FFT & IFFT in OFDM

[Antonio_Magma]

fft and ifft

Elementary questions, hope u guys dun mind..

I often see 1024 point or 1024 bin length FFT & IFFT for OFDM. At first i thought 1024 represents the number of subcarriers for OFDM, but i later realized it wasn't. So what does 1024 represents?

And what is the relationship between the point number/bin lenght and the number of subcarriers?

 

[checkmate]

ofdm fft

1024 point FFT means that a window of 1024 signal samples are taken and use to compute the FFT. This would result in a spectrum of 1024 discrete frequency bins. The same would apply vice versa for IFFT. This is all on FFT/IFFT and has nothing to do with OFDM in general.

In OFDM, you carry out IFFT of the data symbol-modulated spectrum on the transmitter end, giving you a N-point time multi-carrier signal which you send out. This would imply that there are N frequency bins in the spectrum. If the subcarrier spacing is Δf, then the subcarriers are 0, Δf, 2Δf ... (N-1)Δf.

 

[Antonio_Magma]

inverse fft for ofdm

1024 point FFT means that a window of 1024 signal samples are taken and use to compute the FFT. This would result in a spectrum of 1024 discrete frequency bins. The same would apply vice versa for IFFT.

Lets c if i got this right, in simple terms, the 1024 can be considered as an equivalent of 1024 baskets. So when ppl talk about 1024 FFT/IFFT it basically means that the FFT/IFFT process will begin when they have collected 1024 'baskets'. Correct?

In OFDM, you carry out IFFT of the data symbol-modulated spectrum on the transmitter end, giving you a N-point time multi-carrier signal which you send out. This would imply that there are N frequency bins in the spectrum. If the subcarrier spacing is Δf, then the subcarriers are 0, Δf, 2Δf ... (N-1)Δf.

So lets say if i have a 512 point multi-carrier signal, it means that i want to transmit with 512 carriers?

So when it comes to subcarrier spacing or guard interval, please correct me if i'm wrong:
1024 'baskets'
512 carriers 'eggs'
So 1 'basket' would carry 1 'carrier'
And to prevent the 'baskets from crashing' since there is another 512 baskets to spare, i place a basket in between every basket which holds the carrier (eggs), and that would be the guard interval.

Did i got it right?[/quote]

Added after 7 minutes:

In the OFDM case they do not use all of the possible subcarrier frequencies because of some benefit that derives from this.

So it means that with 1024 FFT/IFFT, although i have 1024 'spaces' to place my subcarriers, but to prevent ISI, ICI etc, i might want to place a couple 'empty' spaces between my subcarriers. Correct?

Added after 49 seconds:

Is my analogy accurate?

 

[checkmate]

fft ifft

Let me try to give you a more detailed example.

First, on FFT/IFFT. Let's say you have a signal, and you sample it N times at a certain sampling frequency fs. So you'll have the discretized signal x for n=0 to N-1.
If you do a FFT on this signal, you will get a discrete spectrum f(k) for k=0 to N-1. Now, f(k) is related to the real frequency by f=(k/N)*fs, so the interval between each frequency bin is fs, and there are N frequency bins in total.

Now, we move on to OFDM. You have to decide what subcarrier frequency interval you want. Let's say you decide on M*fs. So the subcarriers f(k) where k=M*c for c=0 to (N/M)-1. Now, there are N/M subcarriers in total.

For practical reasons, we space them out evenly over the discrete spectrum. Also, you have to understand that the sampling frequency fs must be equal or higher than the frequency of the input stream, otherwise you would have to buffer the input stream to prevent overflow.

Now, you take the N/M samples of the input stream and set it as the magnitude of each subcarrier. You then do the IFFT on this spectrum and you get your transmitted signal. Since this spectrum has N frequency bins (of which only N/M are bins occupied by subcarriers), you will get an N-point signal.

Added after 10 minutes:

Lastly, just a note on terminology. We call each discrete time signal a sample, and each discrete frequncy spectrum a frequency bin. We call carriers carriers, or in the case of OFDM, subcarriers.

Baskets and eggs are better used for picnics and breakfast.

 

[Antonio_Magma]

ofdm subcarriers and ifft

Sorry for my poor attempt of 'explaining' with baskets and eggs.

I guess i must have gotten hungry after all the studying.

Added after 12 minutes:

Can you give me any good sites which can help me strengthen my fundamentals on OFDM? Not in the aspects of orthogonality etc...but on sampling, intervals.....more on designing and application ...

Appreciate it checkmate...

Added after 13 minutes:

Now, you take the N/M samples of the input stream and set it as the magnitude of each subcarrier. You then do the IFFT on this spectrum and you get your transmitted signal. Since this spectrum has N frequency bins (of which only N/M are bins occupied by subcarriers), you will get an N-point signal.

So in other words, a N-point FFT/IFFT means that it processes a spectrum of frequencies that is derived from a signal which has N samples. Correct?

 

[checkmate]

ofdm ifft

Sorry for my poor attempt of 'explaining' with baskets and eggs.

I guess i must have gotten hungry after all the studying.

No problem. Have an egg, as long as you get the concepts right.

Added after 12 minutes:

Can you give me any good sites which can help me strengthen my fundamentals on OFDM? Not in the aspects of orthogonality etc...but on sampling, intervals.....more on designing and application ...

I don't have any good sites on OFDM on-hand right now, but there are countless hits on google. Also, concepts on orthogonality, sampling and intervals are basic signal theory. Application of OFDM include ADSL and 802.11 technologies. As for design, the main bulk of design falls on the implementation of an efficient FFT/IFFT unit.

Added after 13 minutes:

Now, you take the N/M samples of the input stream and set it as the magnitude of each subcarrier. You then do the IFFT on this spectrum and you get your transmitted signal. Since this spectrum has N frequency bins (of which only N/M are bins occupied by subcarriers), you will get an N-point signal.

So in other words, a N-point FFT/IFFT means that it processes a spectrum of frequencies that is derived from a signal which has N samples. Correct?

FFT : Gives the N-bin spectrum of a N-sample signal.
IFFT : Gives the N-sample signal of a N-bin spectrum.

 

[Antonio_Magma]

ofdm ifft sampling need help

Thx checkmate, for your patience. Actually my project involves implementing OFDM for power line communications. I'm currently doing some Matlab simulations, so it involves understanding thoroughly the concept and operation of OFDM n FFT/IFFT to construct the algorithm

 

[bleach]

ofdm using ifft theory

we are doing the same project for OFDM...
but i'm poor in OFDM and matlab simulations...can't help much....

 

[Antonio_Magma]

ifft for ofdm

bleach..maybe we can share our experiences n knowledge to help each other...

 

[Megalofiya]

why we take ifft in ofdm

If you are intrested I can email you some ebooks

 

[rajsrikanth]

relationship between fft and ifft

1024 is nothing but the window size that we select. ie., 1024 point fft calculation

 

[varunknp]

Re: fft and ifft

input to ofdm system , please clear what is sub carrier is it refers to a frequency band or single frequency

I often see 1024 point or 1024 bin length FFT & IFFT for OFDM. At first i thought 1024 represents the number of subcarriers for OFDM, but i later realized it wasn't. So what does 1024 represents?

And what is the relationship between the point number/bin lenght and the number of subcarriers?[/quote]