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1. (WO2017189271) DESIGNING FIR FILTERS WITH GLOBALLY MINIMAX-OPTIMAL MAGNITUDE RESPONSE
Note: Text based on automatic Optical Character Recognition processes. Please use the PDF version for legal matters

WHAT IS CLAIM ED IS:

1. A system for filtering a signal received by an electromagnetic receiver, the system comprising:

a filter configuration unit for configuring a first filter of order N to be applied to the signal by determining coefficients h[n] of the first filter, where a target response of the first filter is specified by a target response function D (co) and a variable Kdes indicative of a target ratio of an error in a set of passband frequencies ΩΡ and an error in a set of stopband frequencies Os of the first filter; and a digital filter for generating a filtered signal by applying the first filter to the signal, wherein the filter configuration unit is configured to determine the coefficients h[n] of the first filter based on coefficients g[n] of a second filter of order 2N.

2. The system according to claim 1, wherein the second filter is a minimax-optimal even-symmetric filter.

3. The system according to claim 1, wherein the second filter is a minimax-optimal conjugate-symmetric filter,

4. The system according to any one of claims 1-3, wherein determining the coefficients h[n] of the first filter based on the coefficients g[n] of the second filter comprises:

computing a set of values p[n] by scaling the coefficients g[n] of the second filter by a scaling coefficient a and adding a unit impulse δ[η] scaled by a shifting coefficient b, and

determining the coefficients h[n] of the first filter as a set of (N+l) valu s for which the set of values p[n] is an autocorrelation sequence.

5. The system according to claim 4, wherein determining the coefficients h[n] of the first filter as the set of (N+l) values comprises performing a spectral factorization on the set of values p[nj.

6. The system according to claim 4, wherein determining the coefficients h[n] as the set of (N+l) values comprises determining two or more sets of the (N+l) values for which the set of values p[n] is the autocorrelation sequence, each set of the (N+l) values associated with a different phase characteristic.

7. The system according to claim 6, further comprising selecting a set of (N+l) values from the two or more sets of the (N+l) values for which the set of values pin] is the autocorrelation sequence with a specified phase characteristic.

8. The system according to claim 7, wherein the specified phase characteristic comprises one of a minimum phase or a maximum phase.

9. The system according to any one of claims 1-3, wherein the coefficients g[n] of the second filter are determined using a Remez Exchange algorithm or a Parks-fvicCieilan algorithm.

10. The system according to any one of claims 1-3, wherein the filter configuration unit is configured to determine the coefficients of the first filter based on the coefficients of a second filter of order 2N by:

iterating steps of i) setting a variable K indicative of a ratio of an error in the set of passband frequencies ΩΡ and an error in the set of stopband frequencies Os of the second filter to a new value, and ii) determining coefficients g[n] of the second filter with a target response specified by the target response function £> (ω) and the variable K, until a maximum passband error Δ? of a frequency response Gfe""j of the second filter satisfies a condition with respect to a comparison value based on the variables /C and Kdes, and

determining the coefficients h[n] of the first filter based on the coefficients g[n] of the second filter.

11. The system according to claim 10, wherein determining the coefficients h[n] of the first filter based on the coefficients g[n] of the second filter comprises:

computing a set of values p[n] by scaling the coefficients g[n] of the second filter by a scaling coefficient a and adding a unit impulse δ[η] scaled by a shifting coefficient h, and

determining the coefficients h[n] of the first filter as a set of (N+l) values for which the set of values p[n] is an autocorrelation sequence.

12. The system according to claim 11, wherein the scaling coefficient a is equal to ϋ-des..

KAp SK2

13. The system according to claim 11, wherein the shifting coefficient b is equal to

K - 14. The system according to claim 10, wherein determining the maximum passband error Δρ comprises determining a value indicative of a maximum absolute deviation of the frequency response G(e!,J'} of the second filter from a value of 1 for frequencies within the set of passband frequencies Ωρ.

15. The system according to claim 10, wherein the comparison value is a value indicative 0f j¾

16. The system according to claim 10, wherein the condition with respect to the comparison value comprises a difference between the maximum passband error ΔΡ and the comparison value being within a margin with respect to 0.

17. The system according to claim 10, wherein the condition with respect to the comparison value comprises a ratio between the maximum passband error ΔΡ and the comparison value being within a margin with respect to 1.

18. The system according to claim 10, wherein the condition with respect to the comparison value comprises the maximum passband error Δ? being equal to the comparison value.

19. The system according to claim 10, wherein the target response of the second filter comprises:

a response of the second filter for which a ratio of an error due to a difference between the response of the second filter and the target response function Ο ίω) in the set of passband frequencies ΩΡ and an error due to a difference between the response of the second f ilter and the target response function D (co) in the set of stopband frequencies i¾ is equal to or within a tolerance range of the variable K.

20. The system according to any one of claims 1-3, wherein each of the first filter and the second filter is a finite impulse response (FI R) filter.

21. A computer-implemented method for operating a digital filter, the method comprising:

computing coefficients h[n] of a first filter of order /V, where a target response of the first filter is specified by a target response function 0 (ω) and a variable Kdes indicative of a target ratio of an error in a set of passband frequencies ΩΡ and an error in a set of stopband frequencies QS of the first filter, by performing one or more iterations of

i) setting a variable K indicative of a ratio of an error in the set of passband frequencies ΩΡ and an error in the set of stopband frequencies ¾ of a second filter of order 2N to a new value, and

ii) determining coefficients gin] of the second filter, where a target response of the second filter is specified by the target response function D (a>) and the variable K, where the iterations are performed until a maximum passband error Δρ of a frequency response G(e>") of the second filter satisfies a condition with respect to a comparison value based on the variables K and

determining the coefficients h[n] of the first filter based on the coefficients g[n] of the second filter; and

configuring the digital filter to apply the first filter with the coefficients h[n] to a signal to generate a filtered signal.

22. The method according to daim 20, further comprising receiving a value of the order N, the target response function Ζ) (ω) and the variable ¾B via a user interface.

23. The method according to claims 21 or 22, wherein determining the coefficients h[n] of the first filter based on the coefficients g[n] of the second filter comprises:

computing a set of values p[n] by scaling the coefficients g[n] of the second filter by a scaling coefficient a and adding a unit impulse δ[η] scaled by a shifting coefficient b, and

determining the coefficients h[n] of the first filter as a set of (N+l) values for which the set of values p[n] is an autocorrelation sequence.

24. The method according to claim 23, wherein the scaling coefficient a is eaual to

ΚΔρ

25. The method according to claim 23, wherein the shifting coefficient b is equal to