i have a problem in ofdm modulation .... there is a stream of bits that is converted from serial to parallel and is applied to an IFFT block. based on the definition of IFFT the output should be an complex valued number. how does it represent the real and imaginary parts in the digital domain( bits 0,1) ?


2 Answers 2


You are correct that the output of the IFFT will normally have both a real and imaginary component. That is fine and normal. When the signal is modulated from baseband to the carrier frequency the real part is typically modulated by a sine wave and the imaginary part by a cosine (or vice versa). This allows both parts to coexist without interfering with each other, since sines and cosines have zero cross-correlation.

Regarding how the numbers are represented digitally, they are represented the exact same way that real numbers are represented. The only difference is that there is an extra set of numbers for the imaginary part of the signal.


Your question is somewhat ambiguous but i'll try to answer it according to my understanding of it.
You have an OFDM system, a serial input say s(n). Your block diagram will look like this.
The signal is converted from serial to parallel. The number of parallel channels depend on N point IFFT block. ie. an 8 pt IFFT will have 8 parallel channels & hence the input will be represented in 8 PSK constellation. As seen from the diagram, IFFT separates real & imaginary parts.
If your question is how these 2 signals are represented in digital domain then the answer is since you used 8 PSK constellation to represent them before IFFT, they are represented as 8 PSK only. Both Real & Imaginary parts.
Real & Imaginary parts are just numbers when they are separated. It is when they are combined that they have magnitude & phase information.
These are then converted to Analog signals(continuous time) & modulated using cos & sin(orthogonal carriers).
Then they are added to form s(t). This signal s(t) is transmitted.
If your question is how this signal is represented in digital then the answer is it can either be PCM-ed or PSK-ed depending on transmitting media. It is represented as a bunch of 1 & 0 but order depends on coding

  • $\begingroup$ The constellation has nothing to do with the IFFT length. It can even be different for each channel. Your getting to the right point (Real & Imaginary parts are just numbers) but I think your answer can be improved by pointing out the relevant information. $\endgroup$
    – Deve
    Jul 12, 2013 at 6:40
  • $\begingroup$ Another catch is that each IFFT chunk or block is transmitted once only. That is, each IFFT sequence is pushed out only one time, not in a periodic fashion. So if each IFFT block (sequence) is not purposely made to be periodic, then we don't have an OFDM signal at all. That is, the IFFT signals aren't even physical OFDM signals. You need periodicity (at least some) in the time domain to even begin to generate sub-carriers. $\endgroup$
    – Kenny
    Dec 14, 2023 at 2:08

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