Method and system for efficient and accurate filtering and interpolation
AssigneeASML Holding N.V.
InventorRoberto B. Wiener
Life of this patent
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Abstract
The present invention is directed to efficient and accurate filtering and interpolation techniques. Methods of the present invention reduce the number of required operations and reduce computational errors in the filtering and interpolation of discrete input signals.
Claims14
A method of reducing the number of operations required to interpolate a discrete rectangular input signal having a first sampling rate into a discrete output signal having a second sampling rate, the method comprising the steps of:
- (a) selecting a plurality of input signal values from the input signal, wherein each selected input signal value corresponds to a particular time increment at the first sampling rate;
- and
- (b) generating, at a time increment occurring at the second sampling rate, an output signal value, said step comprising
- (i) calculating a result according to ∑ k = 1 L a k [ F ( t - T k ) - F ( t - T k + 1 ) ] ,
- wherein
- ak is one of the selected plurality of input signal values,
- F(t−Tk) is a first of the plurality of filter response function values, and
- F(t−Tk+1) is a second of the plurality of filter response function values;
- and
- (ii) summing the result with a prior time increment output signal value.
A system for reducing the number of operations required to interpolate a discrete rectangular input signal having a first sampling rate into a discrete output signal having a second sampling rate, the system comprising:
- (a) means for selecting a plurality of input signal values from the input signal, wherein each selected input signal value corresponds to a particular time increment at the first sampling rate;
- and
- (b) means for generating, at a time increment occurring at the second sampling rate, an output signal value, comprising
- (i) means for calculating a result according to ∑ k = 1 L a k [ F ( t - T k ) - F ( t - T k + 1 ) ] ,
- wherein
- ak is one of the selected plurality of input signal values,
- F(t−Tk) is a first of the plurality of filter response function values, and
- F(t−Tk+1) is a second of the plurality of filter response function values;
- and
- (ii) means for summing the result with a prior time increment output signal value.
Dependencies are inferred from the claim text.