Hi,
I am a newbie, so correct me hard if I am wrong.
The oposite of digital is analog. The opposite of discrete is
continuous.
Digital refers to something that is digitized, i.e. having finite
precision.
1/3 is not digital. 0.333 is digital.
Discrete refers to something that is separable and not continuous.
("Countable" seems like a good word to use here, but I am hesitant
because in discrete mathematics, many discrete sets are considered
uncountable.)
So, being discrete and being digital are two independent concepts. It
just happens that there is hardly any digital signal that is
non-discrete at the same time, so the word "digital" is often replaced
by the word "discrete" in a sentence.
Here is a related question that came to my mind: (I guess this
question has no practical value except getting people to come up with
a clearer definition of "digital".)
A signal that is both digital and non-discrete probably cannot exist
in reality, but how about an imaginary signal that is defined
mathematically?
Suppose we have a signal that follows a step function. By definition,
the value is either 0 or 1, and hence can be represented digitally.
But in the time axis, you cannot point out whether the value is 0 or 1
at time 0, i.e. you cannot separate the 0 part of the signal from the
1 part of the signal. Can we call this signal "digital and yet
non-discrete"?
How about the pdf of rand() function in Matlab? Its value is exactly 1
from 0 to 1 , exactly 0 elsewhere, and yet it is a continuous
function.
Regards.
KD
Difference between Digital and Discrete Signal
Started by ●October 12, 2004
Reply by ●October 13, 20042004-10-13
Reply by ●October 13, 20042004-10-13
Let me correct myself:>>1/3 is not digital. 0.333 is digital<<1/3 is not digital in the decimal system, but it is digital in a trinary system.
Reply by ●October 13, 20042004-10-13
Jerry Avins wrote:> glen herrmannsfeldt wrote: > > >> >>Jerry Avins wrote: >> >>(snip on discretizing, digitizing and sampling) >> >> >>>Except, to pick a nit, digital signals can also be, >> >>> and sometimes are, generated by computation. >> >>I have a whole CD of audio test signals that I believe >>was generated by computation. If you want a sine wave >>it is most accurate to compute it than digitize an >>analog wave. >> >>For a philosophy question, is it sampling and digitizing >>a virtual analog signal? > > > I guess that to some extent, it depends on the actual code. > > JerryOr perhaps the comments therein? -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●October 13, 20042004-10-13
"Kedi" <kd20128@yahoo.com> wrote in message news:38640413.0410131357.3574f94b@posting.google.com...> > A signal that is both digital and non-discrete probably cannot exist > in reality, but how about an imaginary signal that is defined > mathematically? >Kedi, How about feeding your analog signal into a comparitor. You will get a 2 level output (digital) yet it is not discrete - ignoring shot noise and other quantum effects. The usual thought behind "discrete" as used in signal processing stems from how discrete is used in mathematics. A set of numbers is said to be discrete if the distance between any two numbers taken from the set is greater than some positive epsilon. With discrete signals, the assumption is they are sampled in time, so the set of time indices is certainly discrete. O&S changed the name of their famous tome from "Digital Signal Processing" to "Discrete-Time Signal Procesing" to reflect the issues of working in discrete time. They give good reasons for this change in the second paragraph of the preface on page XI of their "2nd ed." IHTH, Clay S. Turner
Reply by ●October 13, 20042004-10-13
"Kedi" <kd20128@yahoo.com> wrote in message news:38640413.0410131402.6efe4eda@posting.google.com...> Let me correct myself: > >>>1/3 is not digital. 0.333 is digital<< > > 1/3 is not digital in the decimal system, but it is digital in a trinary > system.To go a step further, you could have an expression (in a computer program) that could be evaluated for any value of the independent variable - so it would "approach" being not discrete. However, then you have the issue of finite arithmetic in the independent variable too - so there is a discrete grid on which the independent variable can be computed. In fact, if we were to say: here is a program to compute the samples of a sinusoid to put on a CD, and we've decided that the sample rate is 44,100 Hz. I can well imagine that the temporal representation would be subject to finite arithmetic as well as the values of the sinusoid that's generated. So, you have "quantization" noise in both dimensions. Or is 44,100 somehow a magic number that avoids quantization errors in time for synthetically generated signals? Fred
Reply by ●October 13, 20042004-10-13
Clay Turner wrote: (snip regarding non-discrete signals)> How about feeding your analog signal into a comparitor. You will get a 2 > level output (digital) yet it is not discrete - ignoring shot noise and > other quantum effects.> The usual thought behind "discrete" as used in signal processing stems from > how discrete is used in mathematics. A set of numbers is said to be discrete > if the distance between any two numbers taken from the set is greater than > some positive epsilon. With discrete signals, the assumption is they are > sampled in time, so the set of time indices is certainly discrete.With a flash A/D converter and gray code output you should be able to get a continuous time digital output from a continuous input. There will be limits to how fast the signals can change, but the time between transitions is a continuous function. Once you have one, what kind of signal processing can you do to it? > O&S changed the name of their famous tome from > "Digital Signal Processing" to "Discrete-Time Signal Procesing" > to reflect the issues of working in discrete time. > They give good reasons for this change in the second > paragraph of the preface on page XI of their "2nd ed." So the newsgroup should change to comp.dtsp then? (Or maybe a separate newgroup, comp.dsp for digital signal processORS, and comp.dtsp for discrete time signal processING.) -- glen
Reply by ●October 14, 20042004-10-14
kd20128@yahoo.com (Kedi) wrote in message news:<38640413.0410131402.6efe4eda@posting.google.com>...> Let me correct myself: > > >>1/3 is not digital. 0.333 is digital<< > > 1/3 is not digital in the decimal system, but it is digital in a trinary system.Wouldn't the correct term be "trigital" if you refer to the trinary number system? "Digital" refers to the binary number system, "decimal" to the base 10 system, etc... Rune
Reply by ●October 14, 20042004-10-14
glen herrmannsfeldt wrote:> For a philosophy question, is it sampling and digitizing > a virtual analog signal?Not really, since you can generate signals that not always can be sampled (if they were analog)... bye, -- Piergiorgio Sartor
Reply by ●October 14, 20042004-10-14
Piergiorgio Sartor wrote:> glen herrmannsfeldt wrote: > >> For a philosophy question, is it sampling and digitizing >> a virtual analog signal? > > > Not really, since you can generate signals that > not always can be sampled (if they were analog)... > > bye,I imagine that you mean "you can generate signals that can not always be a sampling (if they were analog)", but I can't imagine such a signal. Please enlighten me. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●October 14, 20042004-10-14
Rune Allnor wrote:> kd20128@yahoo.com (Kedi) wrote in message news:<38640413.0410131402.6efe4eda@posting.google.com>... > >>Let me correct myself: >> >> >>>>1/3 is not digital. 0.333 is digital<< >> >>1/3 is not digital in the decimal system, but it is digital in a trinary system. > > > Wouldn't the correct term be "trigital" if you refer to the trinary > number system? "Digital" refers to the binary number system, "decimal" > to the base 10 system, etc... > > RuneFalse etymology. "Digital" comes from "digit"; finger. I suppose that it applies to counting from the use of fingers for counting, but I don't know. Now, it's practically a synonym for "numeric", but if it implies any base, well... most of us have ten fingers. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
