The word שִׁדּוּר (shee-DOOR) means a broadcast, like the kind done over TV or the radio. A שידור חָי (shee-DOOR KHAH-ee) is a live broadcast.
לְשַׁדֵּר (le-shah-DEHR) means to broadcast. It follows the same grammatical structure as לְדַבֵּר (le-dah-BEHR) – notice that the two words have the same vowel points. And just like שִׁדּוּר is the noun that comes from the verb לשדר, the noun דִּבּוּר (dee-BOOR) comes from the verb לדבר. You can get a more intuitive sense of such grammatical structures by taking a class with Ulpan La-Inyan.
Aside from actually broadcasting on the air, one can also “broadcast” a message to someone by giving out “vibes.” The Hebrew word לשדר is used for such actions as well.
Why do I mention all this?
Because today (Monday) אֲנִי מְשַׁדֵּר מוּסִיקָה יִשְׂרָאֵלִית (ah-NEE meh-shah-DEHR MOO-zee-kah yees-rah-eh-LEET) – I’m broadcasting Israeli music (and giving linguistic and thematic highlights) on RustyMike Radio… at 3pm Israel time.