Method and apparatus for digital signal filtering
View Patent ↗A Q-Filter is a reconfigurable technique that performs a continuum of linear and nonlinear filtering operations. It is modeled by unique mathematical structure, utilizing a function called the Q-Measure, defined using a set of adjustable kernel parameters to enable efficient hardware and software implementations of a variety of useful, new and conventional, filtering operations. The Q-Measure is is based on an extension of the well-known Sugeno λ-Measure.
1. A method for filtering a signal to produce a filtered signal, the method comprising the steps of:
setting a value of a variable parameter λ;
setting a density generator vector ƒ={ƒ 1 ,ƒ 2 , . . . , ƒ n };
constructing a q-measure based on the variable parameter λ and vector ƒ; and
producing a filtered signal by filtering the signal based on the q-measure.
2. The method of claim 1 wherein the step of constructing the q-measure comprises the step of additionally constructing the q-measure based on a measure generator function.
3. The method of claim 2 wherein the step of constructing the q-measure based on the measure generator function comprises the step of constructing the q-measure based on a normalized measure generator.
4. The method of claim 1 wherein the step of constructing the q-measure comprises the step of constructing the function
q
(
A
)
=
{
∏
x
j
∈
A
(
1
+
λ
f
j
)
-
1
∏
x
j
∈
X
(
1
+
λ
f
j
)
-
1
,
λ
≥
-
1
,
λ
≠
0
∑
x
j
∈
A
f
j
∑
x
j
∈
X
f
j
,
λ
=
0
5. The method of claim 1 wherein the step of setting the value of the variable parameter λ comprises the step of choosing a real value for λ that is greater than or equal to −1.
6. The method of claim 1 wherein the step of setting the density generator vector ƒ={ƒ 1 , ƒ 2 , . . . ,ƒ n } comprises setting elements ƒ j wherein 0≦ƒ j ≦1 for j=1, . . . , n.
7. A filter for producing a filtered signal, the filter comprising:
an input receiving a signal;
an input receiving a variable parameter λ;
an input receiving a density generator vector ƒ={ƒ 1 , ƒ 2 , . . . , ƒ n };
logic circuitry and memory components required for constructing a q-measure based on the variable parameter λ and vector ƒ and outputting a the filtered signal based on lie q-measure.
8. The filter of claim 7 wherein the q-measure is based on a measure generator.
9. The filter of claim 8 wherein the q-measure based on a normalized measure generator.
10. The filter of claim 7 wherein the q-measure for a given set A is set equal to q(A) wherein
q
(
A
)
=
{
∏
x
j
∈
A
(
1
+
λ
f
j
)
-
1
∏
x
j
∈
X
(
1
+
λ
f
j
)
-
1
,
λ
≥
-
1
,
λ
≠
0
∑
x
j
∈
A
f
j
∑
x
j
∈
X
f
j
,
λ
=
0
11. The filter of claim 7 wherein the variable parameter λ comprises a value that is greater than or equal to −1.
12. The filter of claim 7 wherein the density generator vector ƒ={ƒ 1 , ƒ 2 , . . . , ƒ n } comprises elements ƒ j wherein 0≦ƒ j ≦1, . . . , n.