Hi all, I am wondering how to shift simultaneously the postive freq. components and negative freq. components both towards baseband? Suppose the bandlimited signal freq. spectrum is in [-Wx, -Wy] and [Wy, Wx] symmetrically, where Wy>0, Wx>0, Wx>Wy. I understood how to shift both spectrum towards one direction, but shifting both posive spectrum and negative spectrum towards baseband involves two different directions at the same time, how to do that? For example, how to shift [-Wx, -Wy] spectrum to [0, Wx-Wy] and [Wy, Wx] to [-(Wx-Wy), 0] at the same time? Another one, how to shift [-Wx, -Wy] spectrum to [-(Wx-Wy), 0] and [Wy, Wx] to [0, Wx-Wy] at the same time?
how to shift spectrum to baseband?
Started by ●November 11, 2004
Reply by ●November 11, 20042004-11-11
kiki wrote:> Hi all, > > I am wondering how to shift simultaneously the postive freq. > components and negative freq. components both towards baseband? > > Suppose the bandlimited signal freq. spectrum is in > > [-Wx, -Wy] and [Wy, Wx] symmetrically, where Wy>0, Wx>0, Wx>Wy. > > I understood how to shift both spectrum towards one direction, > > but shifting both posive spectrum and negative spectrum towards > baseband involves two different directions at the same time, how to do > that? > > For example, how to shift [-Wx, -Wy] spectrum to [0, Wx-Wy] and [Wy, > Wx] to [-(Wx-Wy), 0] at the same time? > > Another one, how to shift [-Wx, -Wy] spectrum to [-(Wx-Wy), 0] and > [Wy, Wx] to [0, Wx-Wy] at the same time?Look in the literature under (I believe) quadrature demodulators. IIRC Rick Lyon's book has a chapter on this, as well as any discussion of image-reject mixers. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●November 11, 20042004-11-11
I believe the process is called hetrodyning. There are two variaties, real and complex, depending on the type of signal present. Demosulation is a different function though it may use the same operations. In article <10p7j8bl076cm21@corp.supernews.com>, Tim Wescott <tim@wescottnospamdesign.com> wrote:>kiki wrote: > >> Hi all, >> >> I am wondering how to shift simultaneously the postive freq. >> components and negative freq. components both towards baseband? >> >> Suppose the bandlimited signal freq. spectrum is in >> >> [-Wx, -Wy] and [Wy, Wx] symmetrically, where Wy>0, Wx>0, Wx>Wy. >> >> I understood how to shift both spectrum towards one direction, >> >> but shifting both posive spectrum and negative spectrum towards >> baseband involves two different directions at the same time, how to do >> that? >> >> For example, how to shift [-Wx, -Wy] spectrum to [0, Wx-Wy] and [Wy, >> Wx] to [-(Wx-Wy), 0] at the same time? >> >> Another one, how to shift [-Wx, -Wy] spectrum to [-(Wx-Wy), 0] and >> [Wy, Wx] to [0, Wx-Wy] at the same time? > >Look in the literature under (I believe) quadrature demodulators. IIRC >Rick Lyon's book has a chapter on this, as well as any discussion of >image-reject mixers. >
Reply by ●November 12, 20042004-11-12
You could shift first one way, then the other, add the two shifted spectra, and then apply a baseband LPF to reject the double frequency components kiki wrote:> Hi all, > > I am wondering how to shift simultaneously the postive freq. > components and negative freq. components both towards baseband? > > Suppose the bandlimited signal freq. spectrum is in > > [-Wx, -Wy] and [Wy, Wx] symmetrically, where Wy>0, Wx>0, Wx>Wy. > > I understood how to shift both spectrum towards one direction, > > but shifting both posive spectrum and negative spectrum towards > baseband involves two different directions at the same time, how to do > that? > > For example, how to shift [-Wx, -Wy] spectrum to [0, Wx-Wy] and [Wy, > Wx] to [-(Wx-Wy), 0] at the same time? > > Another one, how to shift [-Wx, -Wy] spectrum to [-(Wx-Wy), 0] and > [Wy, Wx] to [0, Wx-Wy] at the same time?
Reply by ●November 12, 20042004-11-12
On 11 Nov 2004 11:28:55 -0800, lunaliu3@yahoo.com (kiki) wrote:>Hi all, > >I am wondering how to shift simultaneously the postive freq. >components and negative freq. components both towards baseband? > >Suppose the bandlimited signal freq. spectrum is in > >[-Wx, -Wy] and [Wy, Wx] symmetrically, where Wy>0, Wx>0, Wx>Wy. > >I understood how to shift both spectrum towards one direction, > >but shifting both posive spectrum and negative spectrum towards >baseband involves two different directions at the same time, how to do >that?Hi,>For example, how to shift [-Wx, -Wy] spectrum to [0, Wx-Wy] and [Wy, >Wx] to [-(Wx-Wy), 0] at the same time?Can you not just multiply your time sequence by: cos(2*pi*Wx*n/Fs) to achieve this? (Fs is the sample rate.)>Another one, how to shift [-Wx, -Wy] spectrum to [-(Wx-Wy), 0] and >[Wy, Wx] to [0, Wx-Wy] at the same time?Can you not just multiply your time sequence by: cos(2*pi*Wy*n/Fs) to achieve this? These two processes (what George Bush calls "real heterodyning") should give you the "baseband" spectra that you desire, but they'll also give you spectral images above and below baseband which you may need to filter out. Good luck, [-Rick-]
Reply by ●November 12, 20042004-11-12
kiki wrote:> Hi all, > > I am wondering how to shift simultaneously the postive freq. > components and negative freq. components both towards baseband? > > Suppose the bandlimited signal freq. spectrum is in > > [-Wx, -Wy] and [Wy, Wx] symmetrically, where Wy>0, Wx>0, Wx>Wy. > > I understood how to shift both spectrum towards one direction, > > but shifting both posive spectrum and negative spectrum towards > baseband involves two different directions at the same time, how to do > that? > > For example, how to shift [-Wx, -Wy] spectrum to [0, Wx-Wy] and [Wy, > Wx] to [-(Wx-Wy), 0] at the same time? > > Another one, how to shift [-Wx, -Wy] spectrum to [-(Wx-Wy), 0] and > [Wy, Wx] to [0, Wx-Wy] at the same time?If I read that correctly, the positive and negative component sets form a redundant pair. Why not simply discard one of them? _Digital_ signal processing is a sub-discipline of signal processing. The best way to treat your signal if it were analog should be clear. That approach works on digital signals too. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●November 12, 20042004-11-12
That's not what you are supposed to do. I asked Fred Harris (fred harris) this question once in a signal processing course at UCSD and he politely explained why it wouldn't work. To make it work, one has to do a Hilbert Transform which gives a complex baseband signal which isn't a simplification. In article <2vk46dF2nilnnU1@uni-berlin.de>, Jerry Avins <jya@ieee.org> wrote:> >If I read that correctly, the positive and negative component sets form >a redundant pair. Why not simply discard one of them? > >_Digital_ signal processing is a sub-discipline of signal processing. >The best way to treat your signal if it were analog should be clear. >That approach works on digital signals too. > >Jerry
Reply by ●November 12, 20042004-11-12
George Bush wrote:> That's not what you are supposed to do. I asked Fred Harris (fred harris) > this question once in a signal processing course at UCSD and he politely > explained why it wouldn't work. To make it work, one has to do a Hilbert > Transform which gives a complex baseband signal which isn't a simplification. > > In article <2vk46dF2nilnnU1@uni-berlin.de>, Jerry Avins <jya@ieee.org> wrote: > >>If I read that correctly, the positive and negative component sets form >>a redundant pair. Why not simply discard one of them? >> >>_Digital_ signal processing is a sub-discipline of signal processing. >>The best way to treat your signal if it were analog should be clear. >>That approach works on digital signals too. >> >>JerryOne can also use a complex filter to remove the negative frequencies. I'd be willing to bet that the nature of a good solution would be suggested by the real-world process that produced the signal in the first place. A made-up question has no such contextual support. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●November 15, 20042004-11-15
"George Bush" <george.w.bush@whitehouse.com> wrote in message news:PQ5ld.82293$Kl3.9355@twister.socal.rr.com...> That's not what you are supposed to do. I asked Fred Harris (fred harris) > this question once in a signal processing course at UCSD and he politely > explained why it wouldn't work. To make it work, one has to do a Hilbert > Transform which gives a complex baseband signal which isn't asimplification. Don't mis-quote fred like that. What he really says (said) was that you can do a lot better using DSP if you didn't model everything from an analog sense. To clarify, if you start with an analog model and just convert your block into digital implementations, you'll be ok but if you know what you want and you didn't let the analog model cloud your mind, you can do a lot better in some applications/situations. Cheers Bhaskar> > In article <2vk46dF2nilnnU1@uni-berlin.de>, Jerry Avins <jya@ieee.org>wrote:> > > >If I read that correctly, the positive and negative component sets form > >a redundant pair. Why not simply discard one of them? > > > >_Digital_ signal processing is a sub-discipline of signal processing. > >The best way to treat your signal if it were analog should be clear. > >That approach works on digital signals too. > > > >Jerry
Reply by ●November 15, 20042004-11-15
Gee. I don't have my notes from that class in '79 so I can't challenge your direct quote. In article <2vscekF2onrrcU1@uni-berlin.de>, "Bhaskar Thiagarajan" <bhaskart@my-deja.com> wrote:>"George Bush" <george.w.bush@whitehouse.com> wrote in message >news:PQ5ld.82293$Kl3.9355@twister.socal.rr.com... >> That's not what you are supposed to do. I asked Fred Harris (fred harris) >> this question once in a signal processing course at UCSD and he politely >> explained why it wouldn't work. To make it work, one has to do a Hilbert >> Transform which gives a complex baseband signal which isn't a >simplification. > >Don't mis-quote fred like that. >What he really says (said) was that you can do a lot better using DSP if you >didn't model everything from an analog sense. To clarify, if you start with >an analog model and just convert your block into digital implementations, >you'll be ok but if you know what you want and you didn't let the analog >model cloud your mind, you can do a lot better in some >applications/situations. > >Cheers >Bhaskar > >> >> In article <2vk46dF2nilnnU1@uni-berlin.de>, Jerry Avins <jya@ieee.org> >wrote: >> > >> >If I read that correctly, the positive and negative component sets form >> >a redundant pair. Why not simply discard one of them? >> > >> >_Digital_ signal processing is a sub-discipline of signal processing. >> >The best way to treat your signal if it were analog should be clear. >> >That approach works on digital signals too. >> > >> >Jerry > >
