"coming" is a participle, and "coming from the radio" is adjectival modifying "melody". "the melody coming from the radio" is a noun phrase. This is a standard pattern in English: the man sitting at the bar the train running along the tracks the elephant wearing my reading glasses I am not convinced that the use of "all" is correct in that sentence, but this does not affect your question.
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GPYI am not convinced that the use of "all" is correct in that sentence,I am pretty sure it is not.