# OFDM

Started by May 6, 2007
```Hi, i'm an undergraduate student doing some project on Stochastic Processes
and
i have a few questions on OFDM.
There are few things that i don't quite understand and they are mainly in
Digital Signal
Processing domain (that is not my field of expertise).
I'm writing code in MATLAB for transmitting data using sound and use OFDM
modulation.

Mathematically the transmitted multicarrier signal is

x(k)=sum(X(i)*exp(j2pi*fi*kT)
(i=0....N-1)

The carrier frequencies are linearily spaced so that fi=fc+i*df
The total bandwith N*df is constrained to equal the sampling
frequency 1/T and then the transmitted signal becomes

x(k)=sum(X(i)*exp(j2pi*k*(fc+i*df)*T)

x(k)=exp(j2pi*k*fc*T)*sum(X(i)*exp(j2pi/N*ik)

Now the summation can be performed by taking an N-point IFFT.
Thus, multicarrier modulation can be performed by modulating
result of IFFT by a single carrier frequency.

Now a few questions:

- what does exactly mean that total bandwith is constrained to equal the
sampling frequency?
Let's say i want to use bandwith from 10kHz to 15kHz. Is the sampling
frequency then 5kHz?

-if the above is true how can then a 10kHz carrier signal be sampled in
MATLAB if sampling
frequency is 5kHz?

-IFFT is giving complex numbers as result. Is it better to modulate cosine
carrier with real part and
sine with imaginary or to expand IFFT input to get real numbers as output.

When i started researching this it seemed quite simple but now when i need
to make it work
it si not so.

```