What is the analog equivalent of aliasing?

On May 12, 5:20 pm, "Green Xenon [Radium]" <gluceg...@excite.com>
wrote:
> Aliasing is a digital entity. What is the analog equivalent of aliasing?


I regard aliasing as a form of information loss
or information ambiguity.  If you sample below half
the bandwidth, you lose information about whether
a certain frequency represented by the samples might
be above or below Fs/2 (unless you pre-notch the
lower frequency, as in under-sampling).

You can get the same thing in the analog domain by
using an analog mixer to mix down a wideband source
and then adding back the original baseband.  You will
then no longer know whether a signal in the result
was from above or below the mixer frequency.

Sampling is just a easy way to mix down stuff above
Fs/2, add it to the baseband, and similarly confuse
the result (unless you bandlimit above or below first).

.


IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M
 http://www.nicholson.com/rhn/dsp.html

On Mon, 12 May 2008 21:16:01 -0700, "Fred Marshall"
<fmarshallx@remove_the_x.acm.org> 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?
>>
             (snipped by Lyons)

Hi,
  Good point Fred.  You made me think of the 
backward-spinning stagecoach wheels in the 
old black & white cowboy movies.  The wheels, 
whose positions are repetitive over time, 
were being sampled by the the camera's shutter.

[-Rick-]

Dnia 13-05-2008 o 06:36:36 Green Xenon [Radium] <glucegen1@excite.com>  
napisa&#4294967295;(a):

[...]
> 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?
[...]

Aliasing means that signal appears in the device's bandwidth.


-- 
Mikolaj

"Green Xenon [Radium]" <glucegen1@excite.com> wrote in news:4828ded3$0$5698
$4c368faf@roadrunner.com:

> Hi:
> 
> Aliasing is a digital entity. What is the analog equivalent of aliasing?
> 
> 
> Thanks,
> 
> Radium

Aliasing is not a digital entity.  It occurs during analog amplitude 
modulation if the carrier frequency is not high enough.


-- 
Scott
Reverse name to reply

On May 13, 12:36&#4294967295;am, "Green Xenon [Radium]" <gluceg...@excite.com>
wrote:

> But won't an analog device just smoothly cut-off a frequency that is
> too high ... without any aliasing?

Stop thinking of signal processing as analog or digital.  Signal
processing is mathematical.  Analog or digital is a detail of its
implementation.

As Fred Marshall said, spectral aliasing is an artifact of temporal
sampling.  A sampled temporal signal results in a periodic spectrum
that is continuous in frequency.  Is that analog or is it digital?

A periodic but continuous temporal signal results in a discrete-
frequency spectrum.  Or, looking at it the other way around, a sampled
spectrum can result in temporal aliasing, the dual of spectral
aliasing.  Is that analog or is it digital?

Now, to confuse things even further, what is commonly called "analog"
is really "continuous time".  But as I pointed out above, a continuous
time signal can have a discrete frequency spectrum.  Similarly, what
is commonly called "digital" is really "discrete time".  But as I
pointed out above, a discrete time signal can have a continuous
frequency spectrum.  So exactly what do you mean when you say,
"Aliasing is a digital entity"?

Greg

 �Similarly, what
> is commonly called "digital" is really "discrete time". �But as I
> pointed out above, a discrete time signal can have a continuous
> frequency spectrum. �So exactly what do you mean when you say,
> "Aliasing is a digital entity"?
>
> Greg

There are singals that are continuous in time and singals that are
sampled and discrete in time.

There are voltages that are continuous in amplitude and voltages that
are quantized and represented as digital values.

Timne sampling and voltage quantization are two different issues.

FM MPX stereo is a good example of a common system that uses time
sampling and can suffer aliasing but is not digitized i.e. is
"analog".

http://transmitters.tripod.com/stereo.htm

Mark

On May 13, 9:44&#4294967295;am, Mark <makol...@yahoo.com> wrote:

> Timne sampling and voltage quantization are two different issues.

Exactly.  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 "digital" is taken to mean "quantized amplitude", the original
statement that "Aliasing is a digital entity" becomes even less
meaningful.

Greg

>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," though with reason, since it is difficult to do anything with
discretely sampled continuous waveforms unless you first digitize them. 
Digital signal processing is essentially quantized DSP.  Perhaps someone
will start to call it QDSP one day and it will stick? :)

Mark

On Tue, 13 May 2008 10:55:59 -0500, "markt" <takatz@pericle.com>
wrote:

>When I first learned the term "DSP," it actually meant "discrete-time
>signal processing."  It has since been morphed to "digital signal
>processing," though with reason, since it is difficult to do anything with
>discretely sampled continuous waveforms unless you first digitize them. 

Check out switched capacitor filters; perfect example of sampling
without quantization. The issue of difficulty is in the eye of the
beholder but it's certainly a lot cheaper to do digital signal
processing in an FPGA coupled with a suitable ADC/DAC then it's to
design your own SCFs.

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