Difference between Digital and Discrete Signal

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

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.
�����������������������������������������������������������������������

"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

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

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.
�����������������������������������������������������������������������

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.

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.
>�����������������������������������������������������������������������
>




		
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