Hello, In an OFDM system, by using N subcarriers we get one OFDM symbol. But before that the data is first mapped into frequency domain by the constellation mapper and we get N-parallel streams as an input to the IFFT process. The IFFT takes these N-parallel streams and produces N-parallel subcarriers in time domain, all these subcarriers are in digital form and has different frequencies. Let’s say each of these subcarriers are represented by X(n). The first subcarrier is x1(n) The second subcarrier is x2(n) … My question is that: Do we have N-samples in each period of one digital subcarrier? For example; the x1(n) has 1 period during the OFDM symbol duration and hence the subcarrier duration, and since it has only one period then it has only N samples during the symbol duration. And say x2(n) has 5 period during the OFDM symbol, then this means x2(n) has again N-samples in each period and hence 5N samples in total during the one OFDM symbol. Is this correct? I would appreciate if you could help on visualizing this? Thanks in advance! --------------------------------------- Posted through http://www.DSPRelated.com
How many samples are there in one period of a subcarrier which is produced after IFFT in OFDM systems?
Started by ●October 20, 2015
Reply by ●October 20, 20152015-10-20
On Tue, 20 Oct 2015 02:31:44 -0500, "runinrainy" <100271@DSPRelated> wrote:>Hello, > >In an OFDM system, by using N subcarriers we get one OFDM symbol. But >before that the data is first mapped into frequency domain by the >constellation mapper and we get N-parallel streams as an input to the IFFT >process. >The IFFT takes these N-parallel streams and produces N-parallel >subcarriers in time domain, all these subcarriers are in digital form and >has different frequencies. Let’s say each of these subcarriers are >represented by X(n). >The first subcarrier is x1(n) >The second subcarrier is x2(n) >… > >My question is that: > >Do we have N-samples in each period of one digital subcarrier? For >example; the x1(n) has 1 period during the OFDM symbol duration and hence >the subcarrier duration, and since it has only one period then it has only >N samples during the symbol duration. And say x2(n) has 5 period during >the OFDM symbol, then this means x2(n) has again N-samples in each period >and hence 5N samples in total during the one OFDM symbol. >Is this correct? >I would appreciate if you could help on visualizing this? > >Thanks in advance! >The bin indices of an FFT indicate how many cycles/N are associated with that bin. Bin zero (0) is DC (or zero cycles/N), bin 1 has one cycle, bin 2 has 2, etc., up to N/2 where the negative frequencies start. This is all considered at baseband, with the center carrier at 0Hz. Since the FFT is N samples long, all of the vectors associated with that FFT process are N samples long. So, no, a subcarrier with 5 cycles over the OFDM symbol isn't 5*N samples long, it is N samples long and goes in bin 5 of the FFT. This discussion ignores the cyclic prefix, which isn't processed by the FFT, anyway. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by ●October 20, 20152015-10-20
Eric Jacobsen <eric.jacobsen@ieee.org> wrote: (snip of question)> The bin indices of an FFT indicate how many cycles/N are associated > with that bin. Bin zero (0) is DC (or zero cycles/N), bin 1 has one > cycle, bin 2 has 2, etc., up to N/2 where the negative frequencies > start. This is all considered at baseband, with the center carrier > at 0Hz.Well, it is periodic, so you can consider the bins from 0/N up to (N-1)/N, or, as you note and is somewhat usual, from 0/N up to (N/2)/N, and then -(N-1)/2/N up to -1/N (or any other set of N sequential frequencies). My favorite example of negative frequencies comes from aliasing in visual (movie or video) images of rotating systems, such as wagon wheels (in westerns) or car wheels (in car commercials). Frequencies map into rotation rates, and the low negative frequencies to wheels turning backwards. Our visual system maps the samples to the lowest absolute value rotation rate consistent with the images.> Since the FFT is N samples long, all of the vectors associated > with that FFT process are N samples long.-- glen
Reply by ●October 20, 20152015-10-20
On Tue, 20 Oct 2015 22:17:14 +0000 (UTC), glen herrmannsfeldt <gah@ugcs.caltech.edu> wrote:>Eric Jacobsen <eric.jacobsen@ieee.org> wrote: > >(snip of question) > >> The bin indices of an FFT indicate how many cycles/N are associated >> with that bin. Bin zero (0) is DC (or zero cycles/N), bin 1 has one >> cycle, bin 2 has 2, etc., up to N/2 where the negative frequencies >> start. This is all considered at baseband, with the center carrier >> at 0Hz. > >Well, it is periodic, so you can consider the bins from 0/N >up to (N-1)/N, or, as you note and is somewhat usual, >from 0/N up to (N/2)/N, and then -(N-1)/2/N up to -1/N >(or any other set of N sequential frequencies).It's not unusual at all. When indexed this way the index has a nice correlation to cycles/aperture. If the index is two's complement, it is consistent even up through the negative frequencies, and still works as a typical array index from 0-(N-1). Many fft routines work this way, where bin 0 is index 0, corresponding to 0 cycles/aperture. Putting the DC (0 Hz) term at the beginning or middle is often referred to as an "unfolded" or "folded" output. "Folding" is what the fftshift() function in Matlab/Octave does, although many call it something else. It shifts the frequencies, it swaps the two transform halves, or it inverts the address MSB (e.g., if you do it in hardware). Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by ●October 26, 20152015-10-26
>On Tue, 20 Oct 2015 22:17:14 +0000 (UTC), glen herrmannsfeldt ><gah@ugcs.caltech.edu> wrote: > >>Eric Jacobsen <eric.jacobsen@ieee.org> wrote: >> >>(snip of question) >> >>> The bin indices of an FFT indicate how many cycles/N are associated >>> with that bin. Bin zero (0) is DC (or zero cycles/N), bin 1 has one >>> cycle, bin 2 has 2, etc., up to N/2 where the negative frequencies >>> start. This is all considered at baseband, with the center carrier >>> at 0Hz. >> >>Well, it is periodic, so you can consider the bins from 0/N >>up to (N-1)/N, or, as you note and is somewhat usual, >>from 0/N up to (N/2)/N, and then -(N-1)/2/N up to -1/N >>(or any other set of N sequential frequencies). > >It's not unusual at all. When indexed this way the index has a nice >correlation to cycles/aperture. If the index is two's complement, it >is consistent even up through the negative frequencies, and still >works as a typical array index from 0-(N-1). Many fft routines work >this way, where bin 0 is index 0, corresponding to 0 cycles/aperture. > >Putting the DC (0 Hz) term at the beginning or middle is often >referred to as an "unfolded" or "folded" output. "Folding" is what >the fftshift() function in Matlab/Octave does, although many call it >something else. It shifts the frequencies, it swaps the two >transform halves, or it inverts the address MSB (e.g., if you do it in >hardware). > > >Eric Jacobsen >Anchor Hill Communications >http://www.anchorhill.comMany thanks Eric, Glen for the answers and detailed explanations. I've got the answer to my question and understand the duration of one sub carrier. It has N samples ( N is the IFFT input) regardless of its frequency. but I would appreciate the discussion ongoing in case you would like to add more explanation here. Thanks again! --------------------------------------- Posted through http://www.DSPRelated.com
