Algorithms and Parallel Computing

14.6 DECIMATOR DAG FOR s₂ = [1 −1]

The DAG corresponding to s₂ is shown in Fig. 14.6. The equitemporal planes are indicated by the gray lines and the time index values are indicated by the grayed numbers associated with the equitemporal planes. We note from the figure that a maximum of 12 tasks or nodes is active at any time step, which corresponds to the anti-aliasing filter length N. It should also be noted that the time values are associated with the high data rate of the decimator input.

Figure 14.6 M-to-1 decimator DAG for the case when M = 3, N = 12, and s₂ = [1 − 1].

Chapters 10 and 11 explained that the projection operation assigns a node or a group of nodes in the DAG to a thread or processor. The number of assigned nodes determines the workload associated with each task. The operation also indicates the input and output data involved in the calculations. The projection operation controls the workload assigned to each thread/processor at each stage of the execution of the SPA. We have three possible valid projection vectors:

(14.18)

(14.19)

(14.20)

These projection ...