Fiber-optic filters can be used for processing wide-band radio-frequency, microwave, and millimetric signals directly in the optical domain avoiding costly electrooptic and optoelectronic conversions. Because these filters sum signals on an intensity basis, they are bound to be positive and, hence, heavily restricted in their achievable performance. Nevertheless, such filters are the only choice because positivity is a consequence of the underlying physical mechanism. In this paper, the authors present a new design methodology to realize an arbitrary filter as a difference of two positive filters, thus overcoming any performance limitation.