1. A state estimating apparatus comprising: a spectrum calculating unit which calculates a power spectrum for each of a plurality of frequencies on a frame-by-frame basis, each frame having a predetermined time length, from a voice signal containing voice of a first speaker and voice of a second speaker transmitted over a telephone line; a band power calculating unit which calculates power of a non-transmission band on a frame-by-frame basis, based on the power spectra of frequencies contained in the non-transmission band among the plurality of frequencies, the non-transmission band being a frequency band over which the voice signal is attenuated by a telephone band filter during transmission over the telephone line; a transmitted-voice judging unit which determines that any frame whose power in the non-transmission band is greater than a threshold value indicating the presence of voice carries the voice of the first speaker; and a state judging unit which judges whether the state of mind of the first speaker is normal or abnormal, based on the frame judged to carry the voice of the first speaker.