Solving DSP problem
in [DSP]
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From: Eric Jacobsen on 21 Jan 2010 13:13 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), 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
From: Eric Jacobsen on 21 Jan 2010 13:08 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), 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
From: glen herrmannsfeldt on 21 Jan 2010 14:43 Jerry Avins <jya(a)ieee.org> wrote: (snip) > Nitpick: acetylsalicylic acid. I remember an ad for an "Amazing New > Analgesic Discovery!": sodium acetylsalicylate. The FTC had the ad pulled. For some reason, I remember it every time except when writing that post. -- glen
From: dvsarwate on 21 Jan 2010 15:46 On Jan 21, 10:06 am, Jerry Avins <j...(a)ieee.org> wrote: > > Nitpick: acetylsalicylic acid. I remember an ad for an "Amazing New > Analgesic Discovery!": sodium acetylsalicylate. The FTC had the ad pulled.. > Perhaps the FTC acted in response to complaints from the makers of Preparation H? Oh, really? That's *not* what analgesic means? :-)
From: Richard Owlett on 21 Jan 2010 17:28
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) > 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. > > |