Reply by Ben Bradley May 13, 20082008-05-13
On Tue, 13 May 2008 10:55:59 -0500, "markt" <takatz@pericle.com>
wrote:

>>Digital has become the label for what is really "discrete >>time / quantized amplitude" (and, often, "discrete time / discrete >>frequency / quantized amplitude in both domains"). It really should >>refer only to amplitude quantization. But that's not the way it's >>commonly used. > >When I first learned the term "DSP," it actually meant "discrete-time >signal processing." It has since been morphed to "digital signal >processing,"
How old are you? You must be a youngster. ;) I presume you learned DSP with the second edition of the Oppenhiem/Schafer book which used the "Discrete-Time" name (from 1999) The first edition (from 1975), the grandaddy of DSP texts, was named (of all things) "Digital Signal Processing." Okay, with a little searching I found a 1976 book titled "Discrete-Time Signal Processing" by Steven A. Trettor, is that the book you used? Just wonderin'...
>though with reason, since it is difficult to do anything with >discretely sampled continuous waveforms unless you first digitize them.
Look up "Bucket Brigade Devices." These were sampled-time analog delay line chips commonly used in electronic organs, electric guitar amps and stomp boxes for reverb and "flanging" effects. They have their own funky sound, different from the funky sound of mechanical spring reverbs. Okay, here's a link: http://en.wikipedia.org/wiki/Bucket_Brigade_Device
>Digital signal processing is essentially quantized DSP. Perhaps someone >will start to call it QDSP one day and it will stick? :)
Quantization is a separate operation (mathematically, even though in practice it usually happens at the same time and in the same circuit as sampling), and for many applications can be dealt with separately. The "Discrete-Time" book also covers quantization - I recall it's called "discrete amplitude." There are still applications where quantization happens at a later time than sampling - in charge-coupled devices, the sampling happens simultaneously time-wise (but in different locations space-wise - this brings up a different example of aliasing that's NOT along the time axis, as when one takes a digital picture of a tweed coat, resulting in a Morie' pattern: http://en.wikipedia.org/wiki/Moir%C3%A9_pattern). The analog samples are shifted to the end of the row, where they are then (usually) digitized. But even nowadays, the samples might still remain in the analog domain, and be sent out as (for one example) a NTSC TV signal. I understand NTSC equipment is going for cheap thesedays... http://en.wikipedia.org/wiki/Charge-Coupled_Device
> >Mark
Reply by Steve Underwood May 13, 20082008-05-13
Jerry Avins wrote:
> Fred Marshall wrote: >> "Green Xenon [Radium]" <glucegen1@excite.com> wrote in message >> news:4828ded3$0$5698$4c368faf@roadrunner.com... >>> Hi: >>> >>> Aliasing is a digital entity. What is the analog equivalent of aliasing? >>> >> >> Aliasing isn't a digital entity it's a sampling entity. That you >> digitize the samples has nothing to do with it. >> >> Sampling is a modulation process. A sample stream is modulated with >> the signal that's sampled. >> >> Because it's a modulation process then one looks for other modulation >> processes that might have similarities. >> >> Plain old amplitude modulation would be a good example where aliasing >> can occur. Assume a baseband signal with bandwidth +/-B. Modulate a >> carrier with it which is at afrequency greater than 2B. You get sum >> and difference frequency components as a result. >> >> Now, reduce the carrier frequency to less than 2B and you get aliasing >> in the general case. > > Yes. All the way.
Aliasing is so pervasive, its a surprise that Nyquist has his name attached to the sampling criterion. It seems like someone in the 19th or even 18th century might have figured it out. Steve
Reply by Greg Berchin May 13, 20082008-05-13
On Tue, 13 May 2008 14:30:15 -0700 (PDT), "Ron N."
<rhnlogic@yahoo.com> wrote:

>> *IF* the original analog signal is band-limited such that the sampling >> satisfies the Nyquist Criterion, then NO information is "wiped out". > >I would reverse that statement.
<snip>
>More a metaphysical point than a technical one I admit...
Works either way for me. If retained information = information - lost information and lost information = 0 then retained information = information Similarly retained information + lost information = information and lost information = 0 then retained information = information Greg
Reply by Ron N. May 13, 20082008-05-13
On May 13, 9:23 am, Greg Berchin <gberc...@sentientscience.com> wrote:
> On May 13, 1:02 pm, "SteveSmith" <Steve.Smi...@SpectrumSDI.com> wrote: > > > In other > > words, it has wiped out all information contained in the original > > analog signal, except at the "sample" locations. > > *IF* the original analog signal is band-limited such that the sampling > satisfies the Nyquist Criterion, then NO information is "wiped out".
I would reverse that statement. The error signal consisting of the difference between the original analog signal and the reconstruction from the samples is precisely the information that is wiped out. You no longer can tell from just the samples whether or not the original signal was sufficiently band-limited for the sampling rate (e.g. that the recording engineer didn't screwed-up and there weren't any shorted capacitors in the anti-alias filters, etc.) Either the information that the error signal is zero (or sufficiently close to be considered zero) is "wiped out", communicated by a side channel, or just accepted by faith (e.g. as when buying a typical music CD). More a metaphysical point than a technical one I admit... IMHO. YMMV. -- rhn A.T nicholson d.0.t C-o-M
Reply by Jerry Avins May 13, 20082008-05-13
Green Xenon [Radium] wrote:
> Fred Marshall wrote: >> "Green Xenon [Radium]" <glucegen1@excite.com> wrote in message >> news:4828ded3$0$5698$4c368faf@roadrunner.com... >>> Hi: >>> >>> Aliasing is a digital entity. What is the analog equivalent of aliasing? >>> >> >> Aliasing isn't a digital entity it's a sampling entity. That you >> digitize the samples has nothing to do with it. >> >> Sampling is a modulation process. A sample stream is modulated with >> the signal that's sampled. >> >> Because it's a modulation process then one looks for other modulation >> processes that might have similarities. >> >> Plain old amplitude modulation would be a good example where aliasing >> can occur. Assume a baseband signal with bandwidth +/-B. Modulate a >> carrier with it which is at afrequency greater than 2B. You get sum >> and difference frequency components as a result. >> >> Now, reduce the carrier frequency to less than 2B and you get aliasing >> in the general case. >> >> Fred >> > > > But won't an analog device just smoothly cut-off a frequency that is too > high -- i.e. at a certain point the cut-off gradually beings and the > higher an incoming frequency is, the more it will be attenuated -- > without any aliasing?
No. Try it and see. Remove one of the filter capacitors from an AC powered audio amplifier. The signal will be modulated by 120 Hz and its harmonics. For each component in the original signal, there will be to others: 120 Hz higher and 120 Hz lower. Those will alias withing the band of the original signal. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
Reply by Jerry Avins May 13, 20082008-05-13
Fred Marshall wrote:
> "Green Xenon [Radium]" <glucegen1@excite.com> wrote in message > news:4828ded3$0$5698$4c368faf@roadrunner.com... >> Hi: >> >> Aliasing is a digital entity. What is the analog equivalent of aliasing? >> > > Aliasing isn't a digital entity it's a sampling entity. That you digitize > the samples has nothing to do with it. > > Sampling is a modulation process. A sample stream is modulated with the > signal that's sampled. > > Because it's a modulation process then one looks for other modulation > processes that might have similarities. > > Plain old amplitude modulation would be a good example where aliasing can > occur. Assume a baseband signal with bandwidth +/-B. Modulate a carrier > with it which is at afrequency greater than 2B. You get sum and difference > frequency components as a result. > > Now, reduce the carrier frequency to less than 2B and you get aliasing in > the general case.
Yes. All the way. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
Reply by robert bristow-johnson May 13, 20082008-05-13
On May 12, 9:42 pm, Jerry Avins <j...@ieee.org> wrote:
> > The OP suffers from the delusion that his imaginings are pears, a > delusion shared by many children of doting parents. >
... On May 12, 9:46 pm, Jerry Avins <j...@ieee.org> wrote:
> > The OP suffers from the delusion that his imaginings are pearls, a > delusion shared by many children of doting parents. >
it was better 4 minutes earlier, Jerry. pears are nummy. personally, i think it was a nice, ripe, Bartlet pear that Eve sunk her teeth into and later implicated and blamed Adam for. apples suck (except for computers). r b-j
Reply by SteveSmith May 13, 20082008-05-13
>On May 13, 1:02=A0pm, "SteveSmith" <Steve.Smi...@SpectrumSDI.com> wrote: > >>=A0In other >> words, it has wiped out all information contained in the original >> analog signal, except at the "sample" locations. > >*IF* the original analog signal is band-limited such that the sampling >satisfies the Nyquist Criterion, then NO information is "wiped out". > >Greg >
Hi Greg, Correct, and the way to show this is the case is by looking at the frequency spectra of the analog singals. Steve
Reply by Greg Berchin May 13, 20082008-05-13
On May 13, 1:02&#2013266080;pm, "SteveSmith" <Steve.Smi...@SpectrumSDI.com> wrote:

>&#2013266080;In other > words, it has wiped out all information contained in the original > analog signal, except at the "sample" locations.
*IF* the original analog signal is band-limited such that the sampling satisfies the Nyquist Criterion, then NO information is "wiped out". Greg
Reply by SteveSmith May 13, 20082008-05-13
Hi Radium,
A very good question, because the answer gives a much deeper understanding
of the sampling theorem.  Say you start with an analog signal, x(t), and
convert it to a digital signal, x(n). Mathematically, this process is
carried out in two steps. 

In the first step, we sample the signal by multiplying it by an impulse
train.  An impulse train is an analog signal that is always zero, except
for periodic spikes (also known as impulses or delta functions).  The
product of these two signals retains the amplitude of the original signal
at the spike locations, but inserts a value of zero in between.  In other
words, it has wiped out all information contained in the original analog
signal, except at the "sample" locations. 

In the second step, we measure the height of each of the successive spikes
in the analog product signal, forming a list of numbers.  Ignoring
quantization, this gives us x[n]. 

Now we make an interesting observation.  From the standpoint of
information content, step 2 does nothing.  That is, the analog product
signal and the list of numbers, contain exactly the same information.  By
this I mean that one description can be used to exactly generate the other,
without any error. This equivalence is very important, it provides a deep
understanding of how the analog and digital worlds relate to each other.   


To answer your original question, since step 2 does nothing, all of the
changes to the information content happen in step 1.  In other words,
aliasing can be viewed as being 100% analog. For instance, this is what
happens in the RF mixing examples provided by the other posts.  

Here's a link if you want to see graphics of the above description.  
Regards,
Steve

http://www.dspguide.com/ch3/2.htm
http://www.dspguide.com/ch3/3.htm