explain zero padding in OFDM

zero padding ofdm

wy implement the zero padding at the ends not in the center
see below, please help





thanks in advance

ofdm zero padding

any one can help please?

zero padding in dft

because we want to make it look cyclic. remeber cyclic convolution? the idea is that using this we maintain the orthogonality of our carriers using the DFT later on

info=zeros(fs,1);

Thank you communication_engineer but i know that, my quistion is why not centering the data why he made the padding on the center not the data at the center?

ofdm zero pad

any replay please!!!!

Added after 2 minutes:

i will donate 20 points for the best explanation

why zero padding in digital communication

hi Aya2002,
Let me tell explain you a simple eg ( using dft symmetry property)
where to maintain DFT symetricity they maintain zero padding at the center rather at the end. this is usaually done for making the spectrum to be symmetric .
for real even seq you expect imaginary spectrum X[k] to be zero.
for real odd seq you expect real X[k] to be zero.

eg.
let your seq be x[n] = { 1,1,1,1,1,1}
by padding zero at the end of the seq,you are changing the transform you are computing. (i.e, you are breaking the DFT symmetry(even or odd seq for periodic seq ). of course With N=6, FFT is perfectly fine on 6 points
But, if you really wanted to pad, you woud have to pad in an "even"
fashion. In this case, you would pad to
[1 1 1 0.5 0 0.5 1 1]

i will explain you with another example:
For example,
the array [1 2 3 8 3 2] is a real-even array, where "1" is the zero-
frequency (DC) element, "8" is the Nyquist element, and "2 3" and "3
2" are the symmetric positive and negative frequency amplitudes,
respectively. To pad it symmetrically to length 8 (although, as I
said above, you really don't need to), you would do [1 2 3 4 0 4 3 2],
where the Nyquist frequency "8" has been split equally between
positive and negative frequencies.

Your data are (almost) symmetric around N/2, not 0.
This would cause a linear phase shift of the spectrum
coefficinets. So to get this to work, account for the N/2 lag in the spectrum.


In short, Whenever U need symmetrical spectrum for real (even or odd) sequences
U must zero pad at the center onwards ( not at the end)


If U understand this concept i will tell regarding periodic odd seq satisfying DFT symmetry.


I hope this will give you clue to some extent

Happy learning

cyclic prefix zero padding

please show me more discussion

zero padding ofdm matlab

Hi aya2002,
Usually one will think zero padding will be done at the end.

ofcourse DFT operates on periodic sequence only( even though aperiodic sequence is there i.e., by making them (aperiodic) circularly symmetric)
by taking this circular symmetric property as advantage, we reduce the DFT computation into half (saving 50% computation and storage)

so when L=i/p seq length =6; it is advisable we dont need to pad zeros. if U want to pad zeros still for better display
we pad zeros symmetrically (rather than at the end; as it changes the transform itself). if your original data is x[n]={1,2,10,5} here L=4; also this is even sequence
If U want to make the seq N=8; then padded symmetrical seq. is
x[n]= {1,2,10,2.5,0,2.5,10,2} here zero is padded at the centre, by taking advantage the dft symmetricity it is enough if we take 1 to (N/2+1) i.e., 1 to 5 (Unique sequences). (In matlab starting array element is 1 )
while remaining seq are redundant data points, whose spectum will b conjugate symmetric.

reason:
If you have a N point real valued input waveform, your samples are the
real valued inputs to the DFT or FFT, and the imaginary parts are set
to zero. e.g.: with N even, outputs 0 and N/2 will be
real and unique, and outputs 1 to N/2-1 will be conjugate symmetric
with outputs N-1 to N/2+1).

if U want to find DFT with N=16;
then the seq would be x[n]={1,2,10,2.5,0,0,0,0,0,0,0,0,0,2.5,10,2}
Here we will take data points 1 to N/2 +1 and then perform DFT. i.e., only first 9 points are considered.

one can wonder at wha point the above spectrum is symmetric.
It is symmetric with respect ot N/2(nyquist point). so to make spectrum to be symmetric around zero one has to introduce the phase lag of N/2 additionally.
then plot will look like from -N/2 to N/2.

till now i told about even seq (x[N-n]=x[n]) ; i didnt mention about odd seq.
x[N-n]= - x[n] for n= 1 to N-1
symmetric odd seq L=5; x[n]={0,2,4,-4,-2}. This element is DC component is set to zero. also there is no nyquist freq. (without zero padding)
if want to padd zero symmetrically, for even N =8;
x[n]={ 0,2,4,0,0,0,-4,-2} while intentionally making nyquist frq and dc component to be zero. here Unique data points are ceil (N+1)/2 i.e., 5 data ponts ( 1 to 5 elements in MATLAB) take first five data points and find fft of that seq. since we know the rest 3 data points exhibit conjugate symmetric. therby it reduces the computation of DFT and memory storage as well.


a word of caution :
zero padding is advisable only whenever the i/p seq length is closer to DFT N-point length.


In ofdm, i think zero padding will related to cyclic prefix(of course i dont know much about cyclic prefix in detail) so that orthogonality is maintained.


Happy learning

cyclic prefix vs zero padding

hi rramya
i understad it very much. My quistion is if i have random data with imaginary parts, why i did the zero pad before the IFFT as shwon in the following matlab code
%DVB-T 2K Transmission
%The available bandwidth is 8 MHz
%2K is intended for mobile services
clear all;
close all;
%DVB-T Parameters
Tu=224e-6; %useful OFDM symbol period
T=Tu/2048; %baseband elementary period
G=0; %choice of 1/4, 1/8, 1/16, and 1/32
delta=G*Tu; %guard band duration
Ts=delta+Tu; %total OFDM symbol period
Kmax=1705; %number of subcarriers
Kmin=0;
FS=4096; %IFFT/FFT length
q=10; %carrier period to elementary period ratio
fc=q*1/T; %carrier frequency
Rs=4*fc; %simulation period
t=0:1/Rs:Tu;
%Data generator (A)
M=Kmax+1;
rand('state',0);
a=-1+2*round(rand(M,1)).'+i*(-1+2*round(rand(M,1))).';
A=length(a);
info=zeros(FS,1);
info(1: (A/2)) = [ a(1: (A/2)).']; %Zero padding
info((FS-((A/2)-1)) :FS) = [ a(((A/2)+1) :A).'];

thanks in advance (i will donate 20 pts for best discussion).

center zero padding

it is clear only know what is the doubt you have????

fft linear phase systems zero-padding

as i know the padding will be done for the ends while he did it by siplit the data and puts the zeros in the center and also the zero padding must be done for the FFT. can you explain please ?

q=10; %carrier period to elementary period ratio

Hi Aya2002,
your data exhibit conjugate or hermitian symmetry where,
x[n]=x*[N-n] which implies real part is even symmetric ansd imaginary part is odd symmetric.

also In your notes they zero padding can be done after N/2 samples.
to maintain symmetry.
so zeros are put in the centre of the seq in your matlab code (last line)

hope it will give you clue

happy learning

zero-padding ofdm

now can i do the padding at the ends?

Added after 39 seconds:

in this same example

ofdm fft zero padding

Hi aya2002,

you can do it but you wont get symmetry of spectrum. if u padd at the end your data gets changed and your transform will get changed. so symmetricity will not be maintained. Also u can't take advantage of DFT symmetry property.
You have to do full N-point computation (tedious task, copunsumption of bw by 50% will not be done as for OFDM is tis the biggest adv )instead of ceil(N+1)/2 computation.

i am telling to the best of my knowlege. I am just a beginner yet. Pl consult some expert advice.

happy learning.

4 times zero padding

enjoy my group

conjugate symmetric ofdm

hi everybody!

what is the purpose of adding zero padding in IFFT? I read upper discussions but there is written about putting in center or edge sides.

please give me a little explanation!

Thank you in advance!

zero padded ofdm

Hi mashhur,
just see this web page: for knowing the answer.


as the ansers are many i ask you to take a look.


Happy learning

ofdm dft property subcarrier index dc

at the end i found what was a problem for me.

Many thanks to you

circular symmetric site:edaboard.com

Hello, Montader, my question is that with Cylic prefix we say that we copy the end of the signal at the begining so I'm confused how it is possible?

Would this mean we have non-causal signal with us, the signal where we put the end of the signal at the front?

do padding+ofdm

Hi communication_engineer,

we are working in the frequency domain not in the time domain so leave the casual and non casual aside.

It is possible in code time to do the copy and paste for the end to paste it in the begining of the signal.

I hope my answere is cleare.