Method and system for Gaussian filter modification for improved modulation characteristics in Bluetooth RF transmitters
Certain aspects of the invention may comprise determining an impulse response of a first Gaussian filter based on a filter length and an oversampling ratio (OSR). The most significant coefficients of the first Gaussian filter may be modified to create a target filter. An upper limit and a lower limit for deviation of the modified most significant coefficients for the target filter may be determined. A magnitude response for the target filter may be constrained based on at least a selected corner frequency, which is related to the OSR. A line search algorithm may be executed on the constrained magnitude response to generate new coefficients for the target filter.
1 . A method for generating a filter with improved modulation characteristics in a communications system, the method comprising:
determining an impulse response of a first Gaussian filter based on a filter length and an oversampling ratio (OSR);
modifying most significant coefficients of said first Gaussian filter to create a target filter;
determining an upper limit and a lower limit for deviation of said modified most significant coefficients for said target filter;
constraining a magnitude response for said target filter based on at least a selected corner frequency, which is related to said OSR; and
executing a line search algorithm on said constrained magnitude response to generate new coefficients for said target filter.
2 . The method according to claim 1 , further comprising constraining said magnitude response to an integer multiple of a discrete time image frequency, which is a reciprocal of said OSR.
3 . The method according to claim 1 , wherein an initial value of said target filter is
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where h M [n],n=1, . . . ,2N is said impulse response of said target filter, h 0 [n],n=1, . . . ,2N is said impulse response of said Gaussian filter, N L represents number of optimization variables, which is a set of said most significant coefficients of said first Gaussian filter.
4 . The method according to claim 1 , wherein said upper limit and said lower limit for deviation of said modified most significant coefficients for said target filter is x L ×h 0 [n]≦h M [n]≦x U ×h 0 [n], ∀ n, where h M [n],n=1, . . . ,2N is said impulse response of said target filter, h 0 [n],n=1, . . . ,2N is said impulse response of said Gaussian filter, x L is said lower limit for deviation and x U is said upper limit for deviation.
5 . The method according to claim 1 , wherein said magnitude response of said target filter is |H M (e j2πf )|≡|H M (e jπ/OSR )|,where H M is said impulse response of said target filter and f C is said selected corner frequency.
6 . The method according to claim 1 , wherein said magnitude response of said target filter is constrained by |H M (e j2πf )|≦A STOP , ∀ f≧2f c , where H M is said impulse response of said target filter, f is a frequency of operation, f C is said selected corner frequency and A STOP is a final magnitude of said magnitude response of said target filter.
7 . The method according to claim 1 , wherein said line search algorithm is applied to a minimization problem given by min{1−|H M (e j2πf c )|}, wherein an initial value of said target filter is
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and subject to x L ×h 0 [n]≦h M [n]≦x U ×h 0 [n], ∀ n and |H M (e j2πf )|≦A STOP , ∀ f≧2f c where h M[n],n= 1, . . . ,2N is said impulse response of said target filter, h 0 [n],n=1, . . . ,2N is said impulse response of said Gaussian filter, N L represents number of optimization variables, which is a set of said most significant coefficients of said first Gaussian filter, x L is said lower limit for deviation, x U is said upper limit for deviation, H M is said impulse response of said target filter, f is a frequency of operation, f C is said selected corner frequency and A STOP is a final magnitude of said magnitude response of said target filter.
8 . A machine-readable storage having stored thereon, a computer program having at least one code section for generating a filter with improved modulation characteristics in a communications system, the at least one code section being executable by a machine for causing the machine to perform steps comprising:
determining an impulse response of a first Gaussian filter based on a filter length and an oversampling ratio (OSR);
modifying most significant coefficients of said first Gaussian filter to create a target filter;
determining an upper limit and a lower limit for deviation of said modified most significant coefficients for said target filter;
constraining a magnitude response for said target filter based on at least a selected corner frequency, which is related to said OSR; and
executing a line search algorithm on said constrained magnitude response to generate new coefficients for said target filter.
9 . The machine-readable storage according to claim 8 , further comprising code for constraining said magnitude response to an integer multiple of a discrete time image frequency, which is a reciprocal of said OSR.
10 . The machine-readable storage according to claim 8 , wherein an initial value of said target filter is
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where h M [n],n=1, . . . ,2N is said impulse response of said target filter, h 0 [n],n=1, . . . ,2N is said impulse response of said Gaussian filter, N L represents number of optimization variables, which is a set of said most significant coefficients of said first Gaussian filter.
11 . The machine-readable storage according to claim 8 , wherein said upper limit and said lower limit for deviation of said modified most significant coefficients for said target filter is x L ×h 0 [n]≦h M [n]≦x U ×h 0 [n], ∀ n, where h M [n], n=1, . . . ,2N is said impulse response of said target filter, h 0 [n],n=1, . . . ,2N is said impulse response of said Gaussian filter, x L is said lower limit for deviation and x U is said upper limit for deviation.
12 . The machine-readable storage according to claim 8 , wherein said magnitude response of said target filter is |H M (e j2πf c )|≡|H M (e jπ/OSR )|, where H M is said impulse response of said target filter and f C is said selected corner frequency.
13 . The machine-readable storage according to claim 8 , wherein said magnitude response of said target filter is constrained by |H M (e j2πf )|≦A STOP , ∀ f≧2f c , where H M is said impulse response of said target filter, f is a frequency of operation, f C is said selected corner frequency and A STOP is a final magnitude of said magnitude response of said target filter.
14 . The machine-readable storage according to claim 8 , wherein said line search algorithm is applied to a minimization problem given by min{1−|H M (e j2πf c )|}, wherein an initial value of said target filter is
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and subject to x L ×h 0 [n]≦h M [n]≦x U ×h 0 [n], ∀ n and |H M (e j2πf )|≦A STOP , ∀ f ≧2f c , where h M [n],n=1, . . . ,2N is said impulse response of said target filter, h 0 [n],n=1, . . . ,2N is said impulse response of said Gaussian filter, N L represents number of optimization variables, which is a set of said most significant coefficients of said first Gaussian filter, x L is said lower limit for deviation, x U is said upper limit for deviation, H M is said impulse response of said target filter, f is a frequency of operation, f C is said selected corner frequency and A STOP is a final magnitude of said magnitude response of said target filter.
15 . A system for generating a filter with improved modulation characteristics in a communications system, the system comprising:
circuitry that determines an impulse response of a first Gaussian filter based on a filter length and an oversampling ratio (OSR);
circuitry that modifies most significant coefficients of said first Gaussian filter to create a target filter;
circuitry that determines an upper limit and a lower limit for deviation of said modified most significant coefficients for said target filter;
circuitry that constrains a magnitude response for said target filter based on at least a selected corner frequency, which is related to said OSR; and
circuitry that executes a line search algorithm on said constrained magnitude response to generate new coefficients for said target filter.
16 . The system according to claim 15 , further comprising circuitry that constrains said magnitude response to an integer multiple of a discrete time image frequency, which is a reciprocal of said OSR.
17 . The system according to claim 15 , wherein an initial value of said target filter is
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where h M [n],n=1, . . . ,2N is said impulse response of said target filter, h 0 [n],n=1, . . . ,2N is said impulse response of said Gaussian filter, N L represents number of optimization variables, which is a set of said most significant coefficients of said first Gaussian filter.
18 . The system according to claim 15 , wherein said upper limit and said lower limit for deviation of said modified most significant coefficients for said target filter is x L ×h 0 [n]≦h M [n]≦x U ×h 0 [n], ∀ n, where h M [n],n=1, . . . ,2N is said impulse response of said target filter, h 0 [n],n=1, . . . ,2N is said impulse response of said Gaussian filter, x L is said lower limit for deviation and x U is said upper limit for deviation.
19 . The system according to claim 15 , wherein said magnitude response of said target filter is |H M (e j2π c )|≡|H M (e jπ/OSR )|, where H M is said impulse response of said target filter and f C is said selected corner frequency.
20 . The system according to claim 15 , wherein said magnitude response of said target filter is constrained by |H M (e j2πf )|≦A STOP , ∀ f≧2f c , where H M is said impulse response of said target filter, f is a frequency of operation, f C is said selected corner frequency and A STOP is a final magnitude of said magnitude response of said target filter.
21 . The system according to claim 15 , wherein said line search algorithm is applied to a minimization problem given by min{1−|H M (e j2πf c )|}, wherein an initial value of said target filter is
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and subject to x L ×h 0 [n]≦h M [n]≦x U ×h 0 [n], ∀ n and |H M (e j2πf )|≦A STOP , ∀ f≧2f c , where h M [n],n=1, . . . ,2N is said impulse response of said target filter, h 0 [n],n=1, . . . ,2N is said impulse response of said Gaussian filter, N L represents number of optimization variables, which is a set of said most significant coefficients of said first Gaussian filter, x L is said lower limit for deviation, x U is said upper limit for deviation, H M is said impulse response of said target filter, f is a frequency of operation, f C is said selected corner frequency and A STOP is a final magnitude of said magnitude response of said target filter.