Is it permissible to broadcast Islamic songs during the funerals of martyrs?

The Sunnah (definition) for someone following a funeral procession is to remain silent. One should not raise their voice with recitation, remembrance (dhikr), or chanting. This is based on what Al-Bayhaqi and Abu Nu'aym narrated from Qays ibn 'Abbad: "The Companions of the Prophet, peace and blessings be upon him, disliked raising the voice at funerals."

Moreover, doing so resembles the Christians who raise their voices with their gospels and remembrances.

Imam An-Nawawi said in Al-Adhkar: "The correct and chosen opinion, and that which the pious predecessors (may Allah be pleased with them) followed, is silence while walking with the funeral procession. No voice should be raised with recitation, remembrance, or anything else." The wisdom behind this is that it brings more tranquility to the heart and allows for greater concentration. As for what the ignorant do, such as reciting over the deceased with excessive stretching of words and distorting their proper places, this is forbidden by scholarly consensus.