Hello If I have a 1MHz signal, and I sample at 100kHz, then I get a DC output. True? If I sample a 1,000,001Hz signal at 100kHz, what do I get as an output? Is it 1Hz? Ed.
Simple sampling question
Started by ●February 28, 2008
Reply by ●February 28, 20082008-02-28
Yes. Eduard Kais wrote:> Hello > > If I have a 1MHz signal, and I sample at 100kHz, then I get a DC output. > True? > > If I sample a 1,000,001Hz signal at 100kHz, what do I get as an output? Is > it 1Hz? > > Ed. > >
Reply by ●February 28, 20082008-02-28
"Andre" <alodwig@gmx.de> wrote in message news:fq694f$i7a$02$1@news.t-online.com...> Yes. > > Eduard Kais wrote: >> Hello >> >> If I have a 1MHz signal, and I sample at 100kHz, then I get a DC output. >> True? >> >> If I sample a 1,000,001Hz signal at 100kHz, what do I get as an output? >> Is it 1Hz?I guess my next question(s) is(are): If I sample at 200kHz, is the output still 1Hz? At what point does the output changed from being 1Hz?
Reply by ●February 28, 20082008-02-28
Eduard Kais wrote:> "Andre" <alodwig@gmx.de> wrote in message > news:fq694f$i7a$02$1@news.t-online.com... >> Yes. >> >> Eduard Kais wrote: >>> Hello >>> >>> If I have a 1MHz signal, and I sample at 100kHz, then I get a DC output. >>> True? >>> >>> If I sample a 1,000,001Hz signal at 100kHz, what do I get as an output? >>> Is it 1Hz? > > I guess my next question(s) is(are): > If I sample at 200kHz, is the output still 1Hz? > At what point does the output changed from being 1Hz?When you sample at 101 KHz, e.g. You have a specific idea in mind. When you figure out how to ask it unambiguously, you will already have the answer. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 28, 20082008-02-28
"Jerry Avins" <jya@ieee.org> wrote in message news:q-2dnXhg36t_f1vanZ2dnUVZ_qjinZ2d@rcn.net...> Eduard Kais wrote: >> "Andre" <alodwig@gmx.de> wrote in message >> news:fq694f$i7a$02$1@news.t-online.com... >>> Yes. >>> >>> Eduard Kais wrote: >>>> Hello >>>> >>>> If I have a 1MHz signal, and I sample at 100kHz, then I get a DC >>>> output. True? >>>> >>>> If I sample a 1,000,001Hz signal at 100kHz, what do I get as an output? >>>> Is it 1Hz? >> >> I guess my next question(s) is(are): >> If I sample at 200kHz, is the output still 1Hz? >> At what point does the output changed from being 1Hz? > > When you sample at 101 KHz, e.g. You have a specific idea in mind. When > you figure out how to ask it unambiguously, you will already have the > answer.No doubt you're right. A dentist by trade, I'm going to have to do some more reading up on math and DSP. The situation is a signal with a frequency range from 19.5 to 20.5MHz, and the sampler can sample up to 2MHz. I'd like to see what the sampled signal looks like at different sample rates. Is there a particular sample rate that will provide a sampled signal that has a frequency range 0-1MHz? (bandwidth?) Or what specific searches can I do to find the explanations myself? Sorry if I haven't got the terminology correct.
Reply by ●February 28, 20082008-02-28
Eduard Kais wrote:> "Jerry Avins" <jya@ieee.org> wrote in message > news:q-2dnXhg36t_f1vanZ2dnUVZ_qjinZ2d@rcn.net... >> Eduard Kais wrote: >>> "Andre" <alodwig@gmx.de> wrote in message >>> news:fq694f$i7a$02$1@news.t-online.com... >>>> Yes. >>>> >>>> Eduard Kais wrote: >>>>> Hello >>>>> >>>>> If I have a 1MHz signal, and I sample at 100kHz, then I get a DC >>>>> output. True? >>>>> >>>>> If I sample a 1,000,001Hz signal at 100kHz, what do I get as an output? >>>>> Is it 1Hz? >>> I guess my next question(s) is(are): >>> If I sample at 200kHz, is the output still 1Hz? >>> At what point does the output changed from being 1Hz? >> When you sample at 101 KHz, e.g. You have a specific idea in mind. When >> you figure out how to ask it unambiguously, you will already have the >> answer. > > No doubt you're right. > A dentist by trade, I'm going to have to do some more reading up on math and > DSP. > > The situation is a signal with a frequency range from 19.5 to 20.5MHz, and > the sampler can sample up to 2MHz. > I'd like to see what the sampled signal looks like at different sample > rates. > Is there a particular sample rate that will provide a sampled signal that > has a frequency range 0-1MHz? (bandwidth?) > Or what specific searches can I do to find the explanations myself? > Sorry if I haven't got the terminology correct.The relevant ideas are images and aliases, with the notion of "beats" (as in tuning an instrument) enlightening the study. Google will help, and you can keep asking here. Steve Smith's book at http://dspguide.com/ is a great resource. Chapter Three is probably the most relevant. Also check out what http://www.bores.com/courses/intro/index.htm offers. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 28, 20082008-02-28
"Eduard Kais" <who_me@hotmail.com> writes:> "Jerry Avins" <jya@ieee.org> wrote in message > news:q-2dnXhg36t_f1vanZ2dnUVZ_qjinZ2d@rcn.net... >> Eduard Kais wrote: >>> "Andre" <alodwig@gmx.de> wrote in message >>> news:fq694f$i7a$02$1@news.t-online.com... >>>> Yes. >>>> >>>> Eduard Kais wrote: >>>>> Hello >>>>> >>>>> If I have a 1MHz signal, and I sample at 100kHz, then I get a DC >>>>> output. True? >>>>> >>>>> If I sample a 1,000,001Hz signal at 100kHz, what do I get as an output? >>>>> Is it 1Hz? >>> >>> I guess my next question(s) is(are): >>> If I sample at 200kHz, is the output still 1Hz? >>> At what point does the output changed from being 1Hz? >> >> When you sample at 101 KHz, e.g. You have a specific idea in mind. When >> you figure out how to ask it unambiguously, you will already have the >> answer. > > No doubt you're right. > A dentist by trade, I'm going to have to do some more reading up on math and > DSP. > > The situation is a signal with a frequency range from 19.5 to 20.5MHz, and > the sampler can sample up to 2MHz. > I'd like to see what the sampled signal looks like at different sample > rates. > Is there a particular sample rate that will provide a sampled signal that > has a frequency range 0-1MHz? (bandwidth?) > Or what specific searches can I do to find the explanations myself? > Sorry if I haven't got the terminology correct.Hi Eduard, I suggest you Google on the terms "bandpass sampling" and/or "undersampling." For example, here's one of the top hits for the latter: http://www.analog.com/UploadedFiles/Associated_Docs/3689418379346Section5.pdf You can also see this described in Rick Lyons' book: @BOOK{lyonsnew, title = "{Understanding Digital Signal Processing}", edition = "Second", author = "{Richard~G.~Lyons}", publisher = "Prentice Hall", year = "2004"} -- % Randy Yates % "She's sweet on Wagner-I think she'd die for Beethoven. %% Fuquay-Varina, NC % She love the way Puccini lays down a tune, and %%% 919-577-9882 % Verdi's always creepin' from her room." %%%% <yates@ieee.org> % "Rockaria", *A New World Record*, ELO http://www.digitalsignallabs.com
Reply by ●February 28, 20082008-02-28
Eduard Kais wrote:> Hello > > If I have a 1MHz signal, and I sample at 100kHz, then I get a DC output. > True? > > If I sample a 1,000,001Hz signal at 100kHz, what do I get as an output? Is > it 1Hz? > > Ed. > >Yes and yes. Remember that the signal is sin(2 * pi * 1000001 * t), and you're sampling it at t = 0, t = 0.00001 ... So the argument _after_ sampling will be sin(2*pi*0), sin(2*pi*10.00001), etc. Then remember that sin(2*pi*(N + x)), where N is _any_ integer is just equal to sin(2*pi*x). The effect is called aliasing, and it usually makes life harder -- but when you're undersampling, it can make your life easier. I have a paper on sampling, that has a section on undersampling: http://www.wescottdesign.com/articles/Sampling/sampling.html. It's more about correcting misconceptions, but you may find it useful. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" gives you just what it says. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●February 29, 20082008-02-29
"Tim Wescott" <tim@seemywebsite.com> wrote in message news:rM6dndGetoRn8FranZ2dnUVZ_jmdnZ2d@web-ster.com...> Eduard Kais wrote: >> Hello >> >> If I have a 1MHz signal, and I sample at 100kHz, then I get a DC output. >> True? >> >> If I sample a 1,000,001Hz signal at 100kHz, what do I get as an output? >> Is it 1Hz? >> >> Ed. >> >> > Yes and yes. Remember that the signal is sin(2 * pi * 1000001 * t), and > you're sampling it at t = 0, t = 0.00001 ... So the argument _after_ > sampling will be sin(2*pi*0), sin(2*pi*10.00001), etc. Then remember that > sin(2*pi*(N + x)), where N is _any_ integer is just equal to sin(2*pi*x). > The effect is called aliasing, and it usually makes life harder -- but > when you're undersampling, it can make your life easier. > > I have a paper on sampling, that has a section on undersampling: > http://www.wescottdesign.com/articles/Sampling/sampling.html. It's more > about correcting misconceptions, but you may find it useful.Very useful. Thanks Tim. Section 3.4 describes exactly (ok, the numbers change, but the principle is the same) what I'm after. Ed.
Reply by ●February 29, 20082008-02-29
"Randy Yates" <yates@ieee.org> wrote in message news:m3prugacgc.fsf@ieee.org...> "Eduard Kais" <who_me@hotmail.com> writes: > >> "Jerry Avins" <jya@ieee.org> wrote in message >> news:q-2dnXhg36t_f1vanZ2dnUVZ_qjinZ2d@rcn.net... >>> Eduard Kais wrote: >>>> "Andre" <alodwig@gmx.de> wrote in message >>>> news:fq694f$i7a$02$1@news.t-online.com... >>>>> Yes. >>>>> >>>>> Eduard Kais wrote: >>>>>> Hello >>>>>> >>>>>> If I have a 1MHz signal, and I sample at 100kHz, then I get a DC >>>>>> output. True? >>>>>> >>>>>> If I sample a 1,000,001Hz signal at 100kHz, what do I get as an >>>>>> output? >>>>>> Is it 1Hz? >>>> >>>> I guess my next question(s) is(are): >>>> If I sample at 200kHz, is the output still 1Hz? >>>> At what point does the output changed from being 1Hz? >>> >>> When you sample at 101 KHz, e.g. You have a specific idea in mind. When >>> you figure out how to ask it unambiguously, you will already have the >>> answer. >> >> No doubt you're right. >> A dentist by trade, I'm going to have to do some more reading up on math >> and >> DSP. >> >> The situation is a signal with a frequency range from 19.5 to 20.5MHz, >> and >> the sampler can sample up to 2MHz. >> I'd like to see what the sampled signal looks like at different sample >> rates. >> Is there a particular sample rate that will provide a sampled signal that >> has a frequency range 0-1MHz? (bandwidth?) >> Or what specific searches can I do to find the explanations myself? >> Sorry if I haven't got the terminology correct. > > Hi Eduard, > > I suggest you Google on the terms "bandpass sampling" and/or > "undersampling." > For example, here's one of the top hits for the latter: > > > http://www.analog.com/UploadedFiles/Associated_Docs/3689418379346Section5.pdf > > You can also see this described in Rick Lyons' book: > > @BOOK{lyonsnew, > title = "{Understanding Digital Signal Processing}", > edition = "Second", > author = "{Richard~G.~Lyons}", > publisher = "Prentice Hall", > year = "2004"}Thanks Jerry, Randy. I know what to look for now. And will probably be back after I've digested it all. Ed.
