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) ?
Solving DSP problem
Started by ●January 18, 2010
Reply by ●January 18, 20102010-01-18
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. -- www.wescottdesign.com
Reply by ●January 18, 20102010-01-18
"Tim Wescott" <tim@seemywebsite.com> wrote in message news:JfmdnWt5A4KS4snWnZ2dnUVZ_uBi4p2d@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
Reply by ●January 18, 20102010-01-18
On Mon, 18 Jan 2010 16:00:18 +0000, invalid wrote:> "Tim Wescott" <tim@seemywebsite.com> wrote in message > news:JfmdnWt5A4KS4snWnZ2dnUVZ_uBi4p2d@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 403Your 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. -- www.wescottdesign.com
Reply by ●January 18, 20102010-01-18
On 18/01/2010 16:00, invalid wrote:> "Tim Wescott"<tim@seemywebsite.com> wrote in message > news:JfmdnWt5A4KS4snWnZ2dnUVZ_uBi4p2d@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 > >Watch for line-wrap. The URL ends with "/sampling.html". Very common problem! Richard Dobson
Reply by ●January 18, 20102010-01-18
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. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●January 18, 20102010-01-18
Tim Wescott wrote:> On Mon, 18 Jan 2010 16:00:18 +0000, invalid wrote: > >> "Tim Wescott" <tim@seemywebsite.com> wrote in message >> news:JfmdnWt5A4KS4snWnZ2dnUVZ_uBi4p2d@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
Reply by ●January 18, 20102010-01-18
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. > > JerryHe'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
Reply by ●January 18, 20102010-01-18
Tauno Voipio wrote:> Tim Wescott wrote: >> On Mon, 18 Jan 2010 16:00:18 +0000, invalid wrote: >> >>> "Tim Wescott" <tim@seemywebsite.com> wrote in message >>> news:JfmdnWt5A4KS4snWnZ2dnUVZ_uBi4p2d@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. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●January 18, 20102010-01-18
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. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
