Re:BEAM is the Cold Fusion of Robotics
on
The Robot Diaries
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· Score: 1
If you would have read the previous comments, you would have found your answer for examples of tasks existing autonomous robots currently do.
BEAM can potentially do anything given a sufficiently complex reactive system. "What have they done?" is the question that I have been posing but have yet to get a serious response. And so given the current state of BEAM, what does it have that will allow it to advance more than normal layered architecture autonomous robots?
What does Tilden have that Brooks failed to deliver on?
In some. I dare you to suggest that 0.001% of obese people (I know that is a huge number of people... Americans being fat tubs of lard and all) have mental illnesses that prevent them from stopping their eating. But for these 0.001% of the people, I say eat all you want! Fill up you fat face. But when you're through, join me in the gym. I doubt think those 0.001% of people that can't stop eating are also the exact same 0.001% of obese people that are allergic to exercise.
Here's my favorite line from my obese adminitrative assistant (a.k.a secretary). "Yeah, I work out. I go to the gym once every other week." Or my other favorite but unrelated was "I'm going to the bank to pay my car loan. It's the American way, right?"
Re:BEAM is the Cold Fusion of Robotics
on
The Robot Diaries
·
· Score: 1
Read my other comment on this topic.
I have been reading about BEAM for many years. I have read plenty of articles about Tilden, gone though many of web pages from BEAM hobbyist and talked to many people. I am still not convinced.
You ever hear the phrase "Extraordinary Claims Demand Extraordinary Proof?" I and thousands of other scientists are waiting for the proof. I know what the robotics community at large can deliver. I've seen much of it and have been involved in it myself. Now I'm waiting to see if Tilden can do better. Brooks with all his media attention and outspoken views and brilliant students could not.
REAL scientists ARE naysayers until they are proven wrong. I dare you to prove me wrong.
I have seen the core circuit of many BEAM robots. How many of the BEAM hobbyists really understand the circuits versus how many copy and then tinker?
Re:BEAM is the Cold Fusion of Robotics
on
The Robot Diaries
·
· Score: 1
Wait a second.. you're trying to impress me with Tilden's robots that can push around moon dust? Or by Tilden's wandering lawnmower? See... that's why I don't get about BEAM. If you're going to impress me, impress me with something that NO OTHER ROBOTIC ARCHITECTURE CAN DO. Is Tilden pushing for reactive robotics? Plenty of people have already put reactive controls on their robots. Is he going for low power consumption? That I could believe if it were not for plenty of other low power devices that are available. You know not all robots have huge amounts of processing power on board. Most of those could easily strap on a solar cell and cyclically charge and move.
Talk the talk, walk the walk, eh? Where are applications of Tilden's robots where the primary task is not accomplished by wandering. His "land-mine finding robots" do just this, walk until they're blown up. His moon dust pushing robot does this just wanders and moves/picks up dust as a side-effect. His lawn mower just wanders around with a cutting blade. This is getting pretty monotonous.
In case you haven't heard since you're not involved in the general robotics field, there's a whole area of robotics called autonomous robotics. Autonomous basically means self controlled. You create it, put it somewhere and it just does what it's supposed to do.
You ever hear of the expression never get into a pissing contest with a skunk? My research in fact was autonomous mobile robotics using robots we designed within our university group. They were small... under 125 cubic centimeters. They could act independently or cooperatively. They could also communicate with a homebase CPU if necessary to upload sensed data. I and plenty of others can deliver. It's not that hard.
The way BEAM delivers is like if I went to a toy store, found a toy car with motors, added a solar cell, added a few components to charge and discharge the capacitor to drive the motors and tada! I have suddenly have a BEAM robot that can do anything! It can drive into a volcano... it can drive on mars... it can drive around a hospital. Give me a break.
So now since you say BEAM is not about performing mundane tasks (have you ever seen the etymology of the word robot?)... what kind of tasks (specific examples) is BEAM about and for extra points, what kind of tasks has BEAM been used for?
I think you don't know most roboticists and you have not read enough about the many very well known robot architectures. It is VERY well known that there is a spectrum of robot architectures from the most reactive (Brooks or Tilden) to the most computational/case based. To say that every little detail has to be programmed it is clear that you also have NEVER programmed a robot.
BEAM is the Cold Fusion of Robotics
on
The Robot Diaries
·
· Score: 2
Sorry BEAM lovers but it just doesn't work. Maybe I'm biased, I have a graduate degree from doing robotics research at a very well known university.
BEAM robotics are interesting from nothing more than an analog circuit perspective. I'll give you that. They are not solving any problems that real robotics professionals and researchers are trying to solve. I do not consider Mark Tilden to be a robotics researcher any more than I consider a computer technician to be an electrical engineer. Until I can see a BEAM robot that does more than scamper around... until I see a BEAM robot that can play soccer... until I see a BEAM robot that cooperate with another BEAM robot... until I see a BEAM robot walk into a volcano, drive on mars, navigate a hospital, retrieve books in a library... I don't want to hear about BEAM
Maybe I'm closed minded, I have seen alot of stuff in my days but I will not be a believer until Mark Tilden can demonstrate more useful functionality. BTW did you all hear that Tilden is moving to software control? He's retreating from the "robustness" of his analog core and realizing how limited it is without higher level control. A reactive low-level is almost universally accepted as a standard part of robot architectures but useful work often needs the upper level control.
That is... they are deterministic finite state machines. Install Windows and bam! you have a nondeterministic finite state machine! Who ever said Microsoft didn't innovate?
Having DNS or whatever not run as root adds one level to a system crack. So I can't get a remote root through DNS? Fine... I'll get remote nobody. Then I'll use a local hole.
You are barking down the wrong tree on this one. His problems clearly revolved around Win2k and other than a compatibility issue with his modem and Windows blowing away his Linux partition, his linux installation sounds like it is working fine.
While I personally expect laptops to be less stable than desktops, I do not think in this case his HP laptop was so much an issue as his installation and configuration of Win2k for it.
If you did your homework you would realize Deep Blue was originally called Deep Thought when it was developed at CMU. IBM did work on chess computer and eventually renamed it Deep Blue. So Deep Blue was its name when it beat Kasparov but Deep Thought is really the same thing.
As for Kasparov... you mean Kasparov had to publish all of his private practice sessions and give them to IBM? Nope... let's put it this way... all of Kasparov's public games were known. All of Deep Blue's public games were known. What they did to practice for the event was unknown. Where is the problem? If I have a game with Kasparov and I am unrated, just joined FIDE and have no public games... and win (it's possible!!!) does that mean I didn't deserve to win? Personally I think Kasparov did not win because he tried to out think Deep Blue and its programmers... kind of like reverse-reverse psychology. He did not play like he would with a human opponent (but then most people realize you often have to play differently with a computer).
Now I absolutely agree that Deep Blue is a nearly worthless effort if their only goal was to beat Kasparov. It has no tact and is a brute force approach to a elegant game. The human mind such as Kasparov's is tuned to such precision that research into how the brain learns I believe is many times more important than trying to find the best way to brute force a game. Uh... but then I supposed the brain is itself a sort of brute-force mechanism with 100 billions neurons. Who knows if the development of large scale parallel computation systems like Deep Blue will eventually lead to developments as inredible as the brain.
The operating system is the least that concerns me. I am much more worried about the students that are at the mercy of the "educators" who decided that laptops are beneficial to students. I doubt the study you were in was the only one of it's kind and I doubt the research found a benefit to having laptops. I think these studies are very important. I sure as hell wouldn't lug it around to my classes and worry about taking notes on it. I went to a very good university for undergrad and grad school (it was a top engineering school) and never once had to bring a textbook to class except for one of my humanities classes. Digital books I could do without. Give me a paper and a pencil and a good teacher.
Blame Canada! If you would get off your lazy canuck ass and read the article you'd realize that we are talking about a government stating that all public university students within the state need laptops. This is completely different from an insignificant unknown private university in Canada. Do you think Acadia was the first university ever to require students have laptops? I hope you aren't that blind.
I also feel sorry for your students hearing that your math students use Maple. Maple and Matlab are far more useful to non-mathematicians. Most universities I know of treat math students to Mathematica. The standard software package for pure mathematics. Maple and Matlab are incredibly useful and should be required in the Physics as well as Engineering programs. It's too bad your school is so far behind.
I use vi and xemacs. One is faster, one has better features. You obviously have chosen your camp.
Just about the only thing you need to worry about with cables is to match impedance. Effects of resistance and capacitance of the cable are the least of your problems if you have a SWR >> 1. With a properly matched cable, impedance within the operating frequency is virtually constant.
Ok, here's the short, short version. Both of my previous attempts to reply haven't gone though. Your spice simulation is using something called sample-and-hold (zero-order-hold). You need a very specific magnitude and phase response of the low-pass filter to get the right output waveform. But if you sample using only delta functions, you can use any old simple filter (i.e. butterworth). If you have access to MATLAB, try playing with fft. If you still don't understand the flaws in your simulation, I'll explain further (or even put together a matlab script to demonstrate).
Don't you forget the difference between theorem and theory!
Theory: hypothesis assumed for the sake of argument or investigation b : an unproved
assumption : CONJECTURE c : a body of theorems presenting a concise systematic
view of a subject
Theorem: an idea accepted or proposed as a demonstrable truth often as a part of a general
theory : PROPOSITION
A theorem is PROVEN based on the validity of axioms. Like a+0 = a is an axiom of mathematics. Therefore my theorem of 3+0 = 3 is PROVEN by substituting 3 for a in the axiom... 3+0 = 3 is not a theory.
Again, theorems are proven to hold true if axioms hold true (like a*0=0 or a*1=a). Theories are hypothesis supported by evidence but not proven. Nyquist's Theorem is a Theorem. BTW what is your educational background? Just wondering...
Maybe you should read that DSP book (by the way Oppenheim & Willsky is not a DSP book, it is a simple signals/systems book... a very common undergraduate electrical engineering textbook). Ok, this may be counter-intuitive because you obviously have had no formal education in signal processing but that triangle wave you drew has actually has many, many frequencies higher than the frequency that you are talking about. How can that be? If you low-pass filter the triangle wave (basically it means smoothing out all the edges) what do get? You get a sine wave exactly like the one you first drew. I suggest you learn a little more about fourier analysis before posting about things like this.
Site A
Site B: http://www.eeap.aston.ac.uk/
teltec/tutorials/Digital%20Baseband%20Transmission /Slides/nyquist%20theorem.htm
Site C
Ok, I thought I had already explained the problem with Site A but here it goes...
First see where he says "the sampling rate here is below the Nyquist frequency" with respect to the first picture? He is wrong. Count the samples from left to right. There are seven samples in the first three periods of the sine wave.
Let's say that each vertical line is 1us. The sampling frequency is (1/10^(-6)) 1MHz. The frequency of the sine wave is (3/(7*10^(-6))) 428.571kHz.
Ok now that you realize he has no idea what he's talking about, look at his bottom picture. He actually thinks that the waveform produced after reconstruction is that jagged edged horrid looking thing. That waveform has tons of high frequency components. If he would understand that #1 those samples are not connect the dots. And #2 whatever waveform you reproduce must be low-pass filtered so those jagged edges should never be there. You'll find that the result is exactly the same sine wave you sampled.
Next he explains the waveform he produced as "aliasing" which again he is completely wrong. Aliasing is the result of a signal being sampled at too low a frequency but it has NOTHING to do with his web page. If you look at the corrrected URL for Site B (I added a reply to my post because/. added an extra space because the URL was too long) you can see where the bell-shaped things are overlapping. That is aliasing. Did you actually believe what you read about Site A after my first comment?
Now to Site C! First of all, Nyquists theorem states that the sampling frequency must be greater than the highest frequency in the sample (look it up!). So your argument about the samples being exactly on all the zero-crossings is irrelevant and incorrect.
Now in the actual site, that first picture is misleading because the waveform on the left is not a sinusoid. It is just something he hacked together in a paint program. It doesn't have the right slopes. The waveform on the right does look like a sinusoid. Now where I said this guy was thinking in the time-domain instead of the frequency-domain... when he said "sampling long enough doesn't work for real live video" he is misunderstanding that that even the most complex waveform can be made periodic by simply stating that the period is infinitly long. It's called Fourier Transform (as opposed to Fourier Series). You resultantly get infinite frequencies but if you cutoff, you are getting virtually the exactly same waveform since the high frequency components are so small.
His "good news" section is even worse. He draws pictures of the sampled waveform in two ways. In the middle he connects the dots and makes the same error as Site A. He doesn't low-pass filter the waveform. Oh, maybe I should explain what low-pass filtering is... if you go to Site B, low-pass filtering throws away all those bell shaped things except the one centered at 0, the middle one. If he low-pass filtered the middle or right waveform he would get EXACTLY the same waveform as the one on the left. There was a nother poster somewhere in this thread that actually did exactly what we are talking about by sampling a waveform, reproducing it with "sample-and-hold" and then low-pass filtering. You'll be surprised at the results he got (I was not).
The more samples/cycle means it is easier to reproduce the waveform they originally sampled because it is easier to design a low-pass filter when the (again go to Site B) space between those bell-shaped things is larger.
Ok, for some reason,/. doesn't like the long URL from Site B so here it is... broken into two lines:
http://www.eeap.aston.ac.uk/
teltec/tutorials/Digital%20Baseband%20Transmission /Slides/nyquist%20theorem.htm
Ok, Chris... I replied to one of your posts and I thought you at least had a clue of what your were talking about. And then I see this post. I'm sorry but you have no understanding of digital signal processing and fourier series. I mean this whole-heartedly that you are missing the fundmental mathematical concepts to understand why a 14.7kHz sine wave can be perfectly reproduced with 44.1kHz sampling and the appropriate filter.
For your education I pulled a couple links from the web:
Site A has two pictures of a sine wave being sampled. This web page is totally wrong. They do not understand aliasing... that picture they are showing with the straight lines shows the reason that you need to have a low-pass filter. With the appropriate low-pass filter, there sine wave in the above picture will be reproduced exactly.
Site B shows the frequency domain. You're probably seen a similiar plot of the horizontal axis being frequency and vertical axis being magnitude. Don't worry about the math if you don't understand it. Just look at the pictures. The top picture shows the sampling period being less than half the period of the highest frequency in the original signal (the bell shaped thing centered at frequency 0. This is like your 14.7kHz sine wave sampled at 44.1kHz. The second is when the period of sampling T equals half the period of the highest frequency (see how the edges of that waveform exactly touch each other?). The bottom picture shows what happens when the sampling period is greater than half the period of the highest frequency. That portion of the bell shaped thing that overlaps one another is sampling noise. In other words everything that is overlapping is lost.
Site C is another site that does not understand nyquist's theorem. They are completely thinking in terms of the time domain instead of the frequency domain. Not to mention that they don't realize you always have to low-pass filter a sampled signal.
Site D actually is correct and should be understandable to even the least mathematically inclined.
You're 100% right. 16 bits is not enough for mastering and mixing. The intermediate values of the mixing must be preserved as accurately as possible to ensure the best possible final result. When the final output is obtained, 16 bits may be enough for listening to. I don't know where your statement about an undigitized output and the 16 bit quantized output is coming from though. I don't think anyone has ever said that the result of 16 bit sampling can exactly reproduce the undigitized output. But are you asserting that the difference is a really big audible difference?
As for the 44.1kHz? If the audio is already sampled at 44.1kHz, you'd better have a serious cutoff at 22kHz or else you're getting alot more distortion at higher frequencies. What exactly are you talking about when you say that amp designers go for pass band into the MHz? If there is any power above 22kHz it is purely noise (that is if the input is a CD, LP is arguable at this point). Now is the higher sampling frequency better? Of course! Just like the 24bit sampling, it makes it easier to reproduce high quanlity recordings.
You seem to be quite an audiophile. I am not. But I wonder, have you ever really tested the validity of your gut feeling about these technologies. I feel that your statements are an amalgam of audiophile "common knowledge" but don't represent the physics and mathematics of sounds and frequency analysis.
The Capability Maturity of Mozilla looks good.
on
Send Some Mo' Zilla
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· Score: 1
Mozilla's designated "Chief Lizard Wrangler" seems pleased with the maturity level the organization's two-and-a-half-year-old pet project has achieved.
Mitchell Baker, whose other titles on the mozilla.org Web site include "manager, problem arbitrator, and speaker to suits," recounted recent happenings within the organization and described some of the development criteria and expectations that will shape Mozilla's 1.0 release.
In keeping with its new roadmap, the new and improved browser is scheduled for its 1.0 release in the second quarter of 2001. "Mozilla 1.0 will, of course, include the features developed for the browser/mail/news application," she said. "Enhanced performance, reduced footprint, improved stability, and architectural correctness and even better standards compliance are additional goals for Mozilla 1.0."
These features are important to Mozilla's present role--and vital to its expansion into new areas, Baker said. "These aspects are important not only to those interested in the browser/mail/news application, but also to that portion of the Mozilla community that is interested in embedding the Mozilla layout engine in other applications and devices, often in combination with a Linux distribution," she added.
Slashdot Mirror
If you would have read the previous comments, you would have found your answer for examples of tasks existing autonomous robots currently do.
BEAM can potentially do anything given a sufficiently complex reactive system. "What have they done?" is the question that I have been posing but have yet to get a serious response. And so given the current state of BEAM, what does it have that will allow it to advance more than normal layered architecture autonomous robots?
What does Tilden have that Brooks failed to deliver on?
In some. I dare you to suggest that 0.001% of obese people (I know that is a huge number of people... Americans being fat tubs of lard and all) have mental illnesses that prevent them from stopping their eating. But for these 0.001% of the people, I say eat all you want! Fill up you fat face. But when you're through, join me in the gym. I doubt think those 0.001% of people that can't stop eating are also the exact same 0.001% of obese people that are allergic to exercise.
Here's my favorite line from my obese adminitrative assistant (a.k.a secretary). "Yeah, I work out. I go to the gym once every other week." Or my other favorite but unrelated was "I'm going to the bank to pay my car loan. It's the American way, right?"
Read my other comment on this topic.
I have been reading about BEAM for many years. I have read plenty of articles about Tilden, gone though many of web pages from BEAM hobbyist and talked to many people. I am still not convinced.
You ever hear the phrase "Extraordinary Claims Demand Extraordinary Proof?" I and thousands of other scientists are waiting for the proof. I know what the robotics community at large can deliver. I've seen much of it and have been involved in it myself. Now I'm waiting to see if Tilden can do better. Brooks with all his media attention and outspoken views and brilliant students could not.
REAL scientists ARE naysayers until they are proven wrong. I dare you to prove me wrong.
I have seen the core circuit of many BEAM robots. How many of the BEAM hobbyists really understand the circuits versus how many copy and then tinker?
Wait a second.. you're trying to impress me with Tilden's robots that can push around moon dust? Or by Tilden's wandering lawnmower? See... that's why I don't get about BEAM. If you're going to impress me, impress me with something that NO OTHER ROBOTIC ARCHITECTURE CAN DO. Is Tilden pushing for reactive robotics? Plenty of people have already put reactive controls on their robots. Is he going for low power consumption? That I could believe if it were not for plenty of other low power devices that are available. You know not all robots have huge amounts of processing power on board. Most of those could easily strap on a solar cell and cyclically charge and move.
Talk the talk, walk the walk, eh? Where are applications of Tilden's robots where the primary task is not accomplished by wandering. His "land-mine finding robots" do just this, walk until they're blown up. His moon dust pushing robot does this just wanders and moves/picks up dust as a side-effect. His lawn mower just wanders around with a cutting blade. This is getting pretty monotonous.
In case you haven't heard since you're not involved in the general robotics field, there's a whole area of robotics called autonomous robotics. Autonomous basically means self controlled. You create it, put it somewhere and it just does what it's supposed to do.
You ever hear of the expression never get into a pissing contest with a skunk? My research in fact was autonomous mobile robotics using robots we designed within our university group. They were small... under 125 cubic centimeters. They could act independently or cooperatively. They could also communicate with a homebase CPU if necessary to upload sensed data. I and plenty of others can deliver. It's not that hard.
The way BEAM delivers is like if I went to a toy store, found a toy car with motors, added a solar cell, added a few components to charge and discharge the capacitor to drive the motors and tada! I have suddenly have a BEAM robot that can do anything! It can drive into a volcano... it can drive on mars... it can drive around a hospital. Give me a break.
So now since you say BEAM is not about performing mundane tasks (have you ever seen the etymology of the word robot?)... what kind of tasks (specific examples) is BEAM about and for extra points, what kind of tasks has BEAM been used for?
I think you don't know most roboticists and you have not read enough about the many very well known robot architectures. It is VERY well known that there is a spectrum of robot architectures from the most reactive (Brooks or Tilden) to the most computational/case based. To say that every little detail has to be programmed it is clear that you also have NEVER programmed a robot.
Sorry BEAM lovers but it just doesn't work. Maybe I'm biased, I have a graduate degree from doing robotics research at a very well known university.
BEAM robotics are interesting from nothing more than an analog circuit perspective. I'll give you that. They are not solving any problems that real robotics professionals and researchers are trying to solve. I do not consider Mark Tilden to be a robotics researcher any more than I consider a computer technician to be an electrical engineer. Until I can see a BEAM robot that does more than scamper around... until I see a BEAM robot that can play soccer... until I see a BEAM robot that cooperate with another BEAM robot... until I see a BEAM robot walk into a volcano, drive on mars, navigate a hospital, retrieve books in a library... I don't want to hear about BEAM
Maybe I'm closed minded, I have seen alot of stuff in my days but I will not be a believer until Mark Tilden can demonstrate more useful functionality. BTW did you all hear that Tilden is moving to software control? He's retreating from the "robustness" of his analog core and realizing how limited it is without higher level control. A reactive low-level is almost universally accepted as a standard part of robot architectures but useful work often needs the upper level control.
That is... they are deterministic finite state machines. Install Windows and bam! you have a nondeterministic finite state machine! Who ever said Microsoft didn't innovate?
Having DNS or whatever not run as root adds one level to a system crack. So I can't get a remote root through DNS? Fine... I'll get remote nobody. Then I'll use a local hole.
You are barking down the wrong tree on this one. His problems clearly revolved around Win2k and other than a compatibility issue with his modem and Windows blowing away his Linux partition, his linux installation sounds like it is working fine.
While I personally expect laptops to be less stable than desktops, I do not think in this case his HP laptop was so much an issue as his installation and configuration of Win2k for it.
If you did your homework you would realize Deep Blue was originally called Deep Thought when it was developed at CMU. IBM did work on chess computer and eventually renamed it Deep Blue. So Deep Blue was its name when it beat Kasparov but Deep Thought is really the same thing.
As for Kasparov... you mean Kasparov had to publish all of his private practice sessions and give them to IBM? Nope... let's put it this way... all of Kasparov's public games were known. All of Deep Blue's public games were known. What they did to practice for the event was unknown. Where is the problem? If I have a game with Kasparov and I am unrated, just joined FIDE and have no public games... and win (it's possible!!!) does that mean I didn't deserve to win? Personally I think Kasparov did not win because he tried to out think Deep Blue and its programmers... kind of like reverse-reverse psychology. He did not play like he would with a human opponent (but then most people realize you often have to play differently with a computer).
Now I absolutely agree that Deep Blue is a nearly worthless effort if their only goal was to beat Kasparov. It has no tact and is a brute force approach to a elegant game. The human mind such as Kasparov's is tuned to such precision that research into how the brain learns I believe is many times more important than trying to find the best way to brute force a game. Uh... but then I supposed the brain is itself a sort of brute-force mechanism with 100 billions neurons. Who knows if the development of large scale parallel computation systems like Deep Blue will eventually lead to developments as inredible as the brain.
The operating system is the least that concerns me. I am much more worried about the students that are at the mercy of the "educators" who decided that laptops are beneficial to students. I doubt the study you were in was the only one of it's kind and I doubt the research found a benefit to having laptops. I think these studies are very important. I sure as hell wouldn't lug it around to my classes and worry about taking notes on it. I went to a very good university for undergrad and grad school (it was a top engineering school) and never once had to bring a textbook to class except for one of my humanities classes. Digital books I could do without. Give me a paper and a pencil and a good teacher.
I also feel sorry for your students hearing that your math students use Maple. Maple and Matlab are far more useful to non-mathematicians. Most universities I know of treat math students to Mathematica. The standard software package for pure mathematics. Maple and Matlab are incredibly useful and should be required in the Physics as well as Engineering programs. It's too bad your school is so far behind.
I use vi and xemacs. One is faster, one has better features. You obviously have chosen your camp.
Ah yes I see... how very big of you to correct his spelling mistake. The world needs more educated people like you.
Just about the only thing you need to worry about with cables is to match impedance. Effects of resistance and capacitance of the cable are the least of your problems if you have a SWR >> 1. With a properly matched cable, impedance within the operating frequency is virtually constant.
Ok, here's the short, short version. Both of my previous attempts to reply haven't gone though. Your spice simulation is using something called sample-and-hold (zero-order-hold). You need a very specific magnitude and phase response of the low-pass filter to get the right output waveform. But if you sample using only delta functions, you can use any old simple filter (i.e. butterworth). If you have access to MATLAB, try playing with fft. If you still don't understand the flaws in your simulation, I'll explain further (or even put together a matlab script to demonstrate).
Theory: hypothesis assumed for the sake of argument or investigation b : an unproved assumption : CONJECTURE c : a body of theorems presenting a concise systematic view of a subject
Theorem: an idea accepted or proposed as a demonstrable truth often as a part of a general theory : PROPOSITION
A theorem is PROVEN based on the validity of axioms. Like a+0 = a is an axiom of mathematics. Therefore my theorem of 3+0 = 3 is PROVEN by substituting 3 for a in the axiom... 3+0 = 3 is not a theory.
Again, theorems are proven to hold true if axioms hold true (like a*0=0 or a*1=a). Theories are hypothesis supported by evidence but not proven. Nyquist's Theorem is a Theorem. BTW what is your educational background? Just wondering...
Maybe you should read that DSP book (by the way Oppenheim & Willsky is not a DSP book, it is a simple signals/systems book... a very common undergraduate electrical engineering textbook). Ok, this may be counter-intuitive because you obviously have had no formal education in signal processing but that triangle wave you drew has actually has many, many frequencies higher than the frequency that you are talking about. How can that be? If you low-pass filter the triangle wave (basically it means smoothing out all the edges) what do get? You get a sine wave exactly like the one you first drew. I suggest you learn a little more about fourier analysis before posting about things like this.
Site An /Slides/nyquist%20theorem.htm
Site B: http://www.eeap.aston.ac.uk/
teltec/tutorials/Digital%20Baseband%20Transmissio
Site C
Ok, I thought I had already explained the problem with Site A but here it goes...
First see where he says "the sampling rate here is below the Nyquist frequency" with respect to the first picture? He is wrong. Count the samples from left to right. There are seven samples in the first three periods of the sine wave.
Let's say that each vertical line is 1us. The sampling frequency is (1/10^(-6)) 1MHz. The frequency of the sine wave is (3/(7*10^(-6))) 428.571kHz.
Ok now that you realize he has no idea what he's talking about, look at his bottom picture. He actually thinks that the waveform produced after reconstruction is that jagged edged horrid looking thing. That waveform has tons of high frequency components. If he would understand that #1 those samples are not connect the dots. And #2 whatever waveform you reproduce must be low-pass filtered so those jagged edges should never be there. You'll find that the result is exactly the same sine wave you sampled.
Next he explains the waveform he produced as "aliasing" which again he is completely wrong. Aliasing is the result of a signal being sampled at too low a frequency but it has NOTHING to do with his web page. If you look at the corrrected URL for Site B (I added a reply to my post because /. added an extra space because the URL was too long) you can see where the bell-shaped things are overlapping. That is aliasing. Did you actually believe what you read about Site A after my first comment?
Now to Site C! First of all, Nyquists theorem states that the sampling frequency must be greater than the highest frequency in the sample (look it up!). So your argument about the samples being exactly on all the zero-crossings is irrelevant and incorrect.
Now in the actual site, that first picture is misleading because the waveform on the left is not a sinusoid. It is just something he hacked together in a paint program. It doesn't have the right slopes. The waveform on the right does look like a sinusoid. Now where I said this guy was thinking in the time-domain instead of the frequency-domain... when he said "sampling long enough doesn't work for real live video" he is misunderstanding that that even the most complex waveform can be made periodic by simply stating that the period is infinitly long. It's called Fourier Transform (as opposed to Fourier Series). You resultantly get infinite frequencies but if you cutoff, you are getting virtually the exactly same waveform since the high frequency components are so small.
His "good news" section is even worse. He draws pictures of the sampled waveform in two ways. In the middle he connects the dots and makes the same error as Site A. He doesn't low-pass filter the waveform. Oh, maybe I should explain what low-pass filtering is... if you go to Site B, low-pass filtering throws away all those bell shaped things except the one centered at 0, the middle one. If he low-pass filtered the middle or right waveform he would get EXACTLY the same waveform as the one on the left. There was a nother poster somewhere in this thread that actually did exactly what we are talking about by sampling a waveform, reproducing it with "sample-and-hold" and then low-pass filtering. You'll be surprised at the results he got (I was not).
The more samples/cycle means it is easier to reproduce the waveform they originally sampled because it is easier to design a low-pass filter when the (again go to Site B) space between those bell-shaped things is larger.
Ok, for some reason, /. doesn't like the long URL from Site B so here it is... broken into two lines:
n /Slides/nyquist%20theorem.htm
http://www.eeap.aston.ac.uk/
teltec/tutorials/Digital%20Baseband%20Transmissio
For your education I pulled a couple links from the web:
Site A has two pictures of a sine wave being sampled. This web page is totally wrong. They do not understand aliasing... that picture they are showing with the straight lines shows the reason that you need to have a low-pass filter. With the appropriate low-pass filter, there sine wave in the above picture will be reproduced exactly.
Site B shows the frequency domain. You're probably seen a similiar plot of the horizontal axis being frequency and vertical axis being magnitude. Don't worry about the math if you don't understand it. Just look at the pictures. The top picture shows the sampling period being less than half the period of the highest frequency in the original signal (the bell shaped thing centered at frequency 0. This is like your 14.7kHz sine wave sampled at 44.1kHz. The second is when the period of sampling T equals half the period of the highest frequency (see how the edges of that waveform exactly touch each other?). The bottom picture shows what happens when the sampling period is greater than half the period of the highest frequency. That portion of the bell shaped thing that overlaps one another is sampling noise. In other words everything that is overlapping is lost.
Site C is another site that does not understand nyquist's theorem. They are completely thinking in terms of the time domain instead of the frequency domain. Not to mention that they don't realize you always have to low-pass filter a sampled signal.
Site D actually is correct and should be understandable to even the least mathematically inclined.
You're 100% right. 16 bits is not enough for mastering and mixing. The intermediate values of the mixing must be preserved as accurately as possible to ensure the best possible final result. When the final output is obtained, 16 bits may be enough for listening to. I don't know where your statement about an undigitized output and the 16 bit quantized output is coming from though. I don't think anyone has ever said that the result of 16 bit sampling can exactly reproduce the undigitized output. But are you asserting that the difference is a really big audible difference?
As for the 44.1kHz? If the audio is already sampled at 44.1kHz, you'd better have a serious cutoff at 22kHz or else you're getting alot more distortion at higher frequencies. What exactly are you talking about when you say that amp designers go for pass band into the MHz? If there is any power above 22kHz it is purely noise (that is if the input is a CD, LP is arguable at this point). Now is the higher sampling frequency better? Of course! Just like the 24bit sampling, it makes it easier to reproduce high quanlity recordings.
You seem to be quite an audiophile. I am not. But I wonder, have you ever really tested the validity of your gut feeling about these technologies. I feel that your statements are an amalgam of audiophile "common knowledge" but don't represent the physics and mathematics of sounds and frequency analysis.
Mozilla's designated "Chief Lizard Wrangler" seems pleased with the maturity level the organization's two-and-a-half-year-old pet project has achieved.
Mitchell Baker, whose other titles on the mozilla.org Web site include "manager, problem arbitrator, and speaker to suits," recounted recent happenings within the organization and described some of the development criteria and expectations that will shape Mozilla's 1.0 release.
In keeping with its new roadmap, the new and improved browser is scheduled for its 1.0 release in the second quarter of 2001. "Mozilla 1.0 will, of course, include the features developed for the browser/mail/news application," she said. "Enhanced performance, reduced footprint, improved stability, and architectural correctness and even better standards compliance are additional goals for Mozilla 1.0."
These features are important to Mozilla's present role--and vital to its expansion into new areas, Baker said. "These aspects are important not only to those interested in the browser/mail/news application, but also to that portion of the Mozilla community that is interested in embedding the Mozilla layout engine in other applications and devices, often in combination with a Linux distribution," she added.