Solving DSP problem
in [DSP]
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From: Jerry Avins on 18 Jan 2010 13:40 Tim Wescott wrote: > On Mon, 18 Jan 2010 09:25:50 -0600, Richello wrote: > >> Dear Sir, >> >> Could you please help me to solve this or give me hints to do so? >> >> An analogue signal x(t)=10cos(500πt) is sampled at 0, T,2T, .... with >> T=1ms. >> >> I want to find a cosine y(t), whose frequency is as close as possible to >> that of x(t), which when sampled with T=1ms yields the same sample >> values as x(t). how can I get the equation of y(t)? .. then if x(nT) >> were the input to a D/A converter, followed by a low-pass smoothing >> filter, why would the output be x(t) and not y(t) ? > > 1: The solution as you state the problem is trivial: y(t) = x(t). I > assume you mean the frequency should be close to but different. > > 2: Have you asked your prof? > > 3: Read this: http://www.wescottdesign.com/articles/Sampling/ > sampling.html. Skip down to the part about aliasing. First, fix the link: http://www.wescottdesign.com/articles/Sampling/sampling.html I'm puzzled by Tim's reference to aliasing. The frequency is 250 Hz and the sample rate is 1000 Hz. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
From: Tauno Voipio on 18 Jan 2010 14:38 Tim Wescott wrote: > On Mon, 18 Jan 2010 16:00:18 +0000, invalid wrote: > >> "Tim Wescott" <tim(a)seemywebsite.com> wrote in message >> news:JfmdnWt5A4KS4snWnZ2dnUVZ_uBi4p2d(a)web-ster.com... >>> 3: Read this: http://www.wescottdesign.com/articles/Sampling/ >>> sampling.html. Skip down to the part about aliasing. >> Rejects attempts to read with error 403 > > Your newsreader (or mine) put the last bit on the following line. > > Try this one, all one line from the 'http' to the following 'html': > http://www.wescottdesign.com/articles/Sampling/sampling.html. Next time, please put the URL in angle brackets: <http://www.wescottdesign.com/articles/Sampling/sampling.html>. -- Tauno Voipio
From: Tim Wescott on 18 Jan 2010 15:36 On Mon, 18 Jan 2010 13:40:37 -0500, Jerry Avins wrote: > Tim Wescott wrote: >> On Mon, 18 Jan 2010 09:25:50 -0600, Richello wrote: >> >>> Dear Sir, >>> >>> Could you please help me to solve this or give me hints to do so? >>> >>> An analogue signal x(t)=10cos(500πt) is sampled at 0, T,2T, .... with >>> T=1ms. >>> >>> I want to find a cosine y(t), whose frequency is as close as possible >>> to that of x(t), which when sampled with T=1ms yields the same sample >>> values as x(t). how can I get the equation of y(t)? .. then if x(nT) >>> were the input to a D/A converter, followed by a low-pass smoothing >>> filter, why would the output be x(t) and not y(t) ? >> >> 1: The solution as you state the problem is trivial: y(t) = x(t). I >> assume you mean the frequency should be close to but different. >> >> 2: Have you asked your prof? >> >> 3: Read this: http://www.wescottdesign.com/articles/Sampling/ >> sampling.html. Skip down to the part about aliasing. > > First, fix the link: > http://www.wescottdesign.com/articles/Sampling/sampling.html > > I'm puzzled by Tim's reference to aliasing. The frequency is 250 Hz and > the sample rate is 1000 Hz. > > Jerry He's asking for a continuous-time signal (presumably not identical to the given one) that gives the same discrete-time signal after sampling. That sounds like aliasing to me. It sounds like a _homework problem_ about aliasing. One I might write were I teaching a signal processing course, I might add. -- www.wescottdesign.com
From: Jerry Avins on 18 Jan 2010 15:49 Tauno Voipio wrote: > Tim Wescott wrote: >> On Mon, 18 Jan 2010 16:00:18 +0000, invalid wrote: >> >>> "Tim Wescott" <tim(a)seemywebsite.com> wrote in message >>> news:JfmdnWt5A4KS4snWnZ2dnUVZ_uBi4p2d(a)web-ster.com... >>>> 3: Read this: http://www.wescottdesign.com/articles/Sampling/ >>>> sampling.html. Skip down to the part about aliasing. >>> Rejects attempts to read with error 403 >> >> Your newsreader (or mine) put the last bit on the following line. >> >> Try this one, all one line from the 'http' to the following 'html': >> http://www.wescottdesign.com/articles/Sampling/sampling.html. > > Next time, please put the URL in angle brackets: > <http://www.wescottdesign.com/articles/Sampling/sampling.html>. Whether that helps or not depends on the sending newsreader. Thunderbird doesn't break any line without delimiter. (Space and dash are delimiters.) Here's a URL: http://www.google.com/search?q=http%3A%2F%2Fwww.cartalk.com%2Fcontent%2Fpuzzler%2Ftranscripts%2F201002%2Fanswer.html&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a and here's a jumk line: ######################################################################################################## Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
From: Jerry Avins on 18 Jan 2010 15:51
Tim Wescott wrote: > On Mon, 18 Jan 2010 13:40:37 -0500, Jerry Avins wrote: > >> Tim Wescott wrote: >>> On Mon, 18 Jan 2010 09:25:50 -0600, Richello wrote: >>> >>>> Dear Sir, >>>> >>>> Could you please help me to solve this or give me hints to do so? >>>> >>>> An analogue signal x(t)=10cos(500πt) is sampled at 0, T,2T, .... with >>>> T=1ms. >>>> >>>> I want to find a cosine y(t), whose frequency is as close as possible >>>> to that of x(t), which when sampled with T=1ms yields the same sample >>>> values as x(t). how can I get the equation of y(t)? .. then if x(nT) >>>> were the input to a D/A converter, followed by a low-pass smoothing >>>> filter, why would the output be x(t) and not y(t) ? >>> 1: The solution as you state the problem is trivial: y(t) = x(t). I >>> assume you mean the frequency should be close to but different. >>> >>> 2: Have you asked your prof? >>> >>> 3: Read this: http://www.wescottdesign.com/articles/Sampling/ >>> sampling.html. Skip down to the part about aliasing. >> First, fix the link: >> http://www.wescottdesign.com/articles/Sampling/sampling.html >> >> I'm puzzled by Tim's reference to aliasing. The frequency is 250 Hz and >> the sample rate is 1000 Hz. >> >> Jerry > > He's asking for a continuous-time signal (presumably not identical to the > given one) that gives the same discrete-time signal after sampling. That > sounds like aliasing to me. > > It sounds like a _homework problem_ about aliasing. One I might write > were I teaching a signal processing course, I might add. Got it. I would have worded it differently, though. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ |