In this paper, a new method for designing digital infinite impulse response filter with nearly linear-phase response is presented using fractional derivative constraints (FDC). The design problem is constructed as a phase optimization problem between the desired and designed phase response of a filter. In order to achieve the highly accurate passband ( pb ) response, phase response is fitted to desired response more precisely using FDC, due to which design problem becomes a multimodal error surface that is constructed from sum of passband error ( e p ) and stopband error ( e s ). Optimal value of FDC is accomplished by minimizing the total error (er 0 ) using improved swarm-based optimization technique, which is formulated by associating the scout bee mechanism of artificial bee colony algorithm with particle swarm optimization and termed as hybrid particle swarm optimization. The simulated results reflect that the improved response in passband along with better transition width is achieved using the proposed method. It is observed that about 90–99% of improvement in passband error can be achieved with 100% reduction in maximum passband ripple. However, slight reduction in stopband attenuation ( A s ), in some cases, results within the permissible limit. The designed filters using this method are also stable toward finite word length effect.

中文翻译：

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使用分数微分约束和混合粒子群优化设计无限脉冲响应滤波器

在本文中，提出了一种使用分数阶导数约束 (FDC) 设计具有近线性相位响应的数字无限脉冲响应滤波器的新方法。设计问题被构造为滤波器的期望相位响应和设计相位响应之间的相位优化问题。为了实现高精度的通带 ( pb ) 响应，使用 FDC 将相位响应更精确地拟合到所需的响应，因此设计问题变成了由通带误差 ( ep ) 和阻带误差 ( ep ) 之和构成的多模态误差面 ( es）。FDC 的最优值是通过使用改进的基于群的优化技术最小化总误差 (er 0 ) 来实现的，该算法是将人工蜂群算法的侦察蜂机制与粒子群优化结合起来制定的，称为混合粒子群优化。仿真结果表明，使用所提出的方法实现了通带响应的改善和更好的过渡宽度。据观察，通过将最大通带纹波降低 100%，可以实现约 90-99% 的通带误差改善。然而，在某些情况下，阻带衰减 (A s ) 的轻微降低会在允许的范围内。使用这种方法设计的滤波器对有限字长效应也很稳定。据观察，通过将最大通带纹波降低 100%，可以实现约 90-99% 的通带误差改善。然而，在某些情况下，阻带衰减 (A s ) 的轻微降低会在允许的范围内。使用这种方法设计的滤波器对有限字长效应也很稳定。据观察，通过将最大通带纹波降低 100%，可以实现约 90-99% 的通带误差改善。然而，在某些情况下，阻带衰减 (A s ) 的轻微降低会在允许的范围内。使用这种方法设计的滤波器对有限字长效应也很稳定。