A profile-reduced or size-reduced filter is to be provided. The filter includes: a metallic casing, an opening provided in the metallic casing, a metallic cover configured to cover the opening, and a TM mode dielectric resonator disposed in the opening and configured to electrically contact a bottom surface of the metallic casing, and the metallic cover. The TM mode dielectric resonator has a height lower than a lowest possible height at which a ¼ wavelength semi-coaxial resonator is disposed in the opening.