We propose a concept for radiometry in the millimeter, the submillimeter, and the far-IR spectral regions, the frequency selective bolometer (FSB). This system uses a bolometer as a coupled element of a tuned quasi-optical interference filter in which the absorption, the transmission, and the reflection characteristics of the filter depend on the frequency in a controlled manner. Several FSB's can be cascaded within a straight light pipe to produce a high-efficiency, compact, multiband radiometer. A prototype design is presented together with its anticipated performance based on a one-dimensional transmission-line model. Instruments based on FSB technology should have several advantages over current multiband bolometric radiometers including smaller and more compact cryogenic optics, reduced demands on cryostat size and weight, high coupling efficiency, minimum constraints on the geometry in the focal plane. An FSB system can be configured as a multiband, close-packed focal-plane array, permitting efficient use of the throughput of a telescope.