio signals.

A system for decoding a digital BTSC-compatible stereo television audio signal to generate a left and right audio output signal comprising:

• a coefficient generator that receives the digital signal from a feedforward branch circuit;
• a spectral expander that uses the generated coefficients to spectrally expand the digital signal;
• an inverter for generating the reciprocal of the digital signal;
• and
• a combiner for digitally combining the output of the expander with the output of the inverter into a combined signal.

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

• a. calculating a reciprocal value that is proportional to the feed-forward variable;
• b. indexing a lookup table using a pre-selected set of bits of the reciprocal value to generate at least one parameter of the filter coefficient function;
• and
• c. linearly interpolating an approximation of the expansion filter coefficient based on 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 encoder from a feed-forward variable, comprising the steps of:

• 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, 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 compression 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 the feed-forward variable;
• b. a lookup table that 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 circuit that interpolates 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.