Solving DSP problem
in [DSP]
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From: Eric Jacobsen on 21 Jan 2010 18:31 On 1/21/2010 3:28 PM, Richard Owlett wrote: > Eric Jacobsen wrote: >> On 1/21/2010 8:14 AM, Tim Wescott wrote: >>> On Wed, 20 Jan 2010 23:55:54 -0800, Andor wrote: >>> >>>> On 19 Jan., 19:45, Tim Wescott<t...(a)seemywebsite.com> wrote: >>>>> On Mon, 18 Jan 2010 23:06:30 -0800, Andor wrote: >>>>>> On 18 Jan., 22:58, Tim Wescott<t...(a)seemywebsite.com> wrote: >>>>>>> On Mon, 18 Jan 2010 15:51:21 -0500, Jerry Avins wrote: >>>>>>>> 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. >>>>>>> I would have worded it differently, too. A set of homework problems >>>>>>> that doesn't contain at least one veiled reference to Bart Simpson, >>>>>>> Batman, Diogenes, Gilligan, or some other major philosopher is a >>>>>>> minor failure, IMHO. >>>>>> Cool - can you reword the OPs problem in that vein? >>>>> I've got it: >>>>> >>>>> Gilligan has sprung a net trap set by natives from the next island >>>>> over; the trap is hung from a tall tree branch, and Gilligan is >>>>> swinging over a small clearing with a period of oscillation of 5 >>>>> seconds (0.2Hz). >>>>> >>>>> The Skipper has also been captured and blindfolded and is being held >>>>> nearby. Every two seconds exactly he manages to pull off the blindfold >>>>> and see Gilligan, but his captors immediately replace the blindfold >>>>> each time. >>>>> >>>>> What is the _closest_ (but not identical) period of oscillation at >>>>> which Gilligan could be swinging such that the Skipper would see >>>>> exactly the same period of oscillation given how often he pulls off >>>>> his >>>>> blindfold? >>>>> >>>>> For extra credit: >>>>> >>>>> The Skipper escapes, and runs to the Professor to explain Gilligan's >>>>> dilemma (including the timing, of course). The Professor (having taken >>>>> signal processing courses along with everything else), knows that >>>>> there >>>>> are two likely periods to the swing, and thus knows the two possible >>>>> lengths of the rope from which Gilligan is suspended (he ignores the >>>>> mass of the rope and assumes the tree is infinitely rigid). >>>>> >>>>> Assuming that the professor gets his math right, how long are his two >>>>> calculated rope lengths? >>>> :-) >>>> >>>> Unfortunately, I don't know Gilligan. Wikipedia has an article about a >>>> sitcom called Gilligan's Island, which I guess you are refering to. >>>> Sounds like an older version of "Lost" ... >>> >>> Well, perhaps if you take all the 'spooky wierd' parts of "Lost" and >>> replace them with 'goofy funny'. >>> >>> "Gilligan's Island" was basic slapstick comedy, set up by the idea that >>> you had seven random US citizens shipwrecked on a Pacific island, driven >>> forward by the fact that the characters that considered themselves in >>> charge and competent weren't, and leavened by the presence of Gilligan, >>> who was a classic clown. >> >> It remains as a big part of Americana culture (at least for a few >> generations for which it was relevant) because of several >> characteristics that made it quite memorable. One was the assembly of >> characters who represented a pretty broad spectrum of society, and >> their interaction with each other in "surviving" on the island in >> their own ways. >> >> An example was the Howell's, a wealthy, high-society couple who >> happened to bring large trunks of clothing and supplies with them, >> despite the premise of the show that it was only "a three hour tour". >> Who brings luggage for a three-hour tour? It's that level of silliness >> that defines the whole adventure. >> >> The professor provided the detailed technical knowledge (about >> ANYTHING) to help them make inventions to survive without much change >> in overall lifestyle. >> >> Then there was Ginger and Mary Ann, two young, highly attractive women >> who provided all sorts of nice plot possibilities, not to mention eye >> candy. For decades a common cultural question here is "Ginger or Mary >> Ann?", and the respondent is expected to explain which they preferred >> and why. >> >> For the most part, though, it was the typical network easy laugh >> comedy of the day (Beverly Hillbillies was another), > > A valid comparison????? > I could see "Beverly Hillbillies" as social commentary a la Jonathan > Swift. (eg Jed's and Grandma's comments) Fair enough. I did like Beverly Hillbillies a lot more than Gilligan, and on the rare occasion that I catch one of the reruns these days I'd probably actually stick around for a BH episode. The humor was a bit edgier with the social commentary aspect that you mention. >> that was just cheap entertainment. When compression algorithms started >> getting pretty good about twenty-five years ago there was a discussion >> about the general theory that the relationship of real information >> content to total entropy could be used to yield pretty high >> compression ratios. A joke example was that it was estimated that all >> of the Gilligan's Island episodes together could be compressed down to >> a single 8kx8 ROM. >> >> -- Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com |