Spectral filters are important building blocks for many applications in integrated photonics, including datacom and telecom, optical signal processing and astrophotonics. Sidewall-corrugated waveguide grating is typically the preferred option to implement spectral filters in integrated photonic devices. However, in the high-index contrast silicon-on-insulator (SOI) platform, designs with corrugation sizes of only a few tens of nanometers are often required, which hinders their fabrication. In this work, we propose a novel geometry to design complex Bragg filters with an arbitrary spectral response in silicon waveguides with laterally coupled Bragg loading segments. The waveguide core is designed to operate with a delocalized mode field, which helps reduce sensitivity to fabrication errors and increase accuracy on synthesized coupling coefficients and the corresponding spectral shape control. We present an efficient design strategy, based on the layer-peeling and layer-adding algorithms, that allows to readily synthesize an arbitrary target spectrum for our cladding-modulated Bragg gratings. The proposed filter concept and design methodology are validated by designing and experimentally demonstrating a complex spectral filter in an SOI platform, with 20 non-uniformly spaced spectral notches with a 3-dB linewidth as small as 210 pm.