FIR filter design based on DA

DFS system and parallel computing have both gained ground in today's cloud computing area, to maximize the data processing volume within a timestamp.

You might have to switch to no-lock nosql to realize high concurrency when it comes to digital signal processing, a good structure such as the butterfly modal using original stand point computing and bit reverse to analog time-frequency transformation in code design really matters.

Utilizing concurrent computing will fullfil the ALU and MAC units to accelerate filtering to turn input into output.

Here's the analysis for the basic rule applied in FIR filter design:





x
is computed in b bit depending on how many bit it has， coefficient is 2^b.

Multiply c
to x
we will get



and then we transform y to another type by creating a triple accumulation loop to a new order:

y=(c[0]xB-1[0]+c[1]+……+c[N-1]xB-1[N-1])2B-1+(c[0]xB-2[0]+c[1]+……+c[N-1]xB-2[N-1])2B-2 (2-4)
.
.
+(c[0]x0[0]+c[1]x0[1]+c[N-1]x0[N-1])



finally we come to the result:

look at the 2-4 formular, the machine concurrently calculate the (c[0]xB-1[0]+c[1]+……+c[N-1]xB-1[N-1])2B-1 part, this is called bit caculation, and then generate the accumulation result by adding these distributed bits