Method for providing a filter and filter

1. A filter having an impulse response of a function that comprises a first partial impulse response and a second partial impulse response, comprising:

a supplementary filter, comprising a digital processing circuitry including at least one output node for an output of the supplementary filter, configured to generate a supplementary impulse response via the digital processing circuitry at the at least one output node;

a first filter, comprising an additional digital processing circuitry including at least one input node coupled to the supplementary filter, configured to generate, by the additional digital processing circuitry, the first partial impulse response using the output at the at least one output node of the supplementary filter and at least one additional input at the at least one input node as inputs of the first filter; and

a second filter, comprising a further digital processing circuitry including at least one additional input node coupled to the supplementary filter, configured to generate, by the further digital processing circuitry, the second partial impulse response using the output at the at least one output node of the supplementary filter and the at least one additional input at the at least one additional input node as inputs of the second filter;

wherein the digital processing circuitries comprise at least a multiplier, a delay element, and an adder; and

wherein the supplementary filter, the first filter and the second filter combine to provide the impulse response.

2. The filter of claim 1 , wherein samples of the impulse response are given by samples of the first partial impulse response at first sample positions and by samples of the second partial impulse response at second sample positions.

3. The filter of claim 2 , wherein the first sample positons are uneven sample positions, and wherein the second sample positions are even sample positions.

4. The filter of claim 1 , wherein the impulse response is given by positive integer powers(1−z −1 ) N with N being a positive integer number and z −1 denoting a delay by a single sampling period.

5. The filter of claim 4 , wherein N=3 and

the first filter has an impulse response of [2 0];

the second filter has an impulse response of [0 2]; and

the supplementary filter has an impulse response of [1 1].

6. The filter of claim 5 , comprising an input node, a delay element, a first multiplier, a second multiplier, a first adder, a second adder, a third adder, a first output node and a second output node, wherein

the input node is coupled to an input of the first adder, an input of the delay element and an input of the first multiplier;

an output of the first multiplier is coupled to an input of the third adder;

an output of the third adder is coupled to the first output node;

an output of the delay element is coupled to an input of the second multiplier and to an input of the first adder;

an output of the first adder is coupled to an input of the third adder and to an input of the second adder;

an output of the second multiplier is coupled to an input of the second adder; and

an output of the second adder is coupled to the second output node.

7. The filter of claim 6 , wherein the first multiplier and the second multiplier are configured to perform a multiplication by two.

8. The filter of claim 5 , comprising a first input node, a second input node, a first multiplier, a second multiplier, a delay element, a first adder, a second adder and a third adder, wherein

the first input node is coupled to an input of the first multiplier and to an input of the first adder;

the second input node is coupled to an input of the second multiplier and to an input of the first adder;

an output of the first multiplier is coupled to an input of the third adder;

an output of the second multiplier is coupled to an input of the second adder;

an output of the second adder is coupled to an input of the delay element;

an output of the delay element is coupled to an input of the third adder;

an output of the first adder is coupled to an input of the second adder and to an input of the third adder.

9. The filter of claim 4 , wherein N=4 and

the first filter has an impulse response of [0 4 0];

the second filter has an impulse response of [4]; and

the supplementary filter has an impulse response of [1 1].

10. The filter of claim 9 , comprising an input node, a first delay element, a second delay element, a first multiplier, a second multiplier, a first adder, a second adder, a third adder, a first output node and a second output node, wherein

the input node is coupled to an input of the first adder and to an input of the first delay element;

an output of the first delay element is coupled to an input of the first adder an input of the first multiplier;

an output of the first multiplier is coupled to an input of the third adder;

an output of the first adder is coupled to an input of the second delay element, an input of the second adder and to the second output node;

an output of the second delay element is coupled to an input of the second adder;

an output of the second adder is coupled to an input of the third adder;

an output of the third adder is coupled to an input of the second multiplier; and

an output of the second multiplier is coupled to the second output node.

11. The filter of claim 10 , wherein the first multiplier and the second multiplier are configured to perform a multiplication by four.

12. The filter of claim 9 , comprising first input node, a second input node, a first multiplier, a second multiplier, a first delay element, a second delay element, a first adder, a second adder, a third adder and a fourth adder, wherein

the first input node is coupled to an input of the first multiplier, an input of the first delay element and an input of the first adder;

the second input node is coupled to an input of the second multiplier;

an output of the second multiplier is coupled to an input of the first adder;

an output of the first adder is coupled to an input of the second adder;

an output of the first delay element is coupled to an input of the second adder;

an output of the first multiplier is coupled to an input of the third adder;

an output of the second adder is coupled to an input of the third adder and an input of the fourth adder;

an output of the third adder is coupled to an input of the second delay element; and

an output of the second delay element is coupled to an input of the fourth adder.

13. The filter of claim 4 , wherein N=5 and

the first filter has an impulse response of [4 0 0];

the second filter has an impulse response of [0 0 4]; and

the supplementary filter has an impulse response of [1 10 1].

14. The filter of claim 13 , comprising an input node, a first delay element, a second delay element, a first multiplier, a second multiplier, a third multiplier, a fourth multiplier, a first adder, a second adder, a third adder, a fourth adder, a fifth adder, first output node and a second output node, wherein

the input node is coupled to an input of the first delay element, an input of the first multiplier and an input of the first adder;

an output of the first multiplier is coupled to an input of the fourth adder;

an output of the fourth adder is coupled to an input of the first output node;

an output of the first adder is coupled to an input of the second adder;

an output of the first delay element is coupled to an input of the second delay element, an input of the third multiplier and an input of the third adder;

an output of the third multiplier is coupled to an input of the third adder;

an output of the third adder is coupled to an input of the fourth multiplier;

an output of the fourth multiplier is coupled to an input of the second adder;

an output of the second adder is coupled to an input of the fourth adder and an input of the fifth adder;

an output of the second delay element is coupled to an input of the first adder and to an input of the second multiplier;

an output of the second multiplier is coupled to an input of the fifth adder; and

an output of the fifth adder is coupled to an input of the second output node.

15. The filter of claim 14 , wherein the first multiplier the second multiplier and the third multiplier are configured to perform a multiplication by four; and

the fourth multiplier is configured to perform a multiplication by two.

16. The filter of claim 13 , comprising a first input node, a second input node, a first multiplier, a second multiplier, a third multiplier, a fourth multiplier, a first delay element, a second delay element, a first adder, a second adder, a third adder, a fourth adder and a fifth adder, wherein

the first input node is coupled to an input of the first multiplier and an input of the first adder;

the second input node is coupled to an input of the second multiplier an input of the first adder;

an output of the first adder is coupled to an input of the fourth multiplier, an input of the second adder and an input of the fifth adder;

an output of the first multiplier is coupled to an input of the fifth adder;

an output of the second multiplier is coupled to an input of the second adder;

an output of the second adder is coupled to an input of the delay element;

an output of the delay element is coupled to an input of the fourth adder;

an output of the fourth multiplier is coupled to an input of the third multiplier and an input of the third adder;

an output of the third multiplier is coupled to an input of the third adder;

an output of the third adder is coupled to an input of the fourth adder;

an output of the fourth adder is coupled to an input of the second delay element;

an output of the second delay element is coupled to an input of the fifth adder.

17. The filter of claim 1 , wherein at least one filter of the first filter and the second filter shares at least one element of a multiplier and a delay element with the supplementary filter.

18. The filter of claim 1 , wherein the filter is a digital filter.

19. A method for a filter having an impulse response, comprising:

generating, via the filter, a first partial impulse response contributing to the impulse response;

generating, via the filter, a second partial impulse response contributing to the impulse response;

generating, via the filter, a common contribution to the first partial impulse response and the second partial impulse response;

providing, via a supplementary filter comprising a digital processing circuitry including at least one output node for an output of the supplementary filter, the common contribution as a supplementary impulse response;

providing, via a first filter comprising an additional digital processing circuitry including at least one input node coupled to the supplementary filter, the first partial impulse response using the common contribution at the at least one output node of the supplementary filter and at least one additional input at the at least one input node as inputs of the first filter;

providing, via a second filter comprising a further digital processing circuitry including at least one additional input node coupled to the supplementary filter, the second partial impulse response using the common contribution at the at least one output node of the supplementary filter and the at least one additional input at the at least one additional input node as inputs of the second filter; and

combining the supplementary filter, the first filter and the second filter to provide the impulse response,

wherein the digital processing circuitries comprise at least a multiplier, a delay element, and an adder.

20. A computer readable non-transitory storage medium having stored thereon a program having a program code comprising executable instructions for performing the method of claim 19 , when the program code comprising executable instructions of the computer program is executed on a computer or processor.

21. A means for filtering with an impulse response comprising a first partial impulse response and a second partial impulse response, comprising:

means for generating a supplementary impulse response;

means for generating the first partial impulse response using an output of the means for generating the supplementary impulse response and at least one additional input as inputs of the first filter;

means for generating the second partial impulse response using an output of the means for generating the supplementary impulse response and the at least one additional input as inputs of the second filter; and

means for combining an output of the means having the first partial impulse response and of the means having the second partial impulse response.