# OFDM Modulation: what's the output of the FFT?

I'm trying to understand how OFDM is used in technologies like Wi-Fi. On the Wikipedia page, an idealized transmitter is presented with this schema:

Data is converted from serial to parallel, mapped to some complex symbols using constellation mapping, then, using the inverse fast fourier transform, is converted to what seems one complex number with a real and imaginary part, which is then converted to some continuous signal using DAC.

On some other diagrams, the output of the IFFT is the same size as the input, and all of the outputs are multiplied by some (orthogonal) carriers before being transmitted, e.g. on this diagram (in French, but it should be clear what is what):

I'm having trouble understanding how these two diagrams relate with each other: are they different systems ?

As the FFT takes as an input a sampled continuous signal (so, let's say $$N$$ complex numbers), the IFFT should output $$N$$ complex numbers, but this does not appear on the Wikipedia diagram. Am I missing something?

## 1 Answer

not missing anything. You're right, if you have an N-point (I)FFT, the input is an N-element vector, and the output is an N-element vector.

The wikipedia diagram just "hides" the fact that these N output elements are "emitted" one after the other from the IFFT block.

• Thanks. So, just to be sure, each of these N outputs are then multiplied by the associated subcarriers, in "parallel", and then summed before transmission as a single wave, right? (if we avoid talking about Cyclic Prefix) – R. G. Aug 3 '20 at 15:37
• No. These outputs are the baseband time domain samples to be transmitted. Nothing happens to them anymore. – Marcus Müller Aug 3 '20 at 15:46