Sample Rate conversion

>
>You should be able to use a Farrow resampler for this.  If the sample 
>times line up with the original samples. They are not changed.
>

I looked around, and it seems that oversampling filtering for OFDM signals
is done using a FIR low pass filter(see the GC5016 datasheet from Texas
Instruments, http://focus.ti.com/docs/prod/folders/print/gc5016.html)

So maybe I need to turn the question around: does an interpolation FIR
filter cause ISI in an OFDM signal?

My understanding is that it does, since there are filter outputs which are
calculated using samples from adjacent OFDM symbols, assuming there are no
gaps in between the symbols.

Basically, I need more information on the subject, but I cannot find
anything about oversampling potentially causing ISI on OFDM signals. It's
as if the problem does not exist, and that leads me believe that I do not
understand the matter properly.

Could anyone point me to a paper or a book that might shed some light on
this?

cocioc wrote:

>>You should be able to use a Farrow resampler for this.  If the sample 
>>times line up with the original samples. They are not changed.
>>
> 
> 
> I looked around, and it seems that oversampling filtering for OFDM signals
> is done using a FIR low pass filter(see the GC5016 datasheet from Texas
> Instruments, http://focus.ti.com/docs/prod/folders/print/gc5016.html)
> 
> So maybe I need to turn the question around: does an interpolation FIR
> filter cause ISI in an OFDM signal?
> 
> My understanding is that it does, since there are filter outputs which are
> calculated using samples from adjacent OFDM symbols, assuming there are no
> gaps in between the symbols.
> 
> Basically, I need more information on the subject, but I cannot find
> anything about oversampling potentially causing ISI on OFDM signals. It's
> as if the problem does not exist, and that leads me believe that I do not
> understand the matter properly.
> 
> Could anyone point me to a paper or a book that might shed some light on
> this?
> 
> 

The low pass filter is specified to remove the signal images that would 
otherwise occur with interpolation.  Ideally, the filter is specified 
to have a pass band such that it passes the full bandwidth of the 
uninterpolated signal, a stop band with enough attenuation to block out 
the images, and a transition that is steep enough to not cut into the 
pass band or allow leakage at the edge of the stopband.  FIR filters are 
typically used here because it is far easier to obtain a linear phase 
characteristic (which means it doesn't "smear" the passband signal) than 
it is with IIR filters.  Of course, it is impractical to have such an 
ideal filter because it would have an infinite number of taps and 
therefore an infinite delay.  In practice, we reduce the length of the 
filter at the price of a less steep transition to something that is 
realizable and that doesn't induce too much ISI.

Ray Andraka <ray@andraka.com> writes:

> cocioc wrote:
>
>>> You should be able to use a Farrow resampler for this.  If the
>>> sample times line up with the original samples. They are not
>>> changed.
>>>
>> I looked around, and it seems that oversampling filtering for OFDM
>> signals
>> is done using a FIR low pass filter(see the GC5016 datasheet from Texas
>> Instruments, http://focus.ti.com/docs/prod/folders/print/gc5016.html)
>> So maybe I need to turn the question around: does an interpolation
>> FIR
>> filter cause ISI in an OFDM signal?
>> My understanding is that it does, since there are filter outputs
>> which are
>> calculated using samples from adjacent OFDM symbols, assuming there are no
>> gaps in between the symbols.
>> Basically, I need more information on the subject, but I cannot find
>> anything about oversampling potentially causing ISI on OFDM signals. It's
>> as if the problem does not exist, and that leads me believe that I do not
>> understand the matter properly.
>> Could anyone point me to a paper or a book that might shed some
>> light on
>> this?
>>
>
> The low pass filter is specified to remove the signal images that
> would otherwise occur with interpolation.  Ideally, the filter is
> specified to have a pass band such that it passes the full bandwidth
> of the uninterpolated signal, a stop band with enough attenuation to
> block out the images, and a transition that is steep enough to not cut
> into the pass band or allow leakage at the edge of the stopband.  FIR
> filters are typically used here because it is far easier to obtain a
> linear phase characteristic (which means it doesn't "smear" the
> passband signal) than it is with IIR filters.  Of course, it is
> impractical to have such an ideal filter because it would have an
> infinite number of taps and therefore an infinite delay.  In practice,
> we reduce the length of the filter at the price of a less steep
> transition to something that is realizable and that doesn't induce too
> much ISI.

I wonder how big an "oversampled," truncated raised-cosine filter would have
to be before the ISI introduced by the truncation is negligible.
-- 
%  Randy Yates                  % "I met someone who looks alot like you,
%% Fuquay-Varina, NC            %             she does the things you do, 
%%% 919-577-9882                %                     but she is an IBM."
%%%% <yates@ieee.org>           %        'Yours Truly, 2095', *Time*, ELO   
http://home.earthlink.net/~yatescr

Randy Yates <yates@ieee.org> writes:

> Ray Andraka <ray@andraka.com> writes:
>
>> cocioc wrote:
>>
>>>> You should be able to use a Farrow resampler for this.  If the
>>>> sample times line up with the original samples. They are not
>>>> changed.
>>>>
>>> I looked around, and it seems that oversampling filtering for OFDM
>>> signals
>>> is done using a FIR low pass filter(see the GC5016 datasheet from Texas
>>> Instruments, http://focus.ti.com/docs/prod/folders/print/gc5016.html)
>>> So maybe I need to turn the question around: does an interpolation
>>> FIR
>>> filter cause ISI in an OFDM signal?
>>> My understanding is that it does, since there are filter outputs
>>> which are
>>> calculated using samples from adjacent OFDM symbols, assuming there are no
>>> gaps in between the symbols.
>>> Basically, I need more information on the subject, but I cannot find
>>> anything about oversampling potentially causing ISI on OFDM signals. It's
>>> as if the problem does not exist, and that leads me believe that I do not
>>> understand the matter properly.
>>> Could anyone point me to a paper or a book that might shed some
>>> light on
>>> this?
>>>
>>
>> The low pass filter is specified to remove the signal images that
>> would otherwise occur with interpolation.  Ideally, the filter is
>> specified to have a pass band such that it passes the full bandwidth
>> of the uninterpolated signal, a stop band with enough attenuation to
>> block out the images, and a transition that is steep enough to not cut
>> into the pass band or allow leakage at the edge of the stopband.  FIR
>> filters are typically used here because it is far easier to obtain a
>> linear phase characteristic (which means it doesn't "smear" the
>> passband signal) than it is with IIR filters.  Of course, it is
>> impractical to have such an ideal filter because it would have an
>> infinite number of taps and therefore an infinite delay.  In practice,
>> we reduce the length of the filter at the price of a less steep
>> transition to something that is realizable and that doesn't induce too
>> much ISI.
>
> I wonder how big an "oversampled," truncated raised-cosine filter would have
> to be before the ISI introduced by the truncation is negligible.

I seem to be thinking myself into a pit, here. 

If the r-c filter is truncated at a zero-crossing, then there would
be no ISI induced. OK, great - so what does that mean? The spectrum
would no longer be zero outside of the interval |f| < W? 
-- 
%  Randy Yates                  % "Maybe one day I'll feel her cold embrace,
%% Fuquay-Varina, NC            %                    and kiss her interface, 
%%% 919-577-9882                %            til then, I'll leave her alone."
%%%% <yates@ieee.org>           %        'Yours Truly, 2095', *Time*, ELO   
http://home.earthlink.net/~yatescr

cocioc wrote:
> My application is an OFDM transmitter. The output of the IFFT needs to be
> oversampled by a factor of 4 (after adding the CP). I thought of doing the
> oversampling by interpolating (inserting "zeroes") and low pass filtering
> the output of the interpolator to remove the unwanted images. I don't
> think this is going to work, though, because the LPF will "smudge" the
> adjacent symbols, destroying the time domain separation between them,
> which is required by the receiver.

An interpolation filter doesn't have to "smudge" any of the
original samples to produce a signal bandlimited to half the
original sample rate.  There are interpolation filters which
will pass all the original samples (the symbols?) unmolested
(FIR filters based on windowed sinc functions, for instance).

In an upsampling process, new intervening samples are usually
created in such a manner that the entire signal at the new
higher sample rate is bandlimited (so that alias images don't
interfere with adjacent OFDM channels for instance).  The fact
that the signal must be bandlimited to some degree requires
that any new samples between the original symbol samples be
"smudgy" combinations of several original samples.


IMHO. YMMV.
-- 
rhn A.T nicholson d.0.t C-o-M

Let's take an example. 

256 point FFT, 1/4 CP, x4 interpolation factor, 64 tap interpolation
filter.

The output of the FFT has 256 points. After adding the CP, the resulting
symbol is 320 points long.

After zero insertion, each symbol has 4 x 320 = 1280 samples.

So, the input to the filter is an OFDM frame, made up of back to back OFDM
symbols, each 1280 samples long.

The convolution between the filter response and the OFDM frame is
equivalent to passing the data stream across the filter window,
multiplying the data samples with the corresponding filter taps and
summing the multiplication results to obtain a filter output sample.

It is obvious that, as one symbols "pulls out" of the filter window, the
next one "moves in", so there will be 64 samples on the output of the
filter which will depend on samples from both OFDM symbols. Therefore, in
time domain, the two symbols have been mixed.

However, as the filter is 64 taps long and the cyclic prefix of the frame
is 256 samples long, the cyclic prefix is long enough to eliminate the
distortion at the receiver.

So here is my conclusion (which may or may not be right):

The interpolation filters are part of the channel the impulse response of
which the CP tries to compensate for. Therefore, as long as the total
response of the channel (which includes the filter response) is shorter
than the CP, this ISI can be completely eliminated at the receiver.

 
>
>An interpolation filter doesn't have to "smudge" any of the
>original samples to produce a signal bandlimited to half the
>original sample rate.  There are interpolation filters which
>will pass all the original samples (the symbols?) unmolested
>(FIR filters based on windowed sinc functions, for instance).
>
>In an upsampling process, new intervening samples are usually
>created in such a manner that the entire signal at the new
>higher sample rate is bandlimited (so that alias images don't
>interfere with adjacent OFDM channels for instance).  The fact
>that the signal must be bandlimited to some degree requires
>that any new samples between the original symbol samples be
>"smudgy" combinations of several original samples.
>
>
>IMHO. YMMV.
>-- 
>rhn A.T nicholson d.0.t C-o-M
>
>

Interpolation filters will degrade EVM a finite amount due to the adjacent
symbols.
However, you should find that there is negligible effect over most the CP
& Symbol.  And even at the edge of the CP or Symbol the EVM would be no
worse than 3%.

Adam

Erik de Castro Lopo wrote:
...
> Gambling(n): A discretionary tax on those asleep during high school maths.

i've heard it (or more specifically the state-run lotteries) as a tax
on the poor or, alternatively, a tax on the ignorant, but i haven't
heard this one.  i would still say it applies better for state-run
lotteries because in commercial gambling (like in Vegas or Atlantic
City, dunno how they do it down-under) only a portion of the "tax" goes
to the various governments.  most of the gambling profits go to the
private interests that own the casinos.  so, if it's a tax for the
ignorant and sleeping during math class, it's also a subsidy for the
rich in the case of the commercial "gaming" industry (amazing on how
dropping two letters rehabilitates a word).

r b-j

robert bristow-johnson wrote:
> Erik de Castro Lopo wrote:
> ...
>> Gambling(n): A discretionary tax on those asleep during high school maths.
> 
> i've heard it (or more specifically the state-run lotteries) as a tax
> on the poor or, alternatively, a tax on the ignorant, but i haven't
> heard this one.  i would still say it applies better for state-run
> lotteries because in commercial gambling (like in Vegas or Atlantic
> City, dunno how they do it down-under) only a portion of the "tax" goes
> to the various governments.  most of the gambling profits go to the
> private interests that own the casinos.  so, if it's a tax for the
> ignorant and sleeping during math class, it's also a subsidy for the
> rich in the case of the commercial "gaming" industry (amazing on how
> dropping two letters rehabilitates a word).

When I was in Montreal a few years after the Expo there, the state-run 
lottery was known as the "Voluntary Tax".

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Jerry Avins wrote:
> robert bristow-johnson wrote:
> > Erik de Castro Lopo wrote:
> > ...
> >> Gambling(n): A discretionary tax on those asleep during high school maths.
> >
> > i've heard it (or more specifically the state-run lotteries) as a tax
> > on the poor or, alternatively, a tax on the ignorant, but i haven't
> > heard this one.  i would still say it applies better for state-run
> > lotteries because in commercial gambling (like in Vegas or Atlantic
> > City, dunno how they do it down-under) only a portion of the "tax" goes
> > to the various governments.  most of the gambling profits go to the
> > private interests that own the casinos.  so, if it's a tax for the
> > ignorant and sleeping during math class, it's also a subsidy for the
> > rich in the case of the commercial "gaming" industry (amazing on how
> > dropping two letters rehabilitates a word).
>
> When I was in Montreal a few years after the Expo there, the state-run
> lottery was known as the "Voluntary Tax".

I've heard of lotteries as variously:
- a tax on people who are bad at math,
- a tax on people who are bad at statistics
  (would "probability" be more appropriate here?),
- a discretionary fee on people who are bad at math
  (a fee could be public or private), and
- a tax on innumericy.

It could also be considered perfectly reasonable financial abitrage
between entities who have a slight differences in the linearity
of their utility functions.


IMHO. YMMV.
-- 
rhn A.T nicholson d.0.t C-o-M