Today, as I was reading about "signals" I constantly kept coming across the term analog signal and discrete signal and digital signal. And I couldn't connect with those terms .. As usual. So I started wondering why is an analog signal called analog? Where did the term discrete come from. And out came the dictionary!
Analog signal : The US version of "Analogue" it simply means analogous ie similar to something else. An analog signal is simply a signal ( ie a symbol) which is exactly similar to another quantity, the quantity that it is modeling. Thats why is analog.
Discrete : The word discrete comes from the latin word discerner ie dis + cernere (to separate) meaning to divide. Discrete would then describe an object that has separate parts or form. Which I guess would rightly describe a run-off-the-mill discrete signal.
Digital signal : I guess most of us would be aware, digit means toe or finger. I think the name digital signal is simply a reflection of the fact that there are finite number of levels in a digital signal, mostly two of course, like the finite number of fingers.
And the way I understand it, continuous and discrete, do not describe the range of values or the kind of values the signal can take, rather, the time axis or the number of values that are taken by the system or the way the signal is sampled basically.
Analog and digital, on the other hand describe the values of the signal. So does the term quantized. An continuous-time system can be quantized and so can a discrete-time system.
You can either measure the signal continuously for ten minutes to get a continuous signal or measure for 1 second every one minute, ten times to get a discrete signal. That'ss the difference. But when you measure, if the signal takes any value, then its analog, or if it takes only specific steps of values, its quantized, and if it only takes a specified set of values, its digital.
So this was today's interesting fact.
Till next time.
Tuesday, May 24, 2011
Wednesday, May 18, 2011
All those Theories!
All this while I have been studying all these theories. Some seem to co-exist, some seem to complement, and some contradict. Why so?
Why all these theories anyway? What is the use?
Every time I read about a theory, I seem to understand where its coming from, atleast superficially. But when I try to compare it with another theory, I come up with a blank. I don't know why... Its like there is some kind of block, that won't let me get to the depth of it.
Its like as I study, over time, science seems to go deeper and deeper into reality, and suddenly, as if someone slapped it, it takes a step back, and starts viewing things in a completely different perspective. And that slap part started with Quantum Theory. Its like it turned everything upside down. I have always had trouble visualizing it, and I am sure I am not the only one.
Even my education, I only now realize, had been like that. And perhaps that is why I found it confusing. My syllabus is college too had a big role to play in that. Every semester we were introduced to new and new subject and concepts without any background or any obvious correlation whatsoever. It was like, one day, you take the radio, pull it apart and study it. Next day you take the fan, pull it apart and study it. Third day you take your computer pull it apart and study it ... and so on. There was absolutely no structure to it.
But the most mind boggling part of all this is the question of which theory to apply where??
All learning happens in start and stops and not always in a straight line, and that is true for development of science too. But I wish I had a little more clarity.
Why all these theories anyway? What is the use?
Every time I read about a theory, I seem to understand where its coming from, atleast superficially. But when I try to compare it with another theory, I come up with a blank. I don't know why... Its like there is some kind of block, that won't let me get to the depth of it.
Its like as I study, over time, science seems to go deeper and deeper into reality, and suddenly, as if someone slapped it, it takes a step back, and starts viewing things in a completely different perspective. And that slap part started with Quantum Theory. Its like it turned everything upside down. I have always had trouble visualizing it, and I am sure I am not the only one.
Even my education, I only now realize, had been like that. And perhaps that is why I found it confusing. My syllabus is college too had a big role to play in that. Every semester we were introduced to new and new subject and concepts without any background or any obvious correlation whatsoever. It was like, one day, you take the radio, pull it apart and study it. Next day you take the fan, pull it apart and study it. Third day you take your computer pull it apart and study it ... and so on. There was absolutely no structure to it.
But the most mind boggling part of all this is the question of which theory to apply where??
All learning happens in start and stops and not always in a straight line, and that is true for development of science too. But I wish I had a little more clarity.
Monday, May 16, 2011
An Observation
In going thru all the material I realized one thing: How much modern theories depend on mathematics.
Mathematics has been a base for science since time immemorial, but I see how extensively maths is being used whether it is to prove what you thought, or it is to find out new patterns and relationships in nature.
That is what is biggest advantage of math. For the ones who know how to use it, math can reveal aspects of nature that would never be revealed using normal human reasoning and conventional language. Its miraculous in that sense.
But truely knowing it and understanding it, knowing how to use it, is no easy task.
Mathematics has been a base for science since time immemorial, but I see how extensively maths is being used whether it is to prove what you thought, or it is to find out new patterns and relationships in nature.
That is what is biggest advantage of math. For the ones who know how to use it, math can reveal aspects of nature that would never be revealed using normal human reasoning and conventional language. Its miraculous in that sense.
But truely knowing it and understanding it, knowing how to use it, is no easy task.
Information Theory
I have now moved on to computers and information theory.
I did try to do some research on accelerated charge in a field .. and got one piece of info that hadn't struck me till now ... All electromagnetic phenomena on earth is happening in the earth's magnetic field and every charge that accelerates on earth accelerates in the omnipresent magnetic field of earth so would always generate an EM wave.
Now the next obvious question would be would an accelerated charge in a absolute vacuum devoid any field still radiate EM wave out of interaction with its own field? Couldn't find an answer for that yet.
Anyways moving on to the current topic : Computers and Information Theory.
Today's "Computer" stands for much more than what the name implies. Today's computer is more of a "simulator" than just a calculator. That idea was first conceived by Alan Turing, british scientist who said there could be a machine that would generate the solution of any problem that can be solved provide all the required steps are pre determined ... An algorithm is predefined.
This machine could be built, today we call them computers, only because of technological advancement of semiconductor physics, and the encoding of "rules of logic" into logic circuits.
Transistors, after its invention in bell labs, underwent a major revolution in terms of application when logic circuits were created, they were now capable of "processing" a set of input signals, converting them into a predefined set of output signals, and then these signals could be interpreted and rendered in the form the user required. A graph. A table. A equation. Anything basically. So computer could now simulate the entire process, that was defined in the algorithm, and give us the results instantly. Now that is immense power if you really think about it.
Personally this is what I have liked about computers and software programming the best. The power to create anything without any rules. If you can write a code for it, you can practically make anything. :)
With the advent of computers, information became even more readily available. All sorts of information. And that became a problem in itself. But the one I'm concerned about is the Engineering problem. And as we all know, Information theory means Shannon's thoery.
Again, Shannon's theory is something I have always hated during my engineering. It just never made sense to me. If we already know something its information content is nil, and if we get an unknown signal, that has information. Its totally counter intuitive. Until I saw it from an engineers perspective. From a Receiver's perspective. If I receive a signal, which I already knew was coming, communicating it was pretty useless to me isn't it? On the other hand, if I receive a unknown signal, now my job would be to find out whether or not its a valid signal. Its like jigsaw puzzle solving. If I already know where a piece should be and what the piece is, I would put it there anyway, but for every new signal I receive, I have to first find out whether its a valid piece of the puzzle, and if it is, then I try to put it somewhere where it would help form the whole content or the picture. So the new signal is a clue, full of some information. That is the way I understand it as of now.
Another interesting thing about Shannon is that he was the one who came up with the idea of logic circuits. He first researched into how the telephone switching relays worked and said they could be designed even more efficiently incorporating Bool's "laws of human thought". And that they infact embodied that exact idea. Now if systems displayed use of logic, then vice versa logic "circuits" could be used to design systems. That is where all of digital electronics began.
Shannon also showed that the digital/binary encoded bit stream was the most efficient way of data transfer that allowed self correction.
As electronics engineer I can really appreciate the far reaching applications of his theory... And the reason it prevailed was simply because he took out the subjectivity. He said, I don't care what the content is, I don't care if you are sending a word doc, a music file, a image or a radio transmission, my theory applies to all, he generalized it and reduced it down to the most basic level so much that it could be applied practically to anything. Genius.
I did try to do some research on accelerated charge in a field .. and got one piece of info that hadn't struck me till now ... All electromagnetic phenomena on earth is happening in the earth's magnetic field and every charge that accelerates on earth accelerates in the omnipresent magnetic field of earth so would always generate an EM wave.
Now the next obvious question would be would an accelerated charge in a absolute vacuum devoid any field still radiate EM wave out of interaction with its own field? Couldn't find an answer for that yet.
Anyways moving on to the current topic : Computers and Information Theory.
Today's "Computer" stands for much more than what the name implies. Today's computer is more of a "simulator" than just a calculator. That idea was first conceived by Alan Turing, british scientist who said there could be a machine that would generate the solution of any problem that can be solved provide all the required steps are pre determined ... An algorithm is predefined.
This machine could be built, today we call them computers, only because of technological advancement of semiconductor physics, and the encoding of "rules of logic" into logic circuits.
Transistors, after its invention in bell labs, underwent a major revolution in terms of application when logic circuits were created, they were now capable of "processing" a set of input signals, converting them into a predefined set of output signals, and then these signals could be interpreted and rendered in the form the user required. A graph. A table. A equation. Anything basically. So computer could now simulate the entire process, that was defined in the algorithm, and give us the results instantly. Now that is immense power if you really think about it.
Personally this is what I have liked about computers and software programming the best. The power to create anything without any rules. If you can write a code for it, you can practically make anything. :)
With the advent of computers, information became even more readily available. All sorts of information. And that became a problem in itself. But the one I'm concerned about is the Engineering problem. And as we all know, Information theory means Shannon's thoery.
Again, Shannon's theory is something I have always hated during my engineering. It just never made sense to me. If we already know something its information content is nil, and if we get an unknown signal, that has information. Its totally counter intuitive. Until I saw it from an engineers perspective. From a Receiver's perspective. If I receive a signal, which I already knew was coming, communicating it was pretty useless to me isn't it? On the other hand, if I receive a unknown signal, now my job would be to find out whether or not its a valid signal. Its like jigsaw puzzle solving. If I already know where a piece should be and what the piece is, I would put it there anyway, but for every new signal I receive, I have to first find out whether its a valid piece of the puzzle, and if it is, then I try to put it somewhere where it would help form the whole content or the picture. So the new signal is a clue, full of some information. That is the way I understand it as of now.
Another interesting thing about Shannon is that he was the one who came up with the idea of logic circuits. He first researched into how the telephone switching relays worked and said they could be designed even more efficiently incorporating Bool's "laws of human thought". And that they infact embodied that exact idea. Now if systems displayed use of logic, then vice versa logic "circuits" could be used to design systems. That is where all of digital electronics began.
Shannon also showed that the digital/binary encoded bit stream was the most efficient way of data transfer that allowed self correction.
As electronics engineer I can really appreciate the far reaching applications of his theory... And the reason it prevailed was simply because he took out the subjectivity. He said, I don't care what the content is, I don't care if you are sending a word doc, a music file, a image or a radio transmission, my theory applies to all, he generalized it and reduced it down to the most basic level so much that it could be applied practically to anything. Genius.
Monday, May 2, 2011
Back after a Haitus!
I had been disconnected to the net in the past 6 months or so and caught up in other stuff. Though I did try to continue my electronic quest.. I'm afraid it wasn't much quantitatively.
But yes, I did manage to read somewhat about stochastic (statistics), process theory and stuff.
And the one place I got stuck at and find myself unable to get out of is Quantum Theory.
It is one of the toughest topics to study and understand.. not much of it is intuitive...
Some of the questions that are not letting me proceed are:
1. Why should an accelerating electrical charge radiate energy according to maxwell's theory?
2. Is an electron orbiting a proton accelerating or having a circular motion at constant velocity?
3. What is frequency? What exactly is oscillating when we refer to crest and trough.. wave.. the wave has to have a medium? Are the photons travellling up and down in the form of a wave to move? Does that make sense?
Been searching for long. Not much clarity. Will update If I find anything.
But yes, I did manage to read somewhat about stochastic (statistics), process theory and stuff.
And the one place I got stuck at and find myself unable to get out of is Quantum Theory.
It is one of the toughest topics to study and understand.. not much of it is intuitive...
Some of the questions that are not letting me proceed are:
1. Why should an accelerating electrical charge radiate energy according to maxwell's theory?
2. Is an electron orbiting a proton accelerating or having a circular motion at constant velocity?
3. What is frequency? What exactly is oscillating when we refer to crest and trough.. wave.. the wave has to have a medium? Are the photons travellling up and down in the form of a wave to move? Does that make sense?
Been searching for long. Not much clarity. Will update If I find anything.
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