  We propose and theoretically and numerically investigate narrowband
integrated filters consisting of identical resonant dielectric ridges on the
surface of a single-mode dielectric slab waveguide. The proposed composite
structures operate near a bound state in the continuum (BIC) and enable
spectral filtering of transverse-electric-polarized guided modes propagating in
the waveguide. We demonstrate that by proper choice of the distances between
the ridges, flat-top reflectance profiles with steep slopes and virtually no
sidelobes can be obtained using just a few ridges. In particular, the structure
consisting of two ridges can optically implement the second-order Butterworth
filter, whereas at a larger number of ridges, excellent approximations to
higher-order Butterworth filters can be achieved. Owing to the BIC supported by
the ridges constituting the composite structure, the flat-top reflection band
can be made arbitrarily narrow without increasing the structure size. In
addition to the filtering properties, the investigated structures support
another type of BICs - Fabry-P\'erot BICs arising when the distances between
the adjacent ridges meet the Fabry-P\'erot resonance condition. In the vicinity
of the Fabry-P\'erot BICs, an effect similar to the electromagnetically induced
transparency is observed, namely, sharp transmittance peaks against the
background of a wide transmittance dip.
