Low-power pulse-shaping digital filters

A method of filtering a series of mapped input data values {x0,x1, . . . ,xN−1}, comprising the steps of:

• (a) successively delaying, in a digital processor, each of the mapped input values to create tap values {t0,t1, . . . ,tN−1};
• (b) multiplying, in the digital processor, each of the tap values {t0,t1, . . . ,tN−1} by A•{h0,h1, . . . ,hN−1}, to produce {At0h0,At1h1, . . . ,AtN−1hN−1} wherein values {h0,h1, . . . ,hN−1} are weight values selected to achieve the desired filter response and A is a factor selected to improve computational efficiency in filtering the input data values;
• (c) summing, in the digital processor, the values {At0h0,At1h1, . . . ,AtN−1hN−1} to produce ∑ k = 0 N - 1 ⁢ At k ⁢ h k ;
• and
• (d) biasing, in the digital processor, the summed values {At0h0,At1h1, . . . ,AtN−1hN−1} to compensate for the factored weight values {At0h0,At1h1, . . . ,AtN−1hN−1} to produce the filtered series of mapped input data values.

A program storage device, readable by a computer, tangibly embodying one or more programs of instructions executable by the computer to perform method steps of filtering an input data stream {x0,x1, . . . ,xN−1}, the method steps comprising the steps of:

• (a) successively delaying and mapping each of the input values to create tap values {t0,t1, . . . ,tN−1};
• (b) multiplying each of the tap values {t0,t1, . . . ,tN−1} by A•{h0,h1, . . . ,hN−1}, to produce {At0h0,At1h1, . . . ,AtN−1hN−1} wherein values {h0,h1, . . . ,hN−1} are weight values selected to achieve a desired filter response and A is a factor selected to improve computational efficiency in filtering the input data stream;
• (c) summing the values {At0h0,At1h1, . . . ,AtN−1hN−1} to produce ∑ k = 0 N - 1 ⁢ At k ⁢ h k ;
• and
• (d) biasing the sum ∑ k = 0 N - 1 ⁢ At k ⁢ h k
• to compensate for the factored weight values to produce a digital filter output.

A method of filtering a series of mapped input data values {x0,x1, . . . ,XN−1}, comprising the steps of:

• (a) successively delaying, in a digital processor, each of the input values to create tap values {t0,t1,t2 . . . ,tN−3,tN−2,tN−1} associated with tap weights {h0,h1,h2 . . . ,hN−3,hN−2hN−1}, wherein the tap weights comprise one or more tap weight pairs {hi−1,hN−i} defined according to a relationship selected from the group comprising hi−1=hN−i and hi−1=−hN−i for i=1,2,3, . . . ,N/2 when N is even and i=1,2,3, . . . , (N+1)/2when N is odd, and wherein each tap weight pair {hi−1,hN−i} is associated with a tap value pair {ti−1,tN−i};
• (b) determining, in the digital processor, a state for each tap value pair {ti−1,tN−i};
• (c) selectively multiplying, in the digital processor each of the tap values by tap weights modified according to the tap weight pair state;
• (d) summing, in the digital processor, the selectively multiplied tap values;
• (e) determining, in the digital processor, a tap weight pair majority case;
• (f) biasing, in the digital processor, the summed values in accordance with the tap weight pair majority case to produce the filtered series of input values.

A method of filtering a series of mapped input data values {x0,x1, . . . ,xN−1}, comprising the steps of:

• (a) successively delaying, in a digital processor, each of the mapped input values to create tap values {t0,t1, . . . ,tN−1};
• (b) multiplying, in the digital processor, each of the tap values {t0,t1, . . . ,tN−1} by values {h0,h1, . . . ,hN−1} and factors {A0,A1, . . . ,AN−1 } to produce {A0t0h0,A1t1h1, . . . ,AN−1tN−1hN−1}wherein values {h0,h1, . . . ,hN−1} are weight values selected to achieve a desired filter response and {A0,A1, . . . ,AN−1} are factors selected to improve computational efficiency in filtering the input data stream;
• (c) summing, in the digital processor, the values {A0t0h0,A1t1h1, . . . ,AN−1tN−1hN−1} to produce ∑ k = 0 N - 1 ⁢ A k ⁢ t k ⁢ h k ;
• and
• (d) biasing, in the digital processor, the summed values ∑ k = 0 N - 1 ⁢ A k ⁢ t k ⁢ h k
• to produce a digital filter output having the filtered series of mapped input data values.

A method of filtering a series of mapped input data values {x0,x1, . . . ,xN−1} comprising the steps of:

• (a) successively delaying, in a digital processor, each of the input values to create a set of tap values {t0,t1, . . . ,tN−1};
• (b) multiplying, in the digital processor, each member of the jth subset, for j=1,2, . . . ,p of the set of tap values {t0,t1, . . . ,tN−1} by corresponding members of corresponding subsets of the set Aj •{h0,h1, . . . ,hN−1} to produce subsets of the set {Ajt0h0, Ajt1h1, . . . ,AjtN−1hN−1} wherein values {h0,h1, . . . ,hN−1} are weight values selected to achieve a desired filter response, and Aj is a factor selected to improve computational efficiency of the digital filter;
• (c) summing, in the digital processor, the values of the members of the p subsets;
• and
• (d) biasing, in the digital processor, the sum of the values of the members of the p subsets to produce a digital filter output having the filtered series of mapped input data values.

An apparatus for filtering a series of mapped input data values {x0,x1, . . . ,xN−1}, comprising:

• (a) means for successively delaying each of the mapped input values {x0,x1, . . . ,xN−1} to create tap values {t0,t1, . . . ,tN−1};
• (b) means for multiplying each of the tap values {t0,t1, . . . ,tN−1} by values {h0,h1, . . . ,hN−1} and factors {A0,A1, . . . ,AN−1} to produce {A0t0h0,A1t1h1, . . . ,AN−1tN−1hN−1} wherein values {h0,h1, . . . ,hN−1} are weight values selected to achieve a desired filter response and {A0,A1, . . . ,AN−1} are factors selected to improve computational efficiency in filtering the input data stream;
• (c) means for summing the values {A0t0h0,A1t1h1, . . . ,AN−1tN−1hN−1} to produce ∑ k = 0 N - 1 ⁢ A k ⁢ t k ⁢ h k ;
• and
• (d) means for biasing the summed values ∑ k = 0 N - 1 ⁢ A k ⁢ t k ⁢ h k
• to produce a digital filter output.