The Federal Communications Commission, in a unanimous vote yesterday, authorized FM radio stations to transmit data, paging signals and other specially targeted signals on a 24-hour basis.

The action marked the second time in two weeks that the FCC has approved a measure expanding the information power of the nation's telecommunications industry.

In a 5-to-2 vote March 31, the FCC authorized broadcasters to transmit written and graphic data to television viewers across the country, with minimum federal regulation.

Both actions are expected to increase competition among commercial and public broadcasters and other organizations anxious to take advantage of the new technologies.

The FCC's vote yesterday overturns previous rules restricting FM radio station use of subchannels to "services of a broadcast nature," such as providing "background music" in supermarkets, department stores and shopping malls.

A subchannel is an inaudible ultrasonic signal that can be added to the regular program signal of an FM radio station, or to the audio signals of televison stations. The signal can be picked up through decoding devices attached to radio and television sets, or through special receivers, such as paging devices capable of displaying text data.

The ultrasonic signal can be used to translate voice, music, text and data. It also can be used to send control signals, such as those used to operate traffic lights and to operate teletype machines. Under the measure approved yesterday, FM radio stations will be allowed to provide all of those services.

The commission's previous rules governing subchannel use "artificially limited the use of subchannels and, thereby, caused underutilization of this valuable resource . . . The new rules will permit the use of FM subchannels for any legitimate communications purpose, whether or not broadcast-related," the FCC said in an agency statement.

In an attempt to encourage wider subchannel use, the FCC said it would reduce the paperwork involved in applying for ultrasonic-signal rights, and would free stations from the need of keeping subchannel program logs.

In a related development yesterday, the FCC also authorized the establishment of long-distance paging operations, which would allow paging messages--such as beeper tones--to be sent across the nation. The commission made available three nationwide frequencies, to be allocated either by comparative hearings--in which competing interests would be allowed to argue for frequency rights--or by lottery.

Companies seeking a national paging network would have to demonstrate their initial ability to serve at least 15 metropolitan areas, and to expand that service nationally after two years' operation.

At the beginning of yesterday's FCC meeting, Commissioner Anne P. Jones, a Republican who has served on the commission since 1979, announced that she will resign by May 31.

Jones, one of two women on the seven-member commission, said she was leaving for unspecified opportunities in the private sector.

Her resignation would come two months before the commission is scheduled to be reduced permanently to five members in a cost-cutting move mandated by the Reagan administration.