No. Analog or other nondigital performance of a sound recording does not infringe the copyright in the sound recording. Unlike other kinds of works, the “public performance” right in sound recordings only extends to digital transmissions of a performance of the recording. (This is also known as “livestreaming” the recording.) An analog radio broadcast of a sound recording does not infringe the copyright in the sound recording.
Having said that, it is important to distinguish between the copyright in the sound recording and the copyright(s) in the work performed on a sound recording. A sound recording of the performance of a song, for example, implicates at least two copyrights: one in the sound recording and one in the musical composition that is performed in the recording. In some cases, there might also be a separate copyright in lyrics. Even if a public performance of a sound recording does not violate the rights of the owner of the sound recording copyright, it might violate a music composer’s and/or lyricist’s copyright.