RESTORING BINARY SIGNAL FROM LOW FREQUENCIES

Can someone points me to the methods to solve the following problem:

Function s(x) is binary {0,1}.  We set high frequencies above some
cuttoff limit to 0.
Resulting function is L(x). How can we restore s(x) from L(x)?

Thank you,

Yuri
0
y_granik (4)
10/31/2008 4:07:30 AM
comp.dsp 20141 articles. 0 followers. allnor (8507) is leader. Post Follow

11 Replies
119 Views

Similar Articles

[PageSpeed] 43
>Function s(x) is binary {0,1}.  We set high frequencies above some
>cuttoff limit to 0.
>Resulting function is L(x). How can we restore s(x) from L(x)?

What exactly is the binary signal?  What is the application?

Too much abstraction will delay your getting a good answer.

Emre
0
eguven (123)
10/31/2008 4:34:40 AM
Ostap wrote:

> Can someone points me to the methods to solve the following problem:

> Function s(x) is binary {0,1}.  We set high frequencies above some
> cuttoff limit to 0.
> Resulting function is L(x). How can we restore s(x) from L(x)?

It depends.  Look in the paper:

Nyquist, Harry. "Certain factors affecting telegraph speed". Bell System 
Technical Journal, 3, 324�346, 1924

It describes your problem very well.

-- glen

0
gah (12850)
10/31/2008 4:36:38 AM
On Oct 30, 9:07=A0pm, Ostap <y_gra...@yahoo.com> wrote:
> Can someone points me to the methods to solve the following problem:
>
> Function s(x) is binary {0,1}. =A0We set high frequencies above some
> cuttoff limit to 0.
> Resulting function is L(x). How can we restore s(x) from L(x)?
>
> Thank you,
>
> Yuri

Binary function is a piece-wise constant function that can have
only two values 0 or 1, say given the interval [0, 10] we define

s(x)=3D0, 0<=3Dx<2
s(x)=3D1, 2<=3Dx<7
s(x)=3D0, 7<=3Dx<=3D7.2
s(x)=3D1, 7.2<=3D10

The application is in the field of optics.

Hope this helps,

Yuri

0
y_granik (4)
10/31/2008 4:42:19 AM
On Oct 31, 12:36=A0am, Glen Herrmannsfeldt <g...@ugcs.caltech.edu>
wrote:
> Ostap wrote:
> > Can someone points me to the methods to solve the following problem:
> > Function s(x) is binary {0,1}. =A0We set high frequencies above some
> > cuttoff limit to 0.
> > Resulting function is L(x). How can we restore s(x) from L(x)?
>
> It depends. =A0Look in the paper:
>
> Nyquist, Harry. "Certain factors affecting telegraph speed". Bell System
> Technical Journal, 3, 324=96346, 1924
>
> It describes your problem very well.
>
> -- glen

What's a good source for BSTJ ???

Thanks,

John
0
sampson164 (501)
10/31/2008 6:15:01 AM
John wrote:

> On Oct 31, 12:36 am, Glen Herrmannsfeldt <g...@ugcs.caltech.edu>
> wrote:
> 
>>Ostap wrote:
>>
>>>Can someone points me to the methods to solve the following problem:
>>>Function s(x) is binary {0,1}.  We set high frequencies above some
>>>cuttoff limit to 0.
>>>Resulting function is L(x). How can we restore s(x) from L(x)?

>>It depends.  Look in the paper:

>>Nyquist, Harry. "Certain factors affecting telegraph speed". Bell System
>>Technical Journal, 3, 324�346, 1924

>>It describes your problem very well.

> What's a good source for BSTJ ???

The library of a good engineering college.  Especially one around
since 1924.

http://www.worldcat.org/oclc/1519469&referer=brief_results

put in your zip code, state, province, or country and it will
find one near you.

-- glen

0
gah (12850)
10/31/2008 6:47:26 AM

Ostap wrote:

> Can someone points me to the methods to solve the following problem:
> 
> Function s(x) is binary {0,1}.  We set high frequencies above some
> cuttoff limit to 0.
> Resulting function is L(x). How can we restore s(x) from L(x)?

Is the function s(x) cyclostationary or not?

If it is cyclostationary, then the task is the typical problem of the 
digital communication and there are many ways for solution depending on 
L(x).

If s(x) is not cyclostationary, then the problem is non-trivial and the 
solution may not be unique.


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




0
10/31/2008 2:18:21 PM
>
>
>Ostap wrote:
>
>> Can someone points me to the methods to solve the following problem:
>> 
>> Function s(x) is binary {0,1}.  We set high frequencies above some
>> cuttoff limit to 0.
>> Resulting function is L(x). How can we restore s(x) from L(x)?
>
>Is the function s(x) cyclostationary or not?
>
>If it is cyclostationary, then the task is the typical problem of the 
>digital communication and there are many ways for solution depending on 
>L(x).
>
>If s(x) is not cyclostationary, then the problem is non-trivial and the 
>solution may not be unique.
>
>
>Vladimir Vassilevsky
>DSP and Mixed Signal Design Consultant
>http://www.abvolt.com
>

Vladimir:

Is the pure "unmodulated" binary signals are considered cyclostationary? I
tend to believe that they are stationary process as I remember from my
digital communication readings! My understanding is that cyclostationary is
a feature in modulated signals due to the built in periodicity in the
carrier! Agree?
>
>
>
0
ytachwali (18)
10/31/2008 3:48:37 PM
>Binary function is a piece-wise constant function that can have
>only two values 0 or 1, say given the interval [0, 10] we define
>
>s(x)=3D0, 0<=3Dx<2
>s(x)=3D1, 2<=3Dx<7
>s(x)=3D0, 7<=3Dx<=3D7.2
>s(x)=3D1, 7.2<=3D10

Here is my take:  if you throw away high frequencies greater than some
cutoff, you lose the sharp transitions and get a smoother signal.  So the
result should be around 0 and 1 most of the time, assuming you keep enough
of the frequency content.

By optics, are you referring to binary optical communication?  Do you have
control over the cutoff frequency, or is there some other constraint such
as channel bandwidth?

Emre
0
eguven (123)
11/1/2008 1:21:46 AM
>Is the function s(x) cyclostationary or not?
>
>If it is cyclostationary, then the task is the typical problem of the 
>digital communication and there are many ways for solution depending on 
>L(x).
>
>If s(x) is not cyclostationary, then the problem is non-trivial and the 
>solution may not be unique.

I don't see how cyclostationarity is relevant.  The OP did not say it
comes from a random process.  In fact his example is rather deterministic.

To the OP: there may be an extremely neat solution to your problem.  If
you have enough Fourier domain measurements, you can reconstruct your
signal *exactly* with an overwhelming probability, assuming the number of
jumps and/or the nonzero values in your signal is  small (i.e. sparse) with
respect to the total number of the samples.  See the below reference [1].

Hope this helps,

Emre

[1] E. J. Candès, J. Romberg and T. Tao. Robust uncertainty principles:
exact signal reconstruction from highly incomplete frequency information.
IEEE Trans. Inform. Theory, 52 489-509.

0
eguven (123)
11/1/2008 1:44:42 AM
>>Is the function s(x) cyclostationary or not?
>>
>>If it is cyclostationary, then the task is the typical problem of the 
>>digital communication and there are many ways for solution depending on

>>L(x).
>>
>>If s(x) is not cyclostationary, then the problem is non-trivial and the

>>solution may not be unique.
>
>I don't see how cyclostationarity is relevant.  The OP did not say it
>comes from a random process.  In fact his example is rather
deterministic.

I understand a deterministic signal can also be cyclostationary; so never
mind that part. 

Still, I don't see why exactly one needs this condition.  Does anyone have
a good explanation?

Emre
0
eguven (123)
11/1/2008 2:34:36 AM
On Oct 31, 6:44=A0pm, "emre" <egu...@ece.neu.edu> wrote:
> To the OP: there may be an extremely neat solution to your problem. =A0If
> you have enough Fourier domain measurements, you can reconstruct your
> signal *exactly* with an overwhelming probability, assuming the number of
> jumps and/or the nonzero values in your signal is =A0small (i.e. sparse) =
with
> respect to the total number of the samples. =A0See the below reference [1=
].
>
> Hope this helps,
>
> Emre
>
> [1] E. J. Cand=E8s, J. Romberg and T. Tao. Robust uncertainty principles:
> exact signal reconstruction from highly incomplete frequency information.
> IEEE Trans. Inform. Theory, 52 489-509.

Emre,

Perfect reference! Thank you very much. We can consider this thread to
be over.

Yuri
0
y_granik (4)
11/1/2008 5:17:24 AM
Reply:
Similar Artilces:

Arbitrary Clock Frequencies From Base Clock
Hello, I have a board with the Xilinx V2 Pro (xc2vp30). I am designing a BPSK demodulator on this board. For the demodulator, I need to generate arbitrary clock frequencies from 8 MHz to 10 MHz in 100 kHz increments from the base clock. How can I do this? Does anyone have any VHDL code I can use for this? Thanks and regards, Abhishek Hi, I do this using this simple Numeric Controlled Oscillator -NCO- code I found in here: http://www.analogservices.com/vhdlmod.htm However the generated clk is not pure in the sense that some periods are a bit longer than others. Robert abhisheknag@gmail....

binary stream with vector of '(unsigned-byte 8)
Hello, I am using vectors of '(unsigned-byte 8) to read/write data from/to sockets. The software interface I have to use implies the use of such vectors, and I don't have access to underground binary stream nor to the socket itself. Since I didn't found any simple/portable method to make a binary- stream to read/write data , I am using adjustable vectors with the fill-pointer and vector-push-extend functions. But I didn't found any standard functions to read from a vector without using an explicit offset each time. Did I miss domething interesting there ? :Nicolas Nicolas Ed...

signal hendlers
Hello I need use in signal handler function some data structure, but I dont know how. I have something like this: #ifdef SA_SIGINFO act.sa_flags |= SA_SIGINFO; #endif in my Signal() implementation ; it gives me that signal handler function have 2 new parameters First is siginfo_t structure pointer but i dont know what type is secound ? void sig_chld(int sig, struct siginfo_t *x, ???) Next problem is how to copy or point data structure , which i want to give my signal handler function, a dont know how the siginfo_t structure looks like? Resoult should be like that: void sig_chld(int ...

System Restore, Virus Restore=?ISO-8859-1?B?ig==?=Same Thing
http://www.mcpmag.com/columns/article.asp?EditorialsID=760 ----- Start Quotes ----- Windows ME and Windows XP have a handy System Restore feature, which periodically make backups of key system files, especially when you install new software or hardware. Unfortunately, virus-infected files can get backed up by System Restore. So, you could clean your system and then roll back to a restore checkpoint and poof! The virus is back. .... Depending on how you feel about System Restore's benefits vs. the risks of bringing a virus back, you might want to disable System Restore ----- End Quotes...

__Shortcut to KILL battery / restore hotsync M500 ?
I've searched the groups and can't find the posts about the graffiti shortcut that will lock the Palm ON, with backlight, so that it will DIE, and thus reset whatever has rendered the USB connection dead. (hoping it's not a static discharge issue) It belongs to a friend, and everything works, including beaming, and a hard reset didn't cure it. This Palm tries to do a hotsync, but the desktop end of it doesn't launch, so the Palm times out with the 'connection could not be established' message on screen. My M505 syncs perfectly on the same cradle. Any...

Cannot restore after Veritas Netbackup restores
Hi There, We have an issue on our db2 restores. We do database dumps every night, and restore them to development servers every morning. This works fine with no errors. However if we backup those images to tape using Veritas netbackup, and then restore those images and try to restore them to the database, we get "The backup image is corrupt". If we run db2ckbkp against that image we get "Unable to decompress image from different platform". This is really urgent as our backups are currently useless to us if we cannot restore them properly. If anyone has even a smal...

Cable return path has outside signals at 22mhz
Hi all In our return plant that we are starting to implement, we are seeing signals in and around 22mhz. Does anyone know of a way of isolating the ingress point they must be coming in at. Seems they are some form of radio navigation signal, as it sounds like a beacon when you use a communication analyzer to look at the signals. Thanks On Aug 2, 6:51 pm, "Dana" <raff...@yahoo.com> wrote: > Hi all > In our return plant that we are starting to implement, we are seeing signals > in and around 22mhz. Does anyone know of a way of isolating the ingress ...

instructor's solutions manual for Signals, Systems & Transforms 4 ED by Phillips, Parr & Riskin
I have the comprehensive instructor's solutions manuals in an electronic format for the following textbooks. They include full solutions to all the problems in the text, but please DO NOT POST HERE, instead send me email including title and edition of the solutions manual u need. NOTE: this service is NOT free My email: markrainsun( at )gmail( dot )com Here are some from my list ... solutions manual to A First Course in Differential Equations (7th ed.) Zill & Diferential Equations (5th ed.)Zill & Cullen solutions manual to A Course in Game Theory by Osborne, Rubinstein soluti...

getting symbol information from elf binary
Guys, I am extremely sorry for posting a question that is not related to C. I tried my best to get some information from web but failed. I would be highly grateful if someone could provide me some hint or direct me to some useful link. My question is that, I want to retrieve the information about all structures from an elf binary. For eg. suppose I use a structure of some type in my C program and then I compile it to get the elf binary. Now, can I get the information about that structure (names of all the fields used in that structure, their type etc) from the elf binary. I believe t...

Restore program
Is there a way to write a program that would backup all home directory objects that had been modified within say, the last 14 days, prior to restoring your home directory backup object? On Tue, 15 Aug 2006 06:07:51 -0500, <rschapin@comcast.net> wrote: > Is there a way to write a program that would backup all home directory > objects that had been modified within say, the last 14 days, > prior to restoring your home directory backup object? There are no time stamps on internal calc objects (only SD card files have modification times). It might be easiest to just make a new c...

5.1 & 5.2 binary compatibility
Hi - I've had a look around this news group but I can't find an answer to my question, which is: I have built an app on AIX 5.1, a customer has AIX 5.2 - will my app run on his 5.2 box? Many thanks, Kevin. kosullivan@elandtech.com (Kevin O'Sullivan) writes: > I have built an app on AIX 5.1, a customer has AIX 5.2 - will my app > run on his 5.2 box? Yes, for most user-level programs [*]. Most likely for many system-level programs. [*] Be sure your exe is linked dynamically against libc -- if it is linked statically, all bets are off. You can see a list of dynamic depende...

Low Voltage Electric Blanket
Sunbeam Queen Premium Box Pattern Olive Green Electric Heated Warming Blanket Price:$129.99 Image: http://bestdeallocator.info/image.php?id=B000XTAH0G Best deal: http://bestdeallocator.info/index.php?id=B000XTAH0G Soft Heat Electric Warming Blanket - Queen Size Chocolate Price:$159.99 Image: http://bestdeallocator.info/image.php?id=B001GRMNOW Best deal: http://bestdeallocator.info/index.php?id=B001GRMNOW Soft Heat Electric Warming Throw Blanket - Wide Wale Natural Price:$89.99 Image: http://bestdeallocator.info/image.php?id=B001S1LY0K Best deal: http://bestdeallocator.info/index.php?id=B...

Restoring from mksysb
I have an RS6000 F50-7025 that currently has a 4GB SCSI boot disk (rootvg). I'm going to replace it with a 9GB disk. I plan to restore from an mksysb tape. I've never done this before. How difficult is the restoration process from mksysb? Is there anything I should know before diving in? I'm making the tape with the command: mkszfile -f'' && mksysb '/dev/rmt0.1' What's the best procedure for booting off this tape? By using bootlist(1)? What exactly happens when you boot off an mksysb tape? Does it just ask you if you want to restore, and then...

Help needed in transfering or backing up/restoring Informix database via ODBC.
I've recently encountered a full file system failure on my Informix server, it's running Informix IDS 9.20 (Linux); access to the Informix tools is not available, changing the allow.hosts file isn't an option (as the file system is damaged); otherwise I'd setup remote access (i.e. dbaccess/dbexport, etc.) - presently Informix is online, the dbspace's and databases have yet to be compromised. So here's the situation, I have ODBC access, I have a backup that is a month old, so I have a current/correct schema from dbexport; I've attempted to export all the ta...

Binary Genetic Algorithm for Feature Selection is avaialble for free (Only on request)
Hi guys; Anybody interested in carrying out GA-based feature selection can contact me via: hezecomp@yahoo.com. It's very easy to use and I commented on each lines for code understanding ...

To restore information after a hard reset
In PC, after one has reformatted the hard disk many times by wiping out the entire Windows and reinstalling it, there is still a method to restore and retrieve the supposedly deleted data. For a Palm, if one perform a hard reset to it several times, is it possible to use some advance technology to restore and retrieve the data that were gone? I appreciate an answer to this question. On Tue, 9 Sep 2003 23:33:33 +0800, "tom" <tom@nospam.com> wrote: >In PC, after one has reformatted the hard disk many times by wiping out the >entire Windows and reinstalling i...

Testbench using Modelsim/VHDL
I'm not sure if this is VHDL or Modelsim issue (other than operator issue), so I'm posting in both groups. It looks like too simple a case to ask someone online, but I've been scratching my head too long on this. I'm relatively new to VHDL (and Modelsim as well). In a testbench, I'm doing a simple signal generation : - assert 'sig1' at a rising edge of a free running clock at some point - deassert 'sig1' at the next rising edge - and on the 3rd edge, do some checking, and so on... However, the simlation waveform shows that 'sig1' is asserted from...

Disk utility
I run Jaguar. I need the 'restore' ability that the Disk Utility from Panther has. I don't want to upgrad emy system, want to wait for Tiger. What can I do? Thanks! -- gipsy boy In article <39Sae.143741$Uh3.14053@biebel.telenet-ops.be>, gipsy boy <x@x.pi> wrote: > I run Jaguar. I need the 'restore' ability that the Disk Utility from > Panther has. I don't want to upgrad emy system, want to wait for Tiger. > What can I do? The first thing would be to describe the problem you're trying to solve rather than what you think the solution is. ...

need matlab code and algorithms for image restoration
hey anybody help me to give matlab code and algorithms for image restoration and image enhancement. thanks. roksy rosky wrote: > > > hey anybody help me to give matlab code and algorithms for image > restoration and image enhancement. > thanks. > roksy Why? /PB ...

Zapping PRAM in OS X (to restore Appletalk?)
I got a strange problem at work. The Macs in the Graphics dept. running OS 10.2.x can see the Appletalk Zones and have no problem printing to two Xerox DC 12s running off Fiery servers and an HP 5si/MX. If you put OS 10.3.x on one of the Macs and print through IP printing to the Xerox DC 12s, they either spew out pages of Postscript code, or have the print jobs continuously stall in the Printer Setup Utility no matter how many times you restart them, or else give the message "will retry connection in 10 seconds". About 10% of the time you actually print what you want. I hav...

Restoring bad pics...
http://cjoint.com/data/lAvdvKQpea.htm The whole image is 1,4 MB, it's a pic from Flickr, a painting from de Heem; http://www.insecula.com/PhotosNew/00/00/05/89/ME0000058932_3.JPG This is what it should look like. Next i will buy the DVD with all that stuff, but i was trying to make it watchable... 1) Use of the perspective tool, cropping... 2) Applying some gaussian blur, then the smart sharpening script. On the sample, because else it takes too much time. 3) adding some contrast, remove yellow (all less than 10%) Anyway it seems that i can't get it sharp and...

US-TX-Austin: DSP Eng., Digital Signal Processing Exp., DSP/Algoritm bckgrnd; DH (45313657602)
US-TX-Austin: DSP Eng., Digital Signal Processing Exp., DSP/Algoritm bckgrnd; DH (45313657602) ============================================================================================== Position: DSP Eng. Reference: SMC01597 Location: Austin TX Duration: DH Skills: Digital Signal Processing Experience. Solid DSP/Algorithm/Communication theory background. Firmware implementation knowledge preferred. BSEE, Master's Preferred - GPA 3.75 or better. Please send your current resume in confidence to <staf...

how to convert binary array into integer
Hi, Does anyone know the api to convert a binary array into integer: for example: 00 00 00 0A =3D> 10 thanks=20 On 8/31/05, hsun <sunh11373@hotmail.com> wrote: > Hi, >=20 > Does anyone know the api to convert a binary array into integer: >=20 > for example: 00 00 00 0A =3D> 10 Have you looked at String#unpack? On Thu, 1 Sep 2005, hsun wrote: > Hi, > > Does anyone know the api to convert a binary array into integer: > > for example: 00 00 00 0A => 10 > > thanks harp:~ > cat a.rb p( [0x0, 0x0, 0x0, 0xA].pack('c*')...

peak signal to nois ratio(psnr)
I use the video and is divided into a set of picture will I pass these pictures on digetal video broadcast terestial (dvb-t), and I want to measure peak signal to noise ratio (psnr) the results came from (40-70 and inf) in the event that thesignal to noise ratio the equal to (5-18) How do I know whether the results are valid or not and what it means psnr =inf ? thank you ...

NT Backup restores directories but not files
Hello Why is it that NT Backup restores directories but not files. All the directories are empty. I have had this on a few occasions at different sites I work at. I tried searching for an answer... not much found. I heard mention of incremental backups being problem, but am sure I haven't used that option anyway. Anyone one help please? Please dont answer if you dont know... rather not have the thread hijacked as sometimes happens :D Thanks. ...