In at least one embodiment of the disclosure, a digital signal processing device is configured to receive a TMDS signal and a hot-plug signal via a digital signal cable. A TMDS signal determination section is configured to determine whether the TMDS signal has been received. A hot-plug signal determination section is configured to determine whether the hot-plug signal has been received every t seconds when the TMDS signal has not been received. A digital signal determination section is configured to determine that a digital signal is present if the TMDS signal is received. A digital signal is determined absent if (a) the hot-plug signal has not been received n times (n being an integer equal to or greater than one), or (b) the hot-plug signal has been received m times (m being an integer equal to or greater than two and m being greater than n).