Angular Momentum (AM) has been considered as a new dimension of wireless transmissions as well as the intrinsic property of Electro-Magnetic (EM) waves. So far, AM is utilized as a discrete mode not only in the quantum states, but also in the statistical beam forming. Traditionally, the continuous value of AM is ignored and only the quantized mode number is identified. However, the recent discovery on electrons in spiral motion producing twisted radiation with AM, including Spin Angular Momentum (SAM) and Orbital Angular Momentum (OAM), proves that the continuous value of AM is available in the statistical EM wave beam. This is also revealed by the so-called fractional OAM, which is reported in optical OAM beams. Then, as the new dimension with continuous real number field, AM should turn out to be a certain spectrum, similar to the frequency spectrum usually in the wireless signal processing. In this letter, we mathematically define the AM spectrum and show the applications in the information theory analysis, which is expected to be an efficient tool for the future wireless communications with AM.