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Hilbert Vs bandpass filter in VSB Modulation

Started by Ajay April 24, 2005
Hi,

I am implementing a RF modulator for video signals. I am caught in
dilemma of choosing between two different implementations strategies,
One that involves taking hilbert transform of the video and then
modulating it while the other  modulates video to IF and then bandpass
it to get the VSB using an appropriate BPfilter.

For last few days, I have been trying to collect information regarding
what is typically done. I successfully collected some of them but are
not sufficient to arrive at any decision. And they are:

1) Hilbert Transformer is difficult to implement while typical approach
of using band pass filter is quite easy.
2) In case Hilbert transform we are working at 13.5 Mhz which is quite
less than 38.9 MHz IF frequency used in case of band pass approach.
And, I believe, clock frequency does regulate the silicon size. Also,
achieving filter paramters are easier at lower frequency than
otherwise.

Now, Please help me come out with a technically sound and vialble
choice. If in case there exits certain other strategies too, do let me
know about them.

Regards,
Ajay

On 24 Apr 2005 04:14:50 -0700, "Ajay" <mishraka@gmail.com> wrote:

>Hi,
Hi Ajay, I'll bet you receive several replies to your post, but I'll bet they'll be somewhat conflicting because different people will interpret your words in different ways. If you give us more information, you receive more useful replies.
>I am implementing a RF modulator for video signals.
What does it mean to "implement an RF modulator?" You're trying to build a system. What is the input to the system? (Please describe the input in both the time and frequency domains with as much detail as possible.) What is the desired output of your system? (Please describe the output in both the time and frequency domains with as much detail as possible.)
>I am caught in >dilemma of choosing between two different implementations strategies, >One that involves taking hilbert transform of the video and then >modulating it while
The output of a Hilbert transformer is a real-valued signal. Is that what you mean? Or do you mean your want to generate a complex (analytic) signal?
> ...the other modulates video to IF and then bandpass >it to get the VSB using an appropriate BPfilter.
What is the bandpass frequency of this BP filter. Are the BP filter's coefficients real or complex. Tell us what you mean by "VSB". Please don't make us guess.
>For last few days, I have been trying to collect information regarding >what is typically done. I successfully collected some of them but are >not sufficient to arrive at any decision. And they are: > >1) Hilbert Transformer is difficult to implement while typical approach >of using band pass filter is quite easy.
Maybe and maybe not. I can build a Hilbert transformer, for narrowband signals, that requires only one multiplication per output sample. Some bandpass filters are computationally intense. We need much more information from you before we can help you make your Hibert vs. bandpass filter comparison.
>2) In case Hilbert transform we are working at 13.5 Mhz which is quite >less than 38.9 MHz IF frequency used in case of band pass approach.
What does it mean to "work at 13.5 MHz?" For that matter, what does the word "work" mean? Remember now Ajay, you understand your problem, but we do not.
>And, I believe, clock frequency does regulate the silicon size. Also, >achieving filter paramters are easier at lower frequency than >otherwise.
What does it mean to "achieve a filter parameter?"
>Now, Please help me come out with a technically sound and vialble >choice. If in case there exits certain other strategies too, do let me >know about them. > >Regards, >Ajay
I fully realize that it's difficult to write a post like yours and make everyone understand its meaning. Ajay, if you can provide more details, more definitions, I'll bet someone here can help. See Ya', [-Rick-]
Hi Rick,

You are right. I need to elucidate some of the points mentioned in your
reply.

> >I am implementing a RF modulator for video signals. > > What does it mean to "implement an RF modulator?" > > You're trying to build a system.
Yes!, I am trying to build a system.
>What is the > input to the system? (Please describe the input > in both the time and frequency domains with as much > detail as possible.)
Input to the system comes from NTSC/PAL encoder which is CVBS video, a composite video. Input is sampled at 13.5 MHz.Bandwidth of the video is 4 Mhz for NTSC, 5MHz for PAL systems.
> What is the desired output of your system? > (Please describe the output > in both the time and frequency domains with as much > detail as possible.)
Eventually output RF modulated signal on the channel 3 and 4 at 61.25MHz and 67.25MHz respectively. But input is first modulated to Intermediate frequency(IF) which is 38.9MHz in case of PAL systems.
> >I am caught in > >dilemma of choosing between two different implementations
strategies,
> >One that involves taking hilbert transform of the video and then > >modulating it while > The output of a Hilbert transformer is a real-valued > signal. Is that what you mean? Or do you mean > your want to generate a complex (analytic) signal?
Strategy No.1 - |--------| |------------| video---> | LPF | ----> | VSB filer |-----> output is IF modulated |------- | |------------| video is first bandlimited to 4.5 Mhz or 5.5 Mhz depending on PAL or NTSC. VSB = vestigial Sideband I want to design a vestigial filter , with an impulse response h(t), as an FIR with passband ranging between -5 Mhz to 0.75Mhz. I wish to achieve it using hilbert transformer. assume Fm = 0.75 Mhz and Fn = 5 Mhz. we can make an hilbert transform of input which shifts phase by 90 degree for all the components above 0.75Mhz and below 5 Mhz and by -90 for -fn<f<-fm. Here I get real and imaginary componets of analytic signal after VSB filtering. o> Now, does this mean that I need to IF modulate them separately? And then add them. o>Also, impulse response will have real and imaginary components. How to implement such VSB filer? Can matlab generate the coefficients? o>I am just aware of theoratical part of such hilbert transformer. Any help on implementing it would be greatly appreciated.
> > ...the other modulates video to IF and then bandpass > >it to get the VSB using an appropriate BPfilter. > What is the bandpass frequency of this BP filter. > Are the BP filter's coefficients real or complex.
Strategy No.2 - we first interpolate our video at the sampling rate f > 2*(38.9 + 5) Mhz and then modulate it with IF = 38.9 Mhz. we get Double sidebands at 38.9Mhz. Now, a bandpass filter with passband 33.90 - 39.65 Mhz and transition band of 0.5Mhz on both sides will give us the vestigial sideband modulation. we are preserving the lower sideband and vestige of upper sideband.
> Tell us what you mean by "VSB". > Please don't make us guess.
Vestigial Sideband Modulation(VSB)
> I fully realize that it's difficult to write a post like yours > and make everyone understand its meaning. > > Ajay, if you can provide more details, more definitions, > I'll bet someone here can help.
I have tried my level best to explain things. But if it is still uncomprehensible, please let me know. I shall try to elaborate those parts. best regards, Ajay Rick Lyons wrote:
> On 24 Apr 2005 04:14:50 -0700, "Ajay" <mishraka@gmail.com> wrote: > > >Hi, > > Hi Ajay, > > I'll bet you receive several replies to your post, > but I'll bet they'll be somewhat conflicting because > different people will interpret your words in different > ways. If you give us more information, you receive more > useful replies. > > >I am implementing a RF modulator for video signals. > > What does it mean to "implement an RF modulator?" > > You're trying to build a system. What is the > input to the system? (Please describe the input > in both the time and frequency domains with as much > detail as possible.) > What is the desired output of your system? > (Please describe the output > in both the time and frequency domains with as much > detail as possible.) > > >I am caught in > >dilemma of choosing between two different implementations
strategies,
> >One that involves taking hilbert transform of the video and then > >modulating it while > > The output of a Hilbert transformer is a real-valued > signal. Is that what you mean? Or do you mean > your want to generate a complex (analytic) signal? > > > ...the other modulates video to IF and then bandpass > >it to get the VSB using an appropriate BPfilter. > > What is the bandpass frequency of this BP filter. > Are the BP filter's coefficients real or complex. > > Tell us what you mean by "VSB". > Please don't make us guess. > > >For last few days, I have been trying to collect information
regarding
> >what is typically done. I successfully collected some of them but
are
> >not sufficient to arrive at any decision. And they are: > > > >1) Hilbert Transformer is difficult to implement while typical
approach
> >of using band pass filter is quite easy. > > Maybe and maybe not. I can build a Hilbert transformer, > for narrowband signals, that requires only one > multiplication per output sample. > Some bandpass filters are computationally > intense. > > We need much more information from you before > we can help you make your Hibert vs. bandpass filter > comparison. > > >2) In case Hilbert transform we are working at 13.5 Mhz which is
quite
> >less than 38.9 MHz IF frequency used in case of band pass approach. > > What does it mean to "work at 13.5 MHz?" > For that matter, what does the word "work" mean? > > Remember now Ajay, you understand your > problem, but we do not. > > >And, I believe, clock frequency does regulate the silicon size.
Also,
> >achieving filter paramters are easier at lower frequency than > >otherwise. > > What does it mean to "achieve a filter parameter?" > > >Now, Please help me come out with a technically sound and vialble > >choice. If in case there exits certain other strategies too, do let
me
> >know about them. > > > >Regards, > >Ajay > > I fully realize that it's difficult to write a post like yours > and make everyone understand its meaning. > > Ajay, if you can provide more details, more definitions, > I'll bet someone here can help. > > See Ya', > [-Rick-]
Ajay wrote:
> Hi, > > I am implementing a RF modulator for video signals. I am caught in > dilemma of choosing between two different implementations strategies, > One that involves taking hilbert transform of the video and then > modulating it while the other modulates video to IF and then bandpass > it to get the VSB using an appropriate BPfilter.
Vestigial sideband, including the 50% carrier, is hard to generate with SSSC techniques, which is what I guess the Hilbert transformer is a candidate for. A suitable filter will probably be the easier way: __________________ | / unity |/ | /|<--Carrier zero / | &#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295; |
> For last few days, I have been trying to collect information regarding > what is typically done. I successfully collected some of them but are > not sufficient to arrive at any decision. And they are: > > 1) Hilbert Transformer is difficult to implement while typical approach > of using band pass filter is quite easy. > 2) In case Hilbert transform we are working at 13.5 Mhz which is quite > less than 38.9 MHz IF frequency used in case of band pass approach. > And, I believe, clock frequency does regulate the silicon size. Also, > achieving filter paramters are easier at lower frequency than > otherwise. > > Now, Please help me come out with a technically sound and vialble > choice. If in case there exits certain other strategies too, do let me > know about them.
An analog modulator, such as used to be common with video games, can be had quite cheaply. Is there a reason to go digital? jerry -- Engineering is the art of making what you want from things you can get. &#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
Jerry Avins wrote:
> Ajay wrote: > > Hi, > > > > I am implementing a RF modulator for video signals. I am caught in > > dilemma of choosing between two different implementations
strategies,
> > One that involves taking hilbert transform of the video and then > > modulating it while the other modulates video to IF and then
bandpass
> > it to get the VSB using an appropriate BPfilter. > > Vestigial sideband, including the 50% carrier, is hard to generate
with
> SSSC techniques, which is what I guess the Hilbert transformer is a > candidate for. A suitable filter will probably be the easier way: > __________________ > | / unity > |/ > | > /|<--Carrier > zero / | > =AF=AF=AF=AF=AF=AF=AF=AF |
In our case , it is different. carrier is placed in passband area. there is a vestige portion of 0.75Mhz after carrier. the transition is of 0.5 Mhz. Do you still think it is difficult to achieve using bandpass? o>Also, can you comment about hilbert option? o>Would the designing hilbert transformer be not difficult? o>also having two threads of operation on x[n] and hilb_x[n] will increase the hardware which can outweigh the advantage of using it. _________^___ / | \ / carrier | \ -------/ | \ ---------
> > > For last few days, I have been trying to collect information
regarding
> > what is typically done. I successfully collected some of them but
are
> > not sufficient to arrive at any decision. And they are: > > > > 1) Hilbert Transformer is difficult to implement while typical
approach
> > of using band pass filter is quite easy. > > 2) In case Hilbert transform we are working at 13.5 Mhz which is
quite
> > less than 38.9 MHz IF frequency used in case of band pass approach. > > And, I believe, clock frequency does regulate the silicon size.
Also,
> > achieving filter paramters are easier at lower frequency than > > otherwise. > > > > Now, Please help me come out with a technically sound and vialble > > choice. If in case there exits certain other strategies too, do let
me
> > know about them. > > An analog modulator, such as used to be common with video games, can
be
> had quite cheaply. Is there a reason to go digital?
As the block is a pert of all digital SOC, it will be disasterous to have an analog RF modulator as per our case is concerned. Moreover, is it easier to implement in analog? -Ajay
> jerry > -- > Engineering is the art of making what you want from things you can
get.
>
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF
FYI.

The picture Jerry drew is the situation in the receiver after passing
through the IF filter, i.e. the carrier is down about 6 dB as it is in
the transition band of the filter
Also this picture is oriented as an RF signal with the video carrier on
the low side.

The picture Ajay drew is the situation in the transmitter.  The
transition band of the filter is narrower and the carrier is in the
passband.  This picture is oriented as an IF signal which by convention
is spectrally inverted compared to the RF signal and has the carrier on
the high side.

These are two different views of the same system.


Also another comment, the baseband video signal contains components
down to DC, I do not believe it is practical to implement a VSB analog
video system using a Hilbert transformer.  The filter method should be
straightforward.

Mark

Jerry Avins wrote:

> Ajay wrote: > >> Hi, >> >> I am implementing a RF modulator for video signals. I am caught in >> dilemma of choosing between two different implementations strategies, >> One that involves taking hilbert transform of the video and then >> modulating it while the other modulates video to IF and then bandpass >> it to get the VSB using an appropriate BPfilter. > > > Vestigial sideband, including the 50% carrier, is hard to generate with > SSSC techniques, which is what I guess the Hilbert transformer is a > candidate for. A suitable filter will probably be the easier way: > __________________ > | / unity > |/ > | > /|<--Carrier > zero / | > &#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295; | > > >> For last few days, I have been trying to collect information regarding >> what is typically done. I successfully collected some of them but are >> not sufficient to arrive at any decision. And they are: >> >> 1) Hilbert Transformer is difficult to implement while typical approach >> of using band pass filter is quite easy. >> 2) In case Hilbert transform we are working at 13.5 Mhz which is quite >> less than 38.9 MHz IF frequency used in case of band pass approach. >> And, I believe, clock frequency does regulate the silicon size. Also, >> achieving filter paramters are easier at lower frequency than >> otherwise. >> >> Now, Please help me come out with a technically sound and vialble >> choice. If in case there exits certain other strategies too, do let me >> know about them. > > > An analog modulator, such as used to be common with video games, can be > had quite cheaply. Is there a reason to go digital? >
The video game style analog modulators generate full-bandwidth AM signals, not VSB signals per broadcast specifications. If the OP needs to build a device that's going to be a good RF citizen then he needs to do more. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Ajay wrote:

> Hi Rick, > > You are right. I need to elucidate some of the points mentioned in your > reply. > > >>>I am implementing a RF modulator for video signals. >> >>What does it mean to "implement an RF modulator?" >> >>You're trying to build a system. > > Yes!, I am trying to build a system. > > >>What is the >>input to the system? (Please describe the input >>in both the time and frequency domains with as much >>detail as possible.) > > Input to the system comes from NTSC/PAL encoder which is CVBS video, a > composite video. > Input is sampled at 13.5 MHz.Bandwidth of the video is 4 Mhz for NTSC, > 5MHz for PAL systems. > > >>What is the desired output of your system? >>(Please describe the output >>in both the time and frequency domains with as much >>detail as possible.) > > Eventually output RF modulated signal on the channel 3 and 4 at > 61.25MHz and 67.25MHz respectively. > But input is first modulated to Intermediate frequency(IF) which is > 38.9MHz in case of PAL systems. >
Is it done in all cases?
> >>>I am caught in >>>dilemma of choosing between two different implementations > > strategies, > >>>One that involves taking hilbert transform of the video and then >>>modulating it while >> >> The output of a Hilbert transformer is a real-valued >>signal. Is that what you mean? Or do you mean >>your want to generate a complex (analytic) signal? > > Strategy No.1 - > |--------| |------------| > video---> | LPF | ----> | VSB filer |-----> output is IF > modulated > |------- | |------------| > video is first bandlimited to 4.5 Mhz or 5.5 Mhz depending on PAL or > NTSC. > VSB = vestigial Sideband > I want to design a vestigial filter , with an impulse response h(t), as > an FIR with passband ranging between -5 Mhz to 0.75Mhz. I wish to > achieve it using hilbert transformer. > assume Fm = 0.75 Mhz and Fn = 5 Mhz. we can make an hilbert transform > of input which shifts phase by 90 degree for all the components above > 0.75Mhz and below 5 Mhz and by -90 for -fn<f<-fm. Here I get real and > imaginary componets of analytic signal after VSB filtering. > o> Now, does this mean that I need to IF modulate them separately? And > then add them.
Yes. You could do well by studying the amateur radio literature on the "phasing method" of single-sideband signal generation (and reception). You actually have an easier job of it with VSB because the hard part of SSB generation with phasing is suppressing the carrier -- that's not an issue for broadcast TV transmission.
> o>Also, impulse response will have real and imaginary components. How > to implement such VSB filer? Can matlab generate the coefficients?
Yes, MatLab can generate the coefficients. Whether there's a toolbox that'll do this for you is an open question. I would investigate the possibility of combining my complex bandpass (-5.0MHz - 0.75MHz) filter with a Hilbert transformer on the Q channel and a straight FIR filter on the I channel. I don't know if it can be done, but it'll save you some taps if it can. I'd also see if I could make a +45 degree phase shifted channel and a -45 degree phase shifted channel, to be modulated and combined for the correct IF channel -- the reason being is that the FIR filter to implement the Hilbert transform has some large peaks, and by making a +45,-45 pair you can reduce the size of the peaks by a factor of nearly 2.
> o>I am just aware of theoratical part of such hilbert transformer. Any > help on implementing it would be greatly appreciated. > > >>>...the other modulates video to IF and then bandpass >>>it to get the VSB using an appropriate BPfilter. >> >>What is the bandpass frequency of this BP filter. >>Are the BP filter's coefficients real or complex. > > Strategy No.2 - > we first interpolate our video at the sampling rate f > 2*(38.9 + 5) > Mhz and then modulate it with IF = 38.9 Mhz. > we get Double sidebands at 38.9Mhz. Now, a bandpass filter with > passband 33.90 - 39.65 Mhz and transition band of > 0.5Mhz on both sides will give us the vestigial sideband modulation. we > are preserving the lower sideband and vestige of > upper sideband. > > >>Tell us what you mean by "VSB". >>Please don't make us guess. > > Vestigial Sideband Modulation(VSB) >
Rick: This is a well-known modulation method if you study TV systems, so it's almost fair for him to expect us to know it.
>
- snip -
>
There are some basic trade offs in implementing SSB (or VSB) which you must pay attention to either in DSP land or analog circuits land. With the Hilbert transform ("phasing") method you must be concerned with how well your filters are matched, and with how well your oscillators are matched when you reconstruct. These issues are eased but not eliminated in the case of a DSP, and they aren't eased at all if you want to come out of the DSP system with two signals in baseband to be modulated up to the RF frequency. With the IF ("filtering") method you must be concerned with the difficulty of building a good filter at your IF frequency. In the analog world this means expensive and possibly touchy IF filters; in the DSP world this means longer filter lengths and higher numerical precision and throughput requirements -- and in DSP-land you still have to reconstruct something to analog! -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Mark wrote:

- snip -
> > Also another comment, the baseband video signal contains components > down to DC, I do not believe it is practical to implement a VSB analog > video system using a Hilbert transformer. The filter method should be > straightforward. > > Mark >
Don't be so sure. Given the nature of the VSB signal the Hilbert-transformed portion of the baseband signal may only come into play in subtracting the depreciated sideband out of the AM signal -- if this is the case then using the Hilbert transform may be very practical indeed. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Ajay wrote:

   ...
> In our case , it is different. carrier is placed in passband area. > there is a vestige portion of 0.75Mhz after carrier. the transition is > of 0.5 Mhz. Do you still think it is difficult to achieve using > bandpass?
No. I'm puzzled about the double amplitude you will experience from the demodulated vestige. With standard vestigial sideband, the vestige energy fills replaces the attenuated main sideband energy below 1 MHz.
> o>Also, can you comment about hilbert option? > o>Would the designing hilbert transformer be not difficult?
Design is easy either with a program or by formula and a window. Implementation can be expensive because the HT needs to be quite long to cover a large relative bandwidth. Then what? You can't simply shift the analytic signal you would make. That would give you single sideband, not vestigial.
> o>also having two threads of operation on x[n] and hilb_x[n] will > increase the hardware which can outweigh the advantage of using it.
What advantage? I can't see how to make it work. Vestigial sideband was invented to achieve much of the benefit of single sideband while avoiding the complexity of generating it. Modifying a method for generating single sideband in order to produce vestigial sideband would only add to the complexity that vestigial was designed to avoid. (In the early days of television, the transmitters generated ordinary double-sideband RF signals. A filter consisting of tuned stubs properly spaced along the waveguide feeding the antenna left only a vestige of the lower sideband and attenuated the low-frequency end of the upper sideband, maintaining flat frequency response. I had the misfortune to be assigned to design one of those filters. Do you know Smith charts?)
> _________^___ > / | \ > / carrier | \ > -------/ | \---------
...
>>An analog modulator, such as used to be common with video games, can >>be had quite cheaply. Is there a reason to go digital? > > > As the block is a pert of all digital SOC, it will be disasterous to > have an analog RF modulator as per our case is concerned.
I see.
> Moreover, is it easier to implement in analog?
I know it's easy and cheap: http://www.freepatentsonline.com/4816905.html http://www.radioshack.com/product.asp?catalog%5Fname=CTLG&product%5Fid=26-609 The modulator probably costs less than $2 for parts and assembly. http://www.radioshack.com/product.asp?catalog%5Fname=CTLG&product%5Fid=26-610 http://www.radioshack.com/product.asp?catalog%5Fname=CTLG&product%5Fid=15-2526 Jerry -- Engineering is the art of making what you want from things you can get. &#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;