DFT without the DC component

Hello,

I was wondering if there is a method to DFT a signal without the DC
component.

For example:

I have a signal x(t) properly sampled to M samples. 
This signal is N-point DFT'ed to get X(f), where N>>M.
Upon processing, the DC sample, X(0) is lost and I am left with X(f),
f=1,...,N-1. The first sample is lost.

Is there any efficient way to construct x(t) again?
Any suggestion is greatly appreciated.

Thank you.

On May 25, 9:31 pm, "m26k9" <maduranga.liyan...@gmail.com> wrote:
> Hello,
>
> I was wondering if there is a method to DFT a signal without the DC
> component.
>
> For example:
>
> I have a signal x(t) properly sampled to M samples.
> This signal is N-point DFT'ed to get X(f), where N>>M.
> Upon processing, the DC sample, X(0) is lost and I am left with X(f),
> f=1,...,N-1. The first sample is lost.
>
> Is there any efficient way to construct x(t) again?
> Any suggestion is greatly appreciated.
>
> Thank you.

Have you tried the suggestions made when you last posted this question
here on March 5? How did they work out and if not, why not?

Would you like to reply to them now?

Dale B. Dalrymple

Thank you.
I have been trying a method to find the average of the time-domain but it
was unsuccessful. I was finally looking to find a relation to X(0) from
X(1) to X(N-1), but that needs (at the least) the summation of the
exponential series and seems unrealistic to perform. I only have X(1) to
X(N-1) to work with at this moment and anything else would need me to
change the transmitter structure and that is not acceptable.

Cheers.

m26k9 wrote:
> 
> Hello,
> 
> I was wondering if there is a method to DFT a signal without the DC
> component.
> 
> For example:
> 
> I have a signal x(t) properly sampled to M samples.
> This signal is N-point DFT'ed to get X(f), where N>>M.
> Upon processing, the DC sample, X(0) is lost and I am left with X(f),
> f=1,...,N-1. The first sample is lost.
> 
> Is there any efficient way to construct x(t) again?
> Any suggestion is greatly appreciated.


Is the question you are asking -> Is there a way to recover the DC
component from the other frequency components?
	
	The answer is no. 

-jim

Thanks Jim.
I guess thats it for that. The only option left so far is to find the
inverse DFT matrix and calculate it back. But sometimes the matrix tends to
get singular.
Anyways thanks a lot.

Cheers.

On May 26, 9:01&#4294967295;am, "m26k9" <maduranga.liyan...@gmail.com> wrote:
> Thanks Jim.
> I guess thats it for that. The only option left so far is to find the
> inverse DFT matrix and calculate it back. But sometimes the matrix tends to
> get singular.
> Anyways thanks a lot.
>
> Cheers.

Why don't you DFT x-mean(x) in the first place?

Hope this helps.

Greg

>On May 26, 9:01=A0am, "m26k9" <maduranga.liyan...@gmail.com> wrote:
>> Thanks Jim.
>> I guess thats it for that. The only option left so far is to find the
>> inverse DFT matrix and calculate it back. But sometimes the matrix
tends =
>to
>> get singular.
>> Anyways thanks a lot.
>>
>> Cheers.
>
>Why don't you DFT x-mean(x) in the first place?
>
>Hope this helps.
>
>Greg
>

Thank you Greg.
But this is a channel estimation and I actually do not have knowledge of
'x'. It's what I am trying to find. I only gave it as an example.
But what you mentioned is very interesting. I would probably need in the
future.
Thank you for the information.

m26k9 wrote:
> Thank you.
> I have been trying a method to find the average of the time-domain but it
> was unsuccessful.

Have you tried to compute the average by dividing the sum of all the 
samples by the number of them? That can fail with floating-point 
arithmetic if the number of samples is large enough to affect the 
exponent. If you think this may be an issue, get back to me and I'll 
outline a way to avoid it.

>                   I was finally looking to find a relation to X(0) from
> X(1) to X(N-1), but that needs (at the least) the summation of the
> exponential series and seems unrealistic to perform. I only have X(1) to
> X(N-1) to work with at this moment and anything else would need me to
> change the transmitter structure and that is not acceptable.

Pretty futile. DC restoration works only when there is a reference. 
AFAIK, you have none.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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m26k9 wrote:
> Thank you.
> I have been trying a method to find the average of the time-domain but it
> was unsuccessful. I was finally looking to find a relation to X(0) from
> X(1) to X(N-1), but that needs (at the least) the summation of the
> exponential series and seems unrealistic to perform. I only have X(1) to
> X(N-1) to work with at this moment and anything else would need me to
> change the transmitter structure and that is not acceptable.
> 
> Cheers.


If you have reason to believe that there is a zero or low 
f(1) component in the original signal then the X(1) 
component in the FT is due to spectral leakage from f(0).

Knowing  or guessing the window used for the FT, you should 
be able to work back and estimate X(0).

  Regards.

>
>If you have reason to believe that there is a zero or low 
>f(1) component in the original signal then the X(1) 
>component in the FT is due to spectral leakage from f(0).
>
>Knowing  or guessing the window used for the FT, you should 
>be able to work back and estimate X(0).
>
>  Regards.
>

Thank you very much.
The values fall in the exact bins and there is no leakage. So I think that
would not work.