Method and system for processing a discrete time input signal where the clock rate of a discrete time output signal is a multiple of the clock rate of input signal samples
View Patent ↗A method and system of efficiently processing a discrete time input signal having a plurality of input signal samples that occur at a first clock rate into a discrete time output signal having a second clock rate that is R times the first clock rate is presented. The method includes receiving the input signal and filtering the input signal with an N-taps finite impulse response (FIR) filter having N filter coefficients. The method reduces the number of required operations and reduces computational errors in the filtering and interpolation of discrete input signals.
1. A method of efficiently processing a discrete time input signal having a plurality of input signal samples that occur at a first clock rate into a discrete time output signal having a second clock rate that is R times the first clock rate, the method comprising the steps of:
receiving the input signal; and
filtering the input signal with an N-taps finite impulse response (FIR) filter having N filter coefficients according to
∑
i
=
k
ceil
[
(
N
+
1
-
k
)
/
R
]
-
1
b
iR
-
k
u
(
(
m
-
i
+
k
)
T
s
)
wherein b iR−k is one of the N filter coefficients, u((m−i+k)T s ) is one of the input signal samples, T s is a slow clock sampling period, m equals (0, 1, 2, 3, . . . ), and k equals (0, 1, 2, . . . , R−1).
2. The method of claim 1 , wherein the input signal is a position signal.
3. The method of claim 1 , wherein each of the N filter coefficients is the result of a discrete convolution of a series of FIR filters.
4. The method of claim 1 , wherein the output signal is sent to a control system that controls a photolithography scanning operation.
5. A system for efficiently processing a discrete time input signal having a plurality of input signal samples that occur at a first clock rate into a discrete time output signal having a second clock rate that is R times the first clock rate, the system comprising:
means for receiving the input signal; and
means for filtering the input signal with an N-taps finite impulse response (FIR) filter having N filter coefficients according to
∑
i
=
k
ceil
[
(
N
+
1
-
k
)
/
R
]
-
1
b
iR
-
k
u
(
(
m
-
i
+
k
)
T
s
)
wherein b iR−k is one of the N filter coefficients, u((m−i+k)T s ) is one of the input signal samples, T s is a slow clock sampling period, m equals (0, 1, 2, 3, . . . ), and k equals (0, 1, 2, . . . , R−1).
6. The system of claim 5 , wherein the input signal is a position signal.
7. The system of claim 5 , wherein each of the N filter coefficients is the result of a discrete convolution of a series of FIR filters.
8. The system of claim 5 , wherein the output signal is sent to a control system that controls a photolithography scanning operation.