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I have cross across an OFDM modulator that says that

A frequency domain sequence is passed into a 64 point IFFT. A cyclis prefix is added (0.8 $\mu$sec) and creates as a result a 4 $\mu$sec time domain sequence (OFDM symbol). I am wondering The input of IFFT is discrete the output is also discrete of length 64. Then what do the authors mean by 3.2 $\mu$sec OFDM symbol? Is it a continuous time domain signal?

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Your question is a little confusing, but I'll give it a shot.

The 64 sample sequence output from the IFFT is a discreet sampled time domain sequence of complex values. (A signal at complex base band) The 3.2usec length comes from the sample rate (Fs) of the system.

In this case it sounds like Fs is 20MHz. That Fs comes from the fact that there are 64 sub-carriers (FFT = 64) therefore the frequency spacing to maintain orthogonality between sub-carriers is 1/Tu = 1/3.2usec = 312.5KHz. Tu is the "used time", which in this case is that 3.2usec. The total bandwidth is then 64*(sub carrier frequency spacing) = 64*312.5kHz = 20MHz. Since the signal is complex Fs = BW.

Fs = BW = NFFT / Tu = 64 / 3.2usec = 20MHz

In my experience an OFDM symbol (or FFT symbol) refers to the data without the cyclic prefix added with its length equal to the FFT size. I call the OFDM symbol plus the cyclic prefix and OFDM frame. Other people may have a different definitions. It looks like this author uses the same definition as me not including the 0.8usec cyclic prefix in what they call an OFDM symbol. That 0.8usec is also called the guard time and acts like a spacing in between successive OFDM symbols offering multipath protection.

Not sure if that will help or not.

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