Digital equalizer capable of varying the center frequency, quality factor, and gain to perform various frequency characteristics

Claim 1

A digital equalizer capable of arbitrarily varying at least one of a center frequency, a quality factor (Q), and a gain of the equalizer to perform various frequency characteristics, said digital equalizer comprising: first delay means for delaying an input digital signal by a sampling period (T); second delay means for delaying the output signal of said first delay means by the sampling period (T); first multiplier means for multiplying the input digital signal by a first coefficient (a 0 ); second multiplier means for multiplying the output signal of said first delay means by a second coefficient (a 1 ); third multiplier means for multiplying the output signal of said second delay means by a third coefficient (a 2 ); adding means for adding the output signals of the first, second, and third multiplier means and first and second feedback signals; third delay means for delaying the output signal of said adding means by the sampling period (T); fourth delay means for delaying the output signal of said third delay means by the sampling period (T); fourth multiplier means for multiplying the output signal of said third delay means by a fourth coefficient (b 1 ) to produce said first feedback signal; fifth multiplier means for multiplying the output signal of said fourth delay means by a fifth coefficient (b 2 ) to produce said second feedback signal; the output signal of said adding means being derived as the output signal of said digital equalizer; said digital equalizer having a transfer function H (z) which is a z-transform of a transfer function H (s) in Laplace transform expressed by ##EQU39## wherein k is a normalizing coefficient, ω o 1 and ω o 2 are angular frequencies of the pole and zero respectively, Q 1 is a quality factor primarily selected for the equalizer to perform a band-pass characteristic, and Q 2 is a quality factor primarily selected for the equalizer to perform a band-elimination characteristic, said transfer function H (s) having conjugate pairs of poles and zeros which lie on positions on the same circle of a radius ω c in the s-plane, wherein ω o 1 and ω o 2 are angular frequencies of the pole and zero respectively, ω c is a center angular frequency of the band-pass characteristic and the band-elimination characteristic performed respectively by said digital equalizer, an angle (θ 1 ) between a line passing one of the positions of the conjugate pair of poles from the origin of the s-plane and the negative real axis and an angle (θ 2 ) between a line passing one of the positions of the conjugate pair of zeros from the origin of the s-plane and the negative real axis being so selected that cos θ 2 /cos θ 1 is equal to the gain Q1/Q2 at the center frequency of the band-pass characteristic and band-elimination characteristic of said digital equalizer respectively, said second coefficient, (a 1 ) being equal to ##EQU40## wherein p equals cos θ 2 , said third coefficient (a 2 ) being equal to e -2 ω c Tp , said fourth coefficient (b 1 ) being equal to ##EQU41## wherein q equals cos θ 1 , said fifth coefficient (b 2 ) being equal to e -2 ω c Tq , and said first coefficient (a 0 ) being equal to ##EQU42##