The present invention is directed to systems and methods which provide an improved compensation filter, as may be used with respect to a decimator, optimally designed using a convex optimization approach. Compensation filters of embodiments of the invention may, for example, be used with respect to a CIC decimator. In accordance with embodiments of the invention, compensation filters are designed with minimum order to approximate target frequency response in the target frequency bands. Additionally or alternatively, compensation filters of embodiments are optimally designed for passband drop and stopband attenuation improvement, such as to satisfy the specified peak ripple in the passband and/or to satisfy the specified peak errors over a set of target sub-bands in the stopband.