Direct Form I Realization of Active Photonic Filters

Abstract

An integrated photonic architecture is introduced and used to realize an optical filter with direct form I realization. The architecture offers gain from semiconductor optical amplifiers, and this gain results in an active optical filter whose filter response depends on the individual gains. The presence of gain provides advantages in filter performance, and tunable and adaptive functionality. The optical filter is modeled as a discrete time system and the z-transform is used in its analysis and design. A low-pass filter design example is presented and the filter coefficients are derived in terms of gains and coupler splitting ratios. The region of stable operations is derived by applying the Schur-Cohn stability test.     

相位与信号的关系

设x(n)和y(n)(n=0,1,2,…)是两个实数列,它们的z变换分别为 本文假定X(z),Y(z)在|z|≤1上解析,在圆周|z|=1上无零点.于是当ω∈[-π,π)时,可把X(e~(iω))和Y(e~(iω))分别写成     

关于z变换的研究及其在解差分方程中的应用

研究了几种序列的z变换,对z变换对表进行了修正和补充,并对单边z变换的时移特性及用z变换求解差分方程作了一定程度的探讨.     

Direct Form I Realization of Active Photonic Filters

An integrated photonic architecture is introduced and used to realize an optical filter with direct form I realization. The architecture offers gain from semiconductor optical amplifiers, and this gain results in an active optical filter whose filter response depends on the individual gains. The presence of gain provides advantages in filter performance, and tunable and adaptive functionality. The optical filter is modeled as a discrete time system and the z-transform is used in its analysis and design. A low-pass filter design example is presented and the filter coefficients are derived in terms of gains and coupler splitting ratios. The region of stable operations is derived by applying the Schur-Cohn stability test.