Dear Group, I have an elementary question. If a sine-wave is sampled such that the samples fall at the times when the value of the wave is zero (meaning at 0 and pi). The sampling frequency thus is twice the frquency of the wave. Is this proper sampling ? How can we reconstruct such a signal ? Of course the power of the signal is non-zero. Is that sufficient to prove that the input signal is a sine wave having frequency as half the sampling frequency? TY
Regarding sampling.
Started by ●January 4, 2007
Reply by ●January 4, 20072007-01-04
Ted wrote:> Dear Group, > > I have an elementary question. If a sine-wave is sampled such that the > samples fall at the times when the value of the wave is zero (meaning > at 0 and pi). > > The sampling frequency thus is twice the frquency of the wave. Is this > proper sampling ? How can we reconstruct such a signal ? Of course the > power of the signal is non-zero. Is that sufficient to prove that the > input signal is a sine wave having frequency as half the sampling > frequency? >A common misconception - signal bandwidth must be < Nyquist, not <= Nyquist. Paul
Reply by ●January 4, 20072007-01-04
Ted wrote:> Dear Group, > > I have an elementary question. If a sine-wave is sampled such that the > samples fall at the times when the value of the wave is zero (meaning > at 0 and pi). > > The sampling frequency thus is twice the frquency of the wave. Is this > proper sampling ? How can we reconstruct such a signal ? Of course the > power of the signal is non-zero. Is that sufficient to prove that the > input signal is a sine wave having frequency as half the sampling > frequency? > > TYThis subject gets a regular thrashing :) See this thread: http://groups.google.com/group/comp.arch.embedded/browse_thread/thread/b8a58d07e0e3f968/0fd20e416fb2756d?q=what+nyquist+didn%27t+say&lnk=ol& Cheers PeteS
Reply by ●January 4, 20072007-01-04
Ted ha escrito:> Dear Group, > > I have an elementary question. If a sine-wave is sampled such that the > samples fall at the times when the value of the wave is zero (meaning > at 0 and pi). > > The sampling frequency thus is twice the frquency of the wave. Is this > proper sampling ? How can we reconstruct such a signal ? Of course the > power of the signal is non-zero. Is that sufficient to prove that the > input signal is a sine wave having frequency as half the sampling > frequency? > > TYDear Ted: The Niquist theorem is based upon frequency domain analysis of sampling. If you use as the sampling frequency twice the frequency of the sine wave you will need an ideal reconstruction (low pass) filter in order to recover it from its samples. It's impossible to implement such a filter. You should normally use a much higher sampling frequency (let's say five times or more the highest frequency of your wave). By the way, it would be nice if you search the group before you post. Your question is fairly common. A valuable source of information is the FAQ (just google "comp.dsp faq"). You can find some links below that address this subject of sampling: http://en.wikipedia.org/wiki/Sampling_%28signal_processing%29 http://en.wikipedia.org/wiki/Sampling_rate http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem Good luck, Sergio
Reply by ●January 4, 20072007-01-04
einsteinhelpme@yahoo.com wrote:> ... You should normally use a much higher sampling frequency > (let's say five times or more the highest frequency of your wave).Try to tell that to the people who make compact disks. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●January 4, 20072007-01-04
Ted wrote:> Dear Group, > > I have an elementary question. If a sine-wave is sampled such that the > samples fall at the times when the value of the wave is zero (meaning > at 0 and pi). > > The sampling frequency thus is twice the frquency of the wave. Is this > proper sampling ? How can we reconstruct such a signal ? Of course the > power of the signal is non-zero. Is that sufficient to prove that the > input signal is a sine wave having frequency as half the sampling > frequency? > > TYHello Ted, in this case with a train of zeroes, nothing gets reconstructed. If you have a phase offset between the sampling and the sine, where your data becomes a,-a,a,-a,a,-a,..., then "ideal" reconstruction will yield a cosine with amplitude a. See my following paper on how the ideal reconstruction creates a cosine. Of course in the real world with real world limitations, you won't "get there." Clay http://www.claysturner.com/dsp/nyquist.pdf
Reply by ●January 4, 20072007-01-04
Ted wrote:> Dear Group, > > I have an elementary question. If a sine-wave is sampled such that the > samples fall at the times when the value of the wave is zero (meaning > at 0 and pi). > > The sampling frequency thus is twice the frquency of the wave. Is this > proper sampling ? How can we reconstruct such a signal ? Of course the > power of the signal is non-zero. Is that sufficient to prove that the > input signal is a sine wave having frequency as half the sampling > frequency?Fs/2 doesn't alias, so it needn't be removed from the signal that gets sampled, and it is not strictly less than Fs/2, so there's no "obligation" to reconstruct it. If the signal has a slightly different phase, a cosine of some amplitude would appear, but an ideal output filter would remove any signal not strictly less than Fs/2. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●January 4, 20072007-01-04
Jerry Avins <jya@ieee.org> wrote in news:9sGdnbJKWL8yjgDYnZ2dnUVZ_vqpnZ2d@rcn.net:> Ted wrote: >> Dear Group, >> >> I have an elementary question. If a sine-wave is sampled such that the >> samples fall at the times when the value of the wave is zero (meaning >> at 0 and pi). >> >> The sampling frequency thus is twice the frquency of the wave. Is this >> proper sampling ? How can we reconstruct such a signal ? Of course the >> power of the signal is non-zero. Is that sufficient to prove that the >> input signal is a sine wave having frequency as half the sampling >> frequency? > > Fs/2 doesn't alias, so it needn't be removed from the signal that gets > sampled, and it is not strictly less than Fs/2, so there's no > "obligation" to reconstruct it. If the signal has a slightly different > phase, a cosine of some amplitude would appear, but an ideal output > filter would remove any signal not strictly less than Fs/2. > > JerryAgreed. If you'd like to talk about "practical" aspects, a nyquist a hair above signal bandwidth isn't what one should shoot for, anyway. -- Scott Reverse name to reply
Reply by ●January 4, 20072007-01-04
Ted wrote:> Dear Group, > > I have an elementary question. If a sine-wave is sampled such that the > samples fall at the times when the value of the wave is zero (meaning > at 0 and pi). > > The sampling frequency thus is twice the frquency of the wave. Is this > proper sampling ? How can we reconstruct such a signal ? Of course the > power of the signal is non-zero. Is that sufficient to prove that the > input signal is a sine wave having frequency as half the sampling > frequency? > > TY >http://www.wescottdesign.com/articles/Sampling/sampling.html -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●January 4, 20072007-01-04
PeteS wrote:> Ted wrote: > >>Dear Group, >> >>I have an elementary question. If a sine-wave is sampled such that the >>samples fall at the times when the value of the wave is zero (meaning >>at 0 and pi). >> >>The sampling frequency thus is twice the frquency of the wave. Is this >>proper sampling ? How can we reconstruct such a signal ? Of course the >>power of the signal is non-zero. Is that sufficient to prove that the >>input signal is a sine wave having frequency as half the sampling >>frequency? >> >>TY > > > This subject gets a regular thrashing :) > > See this thread: > http://groups.google.com/group/comp.arch.embedded/browse_thread/thread/b8a58d07e0e3f968/0fd20e416fb2756d?q=what+nyquist+didn%27t+say&lnk=ol& > > Cheers > > PeteS >Or the article that fell out of it: http://www.wescottdesign.com/articles/Sampling/sampling.html -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html
