Implementation

Our implementation provides signal evaluation at an arbitrary time, where time is specified as an unsigned binary fixed-point number in units of the input sampling period (assumed constant). Figure K.17 shows the time register , and Figure K.18 shows an example configuration of the input signal and lowpass filter at a given time. The time register is divided into three fields: The leftmost field gives the number of samples into the input signal buffer, the middle field is an initial index into the filter coefficient table , and the rightmost field is interpreted as a number between 0 and for doing linear interpolation between samples and (initially) of the filter table. The concatenation of and are called which is interpreted as the position of the current time between samples and of the input signal.

Let the three fields have , , and bits, respectively. Then the input signal buffer contains samples, and the filter table contains ``samples per zero-crossing.'' (The term ``zero-crossing'' is precise only for the case of the ideal lowpass; to cover practical cases we generalize ``zero-crossing'' to mean a multiple of time , where is the lowpass cutoff frequency.) For example, to use the ideal lowpass filter, the table would contain sinc.

Our implementation stores only the ``right wing'' of a symmetric finite-