Difference between Digital and Discrete Signal

Started by Ranga October 12, 2004
Hi,

Can anyone correct the difference between Digital and Discrete signal?

I feel, digital signals can be one and zero.

But discrete signal can be any numeral, say one, two or ten.

The difference between Analog and Discrete/Digital signal is that
signals are periodic in Digital, while analog signals are continuous.

Please guide me.

Regards,
Ranga.
Ranga wrote:

> Hi, > > Can anyone correct the difference between Digital and Discrete signal? > > I feel, digital signals can be one and zero. > > But discrete signal can be any numeral, say one, two or ten. > > The difference between Analog and Discrete/Digital signal is that > signals are periodic in Digital, while analog signals are continuous. > > Please guide me. > > Regards, > Ranga.
A digitized signal is otained most of the time by sampling a discrete signal, once sampled, the signal is digitized (using ADC). For example, in telephony, the signal is sampled at a 8Khz rate, digitized on 13bits, and after digitally compressed using mulaw or alaw. Gerard
"Gerard Lyonnaz" <gerard.lyonnaz@hp.com> wrote in message 
news:416B80AA.6D34DDDB@hp.com...
> Ranga wrote: > >> Hi, >> >> Can anyone correct the difference between Digital and Discrete signal? >> >> I feel, digital signals can be one and zero. >> >> But discrete signal can be any numeral, say one, two or ten. >> >> The difference between Analog and Discrete/Digital signal is that >> signals are periodic in Digital, while analog signals are continuous. >> >> Please guide me. >> >> Regards, >> Ranga. > > A digitized signal is otained most of the time by sampling a discrete > signal, > once sampled, the signal is digitized (using ADC). For example, > in telephony, the signal is sampled at a 8Khz rate, digitized on > 13bits, > and after digitally compressed using mulaw or alaw. > Gerard >
Hmmmmm..... I'd say that a discrete signal is a sequence of samples - no matter how those samples occur or how they are represented. They could be generated by a mathematical expression, etc. There's lots of analysis and texts on discrete systems - without mention of how the representation of the values of the samples is implemented. There are also lots of examples of discrete systems that use "analog" storage mechanisms - like charge-coupled devices, bucket-brigade or switched capacitor filters, etc. A digital signal is necessarily discrete. To make it digital as well means the values are described using finite precision arithmetic. The sample rate or interval, uniform or nonuniform has nothing to do with it. I don't agree that: "A digitized signal is otained most of the time by sampling a discrete signal" That's because sampling is the process that might be used to generate the discrete signal in the first place. Then you need to talk about representation and storage. Rather, I'd say that "A digitized signal is obtained most of the time by sampling a continuous signal (as with a sample-hold) and storing the result using finite precision arithmetic (as out of an ADC) - as would be found in a digital computer." The latter is where the term "analog to digital converter" takes its meaning. Fred
On 11 Oct 2004 23:45:45 -0700, rangampalayam@rediffmail.com (Ranga)
wrote:

>Hi, > >Can anyone correct the difference between Digital and Discrete signal?
In this context, signals can be quantized and sampled. Not all sampled signals are quantized (ie signals in a switched capacitor filter) and not all quantized signals are sampled (output of an analog comparator). A discrete signal is one which is sampled but not necessarily quantized. A digital signal is one which is sampled and quantized. So all discrete signals are digital but not vice versa. An analog to digital converter is a good example of a system where all domains appear at once and shows how processing can be done at all domains. The analog signal is conditioned (possibly with a low pass and/or an analog matched filter) at the input, applied to a sample-hold filter with analog values and then quantized with comparators set at different thresholds (in a flash converter). These blocks can be ordered differently based on your requirements. hth.
Hi,

   Read the First chapter in the book " Digital Signal Processing" A
Computer based approach by SK Mithra, TMH.

  Sathish

"Ranga" <rangampalayam@rediffmail.com> wrote in message
news:6e6631b7.0410112245.3519af4@posting.google.com...
> Hi, > > Can anyone correct the difference between Digital and Discrete signal? > > I feel, digital signals can be one and zero. > > But discrete signal can be any numeral, say one, two or ten. > > The difference between Analog and Discrete/Digital signal is that > signals are periodic in Digital, while analog signals are continuous. > > Please guide me. > > Regards, > Ranga.
"Sathish" <saikumar.mangapuram@de.bosch.com> wrote in message news:<ckgp47$gt6$1@ns2.fe.internet.bosch.com>...
> Hi, > > Read the First chapter in the book " Digital Signal Processing" A > Computer based approach by SK Mithra, TMH. > > Sathish > > "Ranga" <rangampalayam@rediffmail.com> wrote in message > news:6e6631b7.0410112245.3519af4@posting.google.com... > > Hi, > > > > Can anyone correct the difference between Digital and Discrete signal? > > > > I feel, digital signals can be one and zero. > > > > But discrete signal can be any numeral, say one, two or ten. > > > > The difference between Analog and Discrete/Digital signal is that > > signals are periodic in Digital, while analog signals are continuous. > > > > Please guide me. > > > > Regards, > > Ranga.
Hi, Discrete Signals : Obtained by sampling the analog signal at disctrete instants of time. However the magnitude of the discrete signals is same as that of the analog signal at that point in time. (Discrete only in time) Digital Signal : When the magnitude of the discrete signal is quantized to the the nearest integer, we get a digital signal. (Which is both discrete in magnitude & time) Example: Say, after sampling the analog signal, we get discrete signal as below x[0] = 0 x[1] = 0.9 x[2] = 1.8 x[3] = 2.6 x[4] = 2.1 x[5] = 1.8 .... When you want to digitize this signal, you pass it through the ADC & the output would be as below. x[0] = 0 x[1] = 1 x[2] = 2 x[3] = 3 x[4] = 2 x[5] = 2... The above output depends upon the resolution of the ADC . More the resolution, less the quantization error. I hope this helps your question. Regards Sandeep
On 12 Oct 2004 20:29:41 -0700, sandeep_mc81@yahoo.com (Sandeep
Chikkerur) wrote:

  (snipped)
> >Hi, > >Discrete Signals : >Obtained by sampling the analog signal at disctrete instants of time. >However the magnitude of the discrete signals is same as that of the >analog signal at that point in time. >(Discrete only in time) > >Digital Signal : >When the magnitude of the discrete signal is quantized to the the >nearest integer, we get a digital signal. >(Which is both discrete in magnitude & time) > >Example: >Say, after sampling the analog signal, we get discrete signal as below >x[0] = 0 >x[1] = 0.9 >x[2] = 1.8 >x[3] = 2.6 >x[4] = 2.1 >x[5] = 1.8 .... > >When you want to digitize this signal, you pass it through the ADC & >the output >would be as below. >x[0] = 0 >x[1] = 1 >x[2] = 2 >x[3] = 3 >x[4] = 2 >x[5] = 2... > >The above output depends upon the resolution of the ADC . >More the resolution, less the quantization error. > >I hope this helps your question. > >Regards >Sandeep
Hi, very nice explanation! This is good. [-Rick-]
Rick Lyons wrote:

> On 12 Oct 2004 20:29:41 -0700, sandeep_mc81@yahoo.com (Sandeep > Chikkerur) wrote: > > (snipped) > >>Hi, >> >>Discrete Signals : >>Obtained by sampling the analog signal at disctrete instants of time. >>However the magnitude of the discrete signals is same as that of the >>analog signal at that point in time. >>(Discrete only in time) >> >>Digital Signal : >>When the magnitude of the discrete signal is quantized to the the >>nearest integer, we get a digital signal. >>(Which is both discrete in magnitude & time) >> >>Example: >>Say, after sampling the analog signal, we get discrete signal as below >>x[0] = 0 >>x[1] = 0.9 >>x[2] = 1.8 >>x[3] = 2.6 >>x[4] = 2.1 >>x[5] = 1.8 .... >> >>When you want to digitize this signal, you pass it through the ADC & >>the output >>would be as below. >>x[0] = 0 >>x[1] = 1 >>x[2] = 2 >>x[3] = 3 >>x[4] = 2 >>x[5] = 2... >> >>The above output depends upon the resolution of the ADC . >>More the resolution, less the quantization error. >> >>I hope this helps your question. >> >>Regards >>Sandeep > > > Hi, > > very nice explanation! This is good.
Except, to pick a nit, digital signals can also be, and sometimes are, generated by computation. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

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? -- glen
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. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
In principle, sampling is not necessary in order to do filtering digitally.
This is discussed in the following paper:

Y. Tsividis, “Digital signal processing in continuous time: a possibility
for avoiding aliasing and reducing quantization error”, Proceedings 2004
IEEE International Conference on Acoustics, Speech, and Signal Processing,
vol. II, pp. 589-592, Montreal, May 2004.

I would be happy to send a copy of the above paper to anyone who cannot
access it on the IEEE Web site. In this paper, I discuss a method to do
the whole thing in continuous time, without sampling, resulting in a
system with no aliasing. The system has no quantization error at
non-harmonic frequencies, and exhibits 10-15 dB lower total quantization
error than classical DSP, for a given number of bits. Needless to say,
although breadboard measurements and simulations show that the idea works,
there is a lot of work to be done before one can know whether all this is
practically feasible. I would be very much interested in the opinion of
dsp experts on this idea. I welcome any comments!

Yannis Tsividis
Columbia University


>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. >¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ >
This message was sent using the Comp.DSP web interface on www.DSPRelated.com
A digital signal is discrete in both time and amplitude.

A discrete signal can be discrete in time (but have any real-valued amplitude), 
amplitude (and have continuous time), or both (discrete in time and amplitude 
which is what a digital signal is).




In article <6e6631b7.0410112245.3519af4@posting.google.com>, 
rangampalayam@rediffmail.com says...
> >Hi, > >Can anyone correct the difference between Digital and Discrete signal? > >I feel, digital signals can be one and zero. > >But discrete signal can be any numeral, say one, two or ten. > >The difference between Analog and Discrete/Digital signal is that >signals are periodic in Digital, while analog signals are continuous. > >Please guide me. > >Regards, >Ranga.
Piergiorgio Sartor wrote:

> Jerry Avins wrote: > >> No, but there exist properly band-limited signals whose samples appear >> at first glance to be those of a square wave. To find one of those, >> reconstruct the "original" from a computed "square wave". The >> reconstruction necessarily yields the original samples and is >> necessarily bandlimited. > > > Assuming you will resample with the proper phase, > I guess, so under certain conditions. > > There is still the ambiguity problem.
I don't understand. Reconstruction is done by performing digital-to-analog conversion and low-pass filtering with appropriate compensation for sinc roll off. What ambiguity can there be?
>>> I was also thinking (but I did not finished :-)) about a >>> sequence like 1,-1,1,-1,1,-1,... which cannot be classified >>> as square or sine wave. >> >> >> It can be classified if it is known that the sequence represents valid >> -- that is, properly bandlimited -- samples. > > > The above sequence can represent anything, in this > sense we cannot claim it comes from _one_ analog signal.
The assumption that is is a sampling of a signal band-limited to half the sample rate implies that it can only be a cosine. Since the sample rate is exactly twice the signal frequency, the sine term is lost. If that's what you mean by not knowing, we agree. What we do know is that is is a single frequency.
>> In practice, we use very good approximations to GWN. Don't reason from >> the ideal when declaring what's possible where the ideal itself isn't. >> True GWN can't be represented in any physically realizable system, nor >> can it be truly represented with finite word lengths. > > > Actually, it sufficient to be white, not necessarily gaussian. > > I did not make the calculation (so maybe I'm wrong), but I think > the anti-aliasing filter will correlate the samples beyond the > sampling step, so it will not be possible to sample and keep the > uncorrelation, while in the discrete time domain it will be > possible to generate uncorrelated samples.
Uncorrelated samples are not properly bandlimited for sampling.
> Of course this will be a property of the signal, which can be > not considered in the sampling process, so, maybe, a sampleable > signal giving the same "shape" will probably exist, but not with > the same properties (so it will not be identical, in this space). > > bye,
Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Jerry Avins wrote:

> No, but there exist properly band-limited signals whose samples appear > at first glance to be those of a square wave. To find one of those, > reconstruct the "original" from a computed "square wave". The > reconstruction necessarily yields the original samples and is > necessarily bandlimited.
Assuming you will resample with the proper phase, I guess, so under certain conditions. There is still the ambiguity problem.
>>I was also thinking (but I did not finished :-)) about a >>sequence like 1,-1,1,-1,1,-1,... which cannot be classified >>as square or sine wave. > > It can be classified if it is known that the sequence represents valid > -- that is, properly bandlimited -- samples.
The above sequence can represent anything, in this sense we cannot claim it comes from _one_ analog signal.
> In practice, we use very good approximations to GWN. Don't reason from > the ideal when declaring what's possible where the ideal itself isn't. > True GWN can't be represented in any physically realizable system, nor > can it be truly represented with finite word lengths.
Actually, it sufficient to be white, not necessarily gaussian. I did not make the calculation (so maybe I'm wrong), but I think the anti-aliasing filter will correlate the samples beyond the sampling step, so it will not be possible to sample and keep the uncorrelation, while in the discrete time domain it will be possible to generate uncorrelated samples. Of course this will be a property of the signal, which can be not considered in the sampling process, so, maybe, a sampleable signal giving the same "shape" will probably exist, but not with the same properties (so it will not be identical, in this space). bye, -- Piergiorgio Sartor
"Kedi" <kd20128@yahoo.com> wrote in message
news:38640413.0410131357.3574f94b@posting.google.com...
> > 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.
I think the common term here is quantized, rather than digital. Here are my definitions: 1) continuous time/continuous level: analog 2) continuous time/discreet level: quantized 3) discreet time/continuous level: discreet (or discreet time) 4) discreet time/discreet level: digital Here are some audio-centric examples: analog: audio waveform in the air quantized: audio signal passed through a comparator (Jerry's example) discreet: audio signal sent through a CCD (aka bucket-brigade device) such as early non-DSP delay effects units digital: audio signal on CD
Piergiorgio Sartor wrote:
> Jerry Avins wrote: > >> 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. > > > Well, in certain condition, for example a square wave. > > Assuming you have a "generic" sampling system (so with > anti-aliasing filter), you cannot sample all the possible > square waves (some, maybe, you can).
No, but there exist properly band-limited signals whose samples appear at first glance to be those of a square wave. To find one of those, reconstruct the "original" from a computed "square wave". The reconstruction necessarily yields the original samples and is necessarily bandlimited.
> In the other domain (discrete time) you can generate square > waves, some of these cannot be sampled one. > > I was also thinking (but I did not finished :-)) about a > sequence like 1,-1,1,-1,1,-1,... which cannot be classified > as square or sine wave.
It can be classified if it is known that the sequence represents valid -- that is, properly bandlimited -- samples.
> Not to mention gaussian white noise...
In practice, we use very good approximations to GWN. Don't reason from the ideal when declaring what's possible where the ideal itself isn't. True GWN can't be represented in any physically realizable system, nor can it be truly represented with finite word lengths. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Jerry Avins wrote:

> 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.
Well, in certain condition, for example a square wave. Assuming you have a "generic" sampling system (so with anti-aliasing filter), you cannot sample all the possible square waves (some, maybe, you can). In the other domain (discrete time) you can generate square waves, some of these cannot be sampled one. I was also thinking (but I did not finished :-)) about a sequence like 1,-1,1,-1,1,-1,... which cannot be classified as square or sine wave. Not to mention gaussian white noise... bye, -- Piergiorgio Sartor
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... > > Rune
False 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. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
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. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
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