1. A signal receiving apparatus comprising: a first setting module configured to set a rising or falling of an arbitrary high pulse in a preamble interval of a pulse-position modulation signal as a starting point; a calculator configured to calculate a sampling period based on intervals between a plurality of high pulses in the preamble interval; a detector configured to set a multiple of the sampling period from the starting point as reference points in a detection interval and to detect positions where the plurality of high pulses are generated from the reference points; a generator configured to generate a histogram for the positions where the plurality of high pulses are generated; a determination module configured to determine positions obtained by adding a value of a peak in the histogram to the reference points as sampling points in a to-be-reproduced signal interval of the pulse-position modulation signal; and a reproduction module configured to reproduce the to-be-reproduced signal interval based on the sampling points.