FPGA Central

Hello,
I am performing DSP operations on a phase modulated pulse converted t
baseband through analog, complex, downconversion. The phase within th
pulse is stepped at time intervals T. In between updates it is hel
constant, therefore, the the approximate 3dB bandwidth of the signal i
B=1/T. The baseband envelope resembles a sinc function with first nulls a
f=+/-B. I really only want to sample this complex signal at a rate B t
feed into subsequent pulse correlation processes. Complex downconversio
reduces the I and Q A/D sampling rates of a signal with "bandwidth" B to
samples per second, rather than 2B samples per second, but in this cas
signals outside the bandwidth are assumed to be below "processin
sensitivity," I'll call it. In my case, to achieve no overlap, I need a
unobtainable filter that chops the spectrum off perfectly at B/2, otherwis
there is going to be mucho overlap of the A/D sampling replications and th
bandwidth of interest. To achieve overlap within the BW of interest that i
below "processing sensitivity" it seems I need a linear phase filter with
very aggressive rolloff ahead of the A/D converters that will probabl
start to roll off ahead of the 3dB points of the spectrum. I will have t
try to achieve a compromise between overlap and loss of SNR.
Interestingly, I haven’t seen any ill effects of the replication overlap
in my simulations, that include no filtering, but I know they are there an
it concerns me. If I oversample, I don’t have enough FPGA resources t
deal with the additional samples – they have to be thrown away. So if
decimate back down it seems that I really have the same problem of needin
to filter aggressively again, although digitally, which costs les
resources just to do in analog, ahead of the A/D converters. Am I lookin
at this correctly?
Thanks,
John M.

On 11 Sep, 07:19, "JM1970" <ra...@sbcglobal.net> wrote:
> Hello,
> I am performing DSP operations on a phase modulated pulse converted to
> baseband through analog, complex, downconversion. *The phase within the
> pulse is stepped at time intervals T. In between updates it is held
> constant, therefore, the the approximate 3dB bandwidth of the signal is
> B=1/T. *

Are you sure about that? If all you have done is to mix
from RF to baseband, the pulse is still phase modulated,
right? If so, the bandwidth might be far larger than
you think.

It's been ages since I looked into these things, so I
can't help with the details. But you should review the
theory for phase modulated signals. As I recall, PM is
a somewhat restricted case of frequency modulation.

Rune

JM1970 wrote:
> Hello,
> I am performing DSP operations on a phase modulated pulse converted to
> baseband through analog, complex, downconversion. The phase within the
> pulse is stepped at time intervals T. In between updates it is held
> constant, therefore, the the approximate 3dB bandwidth of the signal is
> B=1/T.

Not so. The bandwidth at baseband is the same as the bandwidth before
downconversion, whether analog or complex. Abrupt phase changes will
create HUGE sideband components. Even if the modulating signal is
lowpassed before going to the modulator, the bandwidth is likely to be
much larger than you imagine.

> The baseband envelope resembles a sinc function with first nulls at
> f=+/-B. I really only want to sample this complex signal at a rate B to
> feed into subsequent pulse correlation processes. Complex downconversion
> reduces the I and Q A/D sampling rates of a signal with "bandwidth" B to B
> samples per second, rather than 2B samples per second, but in this case
> signals outside the bandwidth are assumed to be below "processing
> sensitivity,"

You still have 2B samples/sec. It's just that one of them is imaginary.

> I'll call it. In my case, to achieve no overlap, I need an
> unobtainable filter that chops the spectrum off perfectly at B/2, otherwise
> there is going to be mucho overlap of the A/D sampling replications and the
> bandwidth of interest. To achieve overlap within the BW of interest that is
> below "processing sensitivity" it seems I need a linear phase filter with a
> very aggressive rolloff ahead of the A/D converters that will probably
> start to roll off ahead of the 3dB points of the spectrum. I will have to
> try to achieve a compromise between overlap and loss of SNR.

What is overlapping?

> Interestingly, I haven't seen any ill effects of the replication overlap,
> in my simulations, that include no filtering, but I know they are there and
> it concerns me. If I oversample, I don't have enough FPGA resources to
> deal with the additional samples - they have to be thrown away. So if I
> decimate back down it seems that I really have the same problem of needing
> to filter aggressively again, although digitally, which costs less
> resources just to do in analog, ahead of the A/D converters. Am I looking
> at this correctly?

I don't understand you well enough to answer that.

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

JM1970 wrote:

> Hello,
> I am performing DSP operations on a phase modulated pulse converted to
> baseband through analog, complex, downconversion. The phase within the
> pulse is stepped at time intervals T.

So the signal is cyclostationary and it is sufficient to sample with the
rate of 1/2T, unless you have to filter out the noise also.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

>JM1970 wrote:
>> Hello,
>> I am performing DSP operations on a phase modulated pulse converted to
>> baseband through analog, complex, downconversion. The phase withi
the
>> pulse is stepped at time intervals T. In between updates it is held
>> constant, therefore, the the approximate 3dB bandwidth of the signa
is
>> B=1/T.
>
>Not so. The bandwidth at baseband is the same as the bandwidth before
>downconversion, whether analog or complex. Abrupt phase changes will
>create HUGE sideband components. Even if the modulating signal is
>lowpassed before going to the modulator, the bandwidth is likely to be
>much larger than you imagine.
>
>> The baseband envelope resembles a sinc function with first null
at
>> f=+/-B. I really only want to sample this complex signal at a rate
to
>> feed into subsequent pulse correlation processes. Comple
downconversion
>> reduces the I and Q A/D sampling rates of a signal with "bandwidth"
to B
>> samples per second, rather than 2B samples per second, but in thi
case
>> signals outside the bandwidth are assumed to be below "processing
>> sensitivity,"
>
>You still have 2B samples/sec. It's just that one of them is imaginary.
>
>> I'll call it. In my case, to achieve no overlap, I nee
an
>> unobtainable filter that chops the spectrum off perfectly at B/2
otherwise
>> there is going to be mucho overlap of the A/D sampling replications an
the
>> bandwidth of interest. To achieve overlap within the BW of interes
that is
>> below "processing sensitivity" it seems I need a linear phase filte
with a
>> very aggressive rolloff ahead of the A/D converters that will probably
>> start to roll off ahead of the 3dB points of the spectrum. I will hav
to
>> try to achieve a compromise between overlap and loss of SNR.
>
>What is overlapping?
>
>> Interestingly, I haven't seen any ill effects of the replicatio
overlap,
>> in my simulations, that include no filtering, but I know they are ther
and
>> it concerns me. If I oversample, I don't have enough FPGA resource
to
>> deal with the additional samples - they have to be thrown away. So i
I
>> decimate back down it seems that I really have the same problem o
needing
>> to filter aggressively again, although digitally, which costs less
>> resources just to do in analog, ahead of the A/D converters. Am
looking
>> at this correctly?
>
>I don't understand you well enough to answer that.
>
>Jerry
>--
>Engineering is the art of making what you want from things you can get.
>ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï ¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿ ½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï ¿½ï¿½ï¿½ï¿½ï¿½
>
Hi Jerry,
The phase samples comprising the transmitted pulse correspond to sample
of a linear frequency chirp from -B/2 to B/2 made at intervals Ts=1/B. Th
IF spectrum envelope of this definitely traces out a sinc function, with
3dB bandwidth approximately equal to B, although it looks a tad bit ragged
I am sure of this.

The Nyquist criteria on processing the downconverted information is what
am unsure of, so please let me know if this reasoning is sound:

When the IF is converted to baseband in the I and Q channels of th
demodulator they have the same envelope as before as you point out, th
bandwidth is still B, but specta are now centered about 0Hz.

If I had a perfect, "brick-wall" filter ahead of each A/D converter with
bandwidth B/2, then it would seem I could sample the I and Q signals eac
at a rate of B. Some signal power in the is lost in this process, bu
let's ignore that for now.

The reson why I can sample at B, is that the spectral replications arisin
from the sampling process of the signal do not overlap (they butt right u
against one another).

In actual practice, the filter will not be brick-wall. The cutof
frequency and shape of the passband "skirt" will dictate how much th
replications overlap the signal of interest - I guess this is overla
called aliasing.

To be completely honest, I am not sure why the overlap in my application
is a bad thing if it is kept acceptably small. What acceptably small
means, I am not quite sure of yet, maybe 20dB down. Anyway, I guess if
"unacceptabley small" replication energy is within my bandwidth of
interest, it's going to show up somewhere down the processing pipe and bite
me.

What can I do other than the aforementioned? If I sample at twice the
rate, I am out of the woods as far as overlap is concerned, but I can't
handle twice as many samples. If I throw out every other sample, then I'm
back to square one.

John M.

JM1970 wrote:
>> JM1970 wrote:
>>> Hello,
>>> I am performing DSP operations on a phase modulated pulse converted to
>>> baseband through analog, complex, downconversion. The phase within
> the
>>> pulse is stepped at time intervals T. In between updates it is held
>>> constant, therefore, the the approximate 3dB bandwidth of the signal
> is
>>> B=1/T.
>> Not so. The bandwidth at baseband is the same as the bandwidth before
>> downconversion, whether analog or complex. Abrupt phase changes will
>> create HUGE sideband components. Even if the modulating signal is
>> lowpassed before going to the modulator, the bandwidth is likely to be
>> much larger than you imagine.
>>
>>> The baseband envelope resembles a sinc function with first nulls
> at
>>> f=+/-B. I really only want to sample this complex signal at a rate B
> to
>>> feed into subsequent pulse correlation processes. Complex
> downconversion
>>> reduces the I and Q A/D sampling rates of a signal with "bandwidth" B
> to B
>>> samples per second, rather than 2B samples per second, but in this
> case
>>> signals outside the bandwidth are assumed to be below "processing
>>> sensitivity,"
>> You still have 2B samples/sec. It's just that one of them is imaginary.
>>
>>> I'll call it. In my case, to achieve no overlap, I need
> an
>>> unobtainable filter that chops the spectrum off perfectly at B/2,
> otherwise
>>> there is going to be mucho overlap of the A/D sampling replications and
> the
>>> bandwidth of interest. To achieve overlap within the BW of interest
> that is
>>> below "processing sensitivity" it seems I need a linear phase filter
> with a
>>> very aggressive rolloff ahead of the A/D converters that will probably
>>> start to roll off ahead of the 3dB points of the spectrum. I will have
> to
>>> try to achieve a compromise between overlap and loss of SNR.
>> What is overlapping?
>>
>>> Interestingly, I haven't seen any ill effects of the replication
> overlap,
>>> in my simulations, that include no filtering, but I know they are there
> and
>>> it concerns me. If I oversample, I don't have enough FPGA resources
> to
>>> deal with the additional samples - they have to be thrown away. So if
> I
>>> decimate back down it seems that I really have the same problem of
> needing
>>> to filter aggressively again, although digitally, which costs less
>>> resources just to do in analog, ahead of the A/D converters. Am I
> looking
>>> at this correctly?
>> I don't understand you well enough to answer that.
>>
>> Jerry
>> --
>> Engineering is the art of making what you want from things you can get.
>>
> Hi Jerry,
> The phase samples comprising the transmitted pulse correspond to samples
> of a linear frequency chirp from -B/2 to B/2 made at intervals Ts=1/B. The
> IF spectrum envelope of this definitely traces out a sinc function, with a
> 3dB bandwidth approximately equal to B, although it looks a tad bit ragged.
> I am sure of this.
>
> The Nyquist criteria on processing the downconverted information is what I
> am unsure of, so please let me know if this reasoning is sound:
>
> When the IF is converted to baseband in the I and Q channels of the
> demodulator they have the same envelope as before as you point out, the
> bandwidth is still B, but specta are now centered about 0Hz.
>
> If I had a perfect, "brick-wall" filter ahead of each A/D converter with a
> bandwidth B/2, then it would seem I could sample the I and Q signals each
> at a rate of B. Some signal power in the is lost in this process, but
> let's ignore that for now.

Forget the brick wall filter. Even if it were physically realizable in
finite time, the ringing (Gibbs phenomenon) would kill you. sample 20%
faster and use a filter you can build.

> The reson why I can sample at B, is that the spectral replications arising
> from the sampling process of the signal do not overlap (they butt right up
> against one another).

You can sample at B per I and Q channel. That's 2B overall.

> In actual practice, the filter will not be brick-wall. The cutoff
> frequency and shape of the passband "skirt" will dictate how much the
> replications overlap the signal of interest - I guess this is overlap
> called aliasing.

See above.

> To be completely honest, I am not sure why the overlap in my application
> is a bad thing if it is kept acceptably small. What acceptably small
> means, I am not quite sure of yet, maybe 20dB down.

the peak of the first sidelobe of a sinc is .212; -13 db.

> Anyway, I guess if
> "unacceptabley small" replication energy is within my bandwidth of
> interest, it's going to show up somewhere down the processing pipe and bite
> me.

I rarely use an anti-alias filter for a servo, but I oversample at least
5x and 10x if I can manage it.

> What can I do other than the aforementioned? If I sample at twice the
> rate, I am out of the woods as far as overlap is concerned, but I can't
> handle twice as many samples. If I throw out every other sample, then I'm
> back to square one.

Sample at an achievable but still modest rate.

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