Multiplier-less Multiplication by Constants - Digital Design of Signal Processing Systems: A Practical Approach - page 291

// Generating a number of input samples
always @ (counter)
begin
// A new sample at every sample clock
if (counter == 15)
new_val = X_reg-1;
end

// Increment counter that controls the DA architecture to be placed in a con-
troller
always @ (posedge CLKg)
begin
counter <= counter+1;
X_reg <= new_val;
end
initial
$monitor ($time, " X_reg=%d, YN=%d, YND=%d\n", X_reg, YN, YND);
endmodule

It is obvious from the configuration of a DA-based design that the size of ROM increases with an
increase in the number of coefficients of the filter. For example, a 128-coefficients FIR filter requires
a ROM of size 2 128 . This size is prohibitively large and several techniques are used to reduce the
ROM requirement [22-25].

6.8.3 M-parallel Sub-filter-based Design
This technique divides the filter into M sub-filters of length L, and each sub-filter is implemented as
an independent DA-based module. For computing the output of the filter, the results of all M sub-
filters are first compressed using any reduction tree, and the final sum and carry are added using
a CPA. For a filter of length K, the length of each sub-filter is L K/M. The filter is preferably

designed to be of length LM, or one of the sub-filters may be of a little shorter length than the rest.
For the parallel case, the convolution summation can be rewritten as:

¼

M 1 L 1

y½n¼

0 h½i

* Lþkx½nði * LþkÞ

i¼ 0 k¼

The inner summation implements each individual sub-filter. These filters are designed using
a DA-based MAC calculator. The outer summation then sums the outputs of all sub-filters. The
summation is implemented as a compression tree and a CPA. The following example illustrates
the design.
Example: The architecture designs an 18-coefficient FIR filter using six sub-filters. For the
design L ¼ 3andM ¼ 6, and the architecture is shown in Figure 6.21. Each sub-filter implements
a2 3

5, depends on the maximum absolute
value of its contents. The output of each ROM is input to a compression tree. For the MSBs in the

¼ 8 deep ROM. The width of each ROM, P i for i ¼ 0 ...