A new photonic signal processor topology that simultaneously achieves both a high-Q and a high skirt selectivity and stopband attenuation filter response is presented. It is based on a novel dual-cavity bandpass optical structure in which two pairs of active fiber Bragg grating cavities are used with an optical gain offset to control the poles and stopband attenuation characteristics of the filter. This concept enables a large improvement in the filter stopband attenuation, rejection bandwidth, and skirt selectivity to be realized. Measured results demonstrate both a narrow bandpass bandwidth of 0.4% of center frequency and a skirt selectivity factor of 16.6 for 40 dB rejection, which corresponds to a 6.5-fold improvement in comparison to conventional single cavity high-Q structures. To our knowledge, this is the best skirt selectivity reported for a photonic bandpass filter to date. The new photonic filter structure has been experimentally verified and excellent agreement between measured and predicted responses is shown.