10.2 THE 1-D FIR DIGITAL FILTER ALGORITHM
The 1-D FIR digital filter algorithm is an example of a RIA that can be expressed as the set of difference equations
where a(j) is the filter coefficient and N is the filter length. y(i) is our output variable, which depends on the i index only. On the other hand, a(i) is an input variable that depends on the j index only and x(i − j) is another input variable that depends on both the i and j indices. The above equation describes two iterations. One iteration is over the index i and the other iteration is over the index j, which is to be repeated N times. The data type in the above equation determines the algorithm granularity. This will ultimately determine the computation load of each task, which will translate to software threads or hardware systolic array processing elements (PEs).