Is the RasPi capable of DVB-T?
From my experience in pro-TV, the signal path goes something like this. Pictures @ 270Mb/s & AES sound @ 32/44.1/48/96 Kb/s goes to an encoder and comes out MPEG as a transprt stream at anywhere up to 10Mb/s. This data goes into a mux with others, to form a bouquet for transmission (if stat-muxing is in use, data goes back to the encoder to raise / lower the encoding compression according to available data-rate). This is sent onwards, in a terrestrial system, to where I lose focus, but which seems to have similarities with FFT. Then to the modulator / transmitter.
What we have with RasPi is a picture source (camera module) and sound source (USB mic), or what-ever we can force into it through USB. We also have some of the encoder - HDMI seems to carry some sort of data stream, albeit uncompressed, though RasPi seems not quite quick enough to convert it to the required MPEG stream. Maybe an off-board MPEG encoder exists. Or the data-stream from a DVD would work if that's your source.
But what I would like RasPi to do is the FFT-like bit. In comes MPEG, out goes ready-to-go DVB-T, put it into a UHF modulator onto a cable into the aerial socket on your TV.