This paper deals with a wide-band audio filtering technique for the compensation of presbycusis. Instead of restoring frequencies only up to 4~kHz (obtaining telephone--like quality), we propose to preserve frequency components up to 8~kHz, however possibly attenuated by unrecoverable hearing loss. Wide--band speech, in fact, carries important perceptual information that enhances both speech naturalness and intelligibility. A filtering technique that compensates hearing loss up to a given cut-off frequency is presented. A formal Diagnostic Rhyme Test was performed to test the intelligibility of speech processed using the proposed technique versus regular telephone--band\-width speech. The results show a significant intelligibility gain, proving the potential of wide-band hearing aids for the compensation of presbycusis.