>>>>Funny that the replies to your post are dealing with the DAC waveform
>>>>without responding to the fact that you are likely confusing the DAC
>>>>with the ADC in your question.
>>>
>>> I would take this question at face value; I don't think it's
confused.
>>>
Both DAC and ADC (theoretically) show sort of broadcast of signal. A DAC
without sinc envelope and no further filter will broadcast frequency to
infinite points. In fact some NCO are based on having a high image as
their output instead of the fundamental.
An ADC similarly receives frequency from infinite points into the digital
domain (assuming no filter).
Though I can't explain it in terms of energy physics.
Kaz
---------------------------------------
Posted through http://www.DSPRelated.com
Reply by Randy Yates●June 6, 20152015-06-06
Randy Yates <yates@digitalsignallabs.com> writes:
> spope33@speedymail.org (Steve Pope) writes:
>
>> rickman <gnuarm@gmail.com> wrote:
>>
>>>On 6/5/2015 7:07 AM, kaz wrote:
>>
>>>> A related question. A DAC device produces multiple (infinite) images of a
>>>> frequency. How come energy be infinite or should we say a receiver can
>>>> detect the frequency at any point that corresponds to an image.
>>
>>>Funny that the replies to your post are dealing with the DAC waveform
>>>without responding to the fact that you are likely confusing the DAC
>>>with the ADC in your question.
>>
>> I would take this question at face value; I don't think it's confused.
>>
>>>It is the sampled output of an ADC which
>>>can be considered to contain infinite aliased copies of the baseband
>>>signals at the various reflection points. The energy in that waveform
>>>is not infinite because these are just alternate ways of looking at the
>>>same signals, not added signals.
>>
>> Okay
>>
>>>The output waveform of a DAC does indeed have energy at higher
>>>frequencies, but at diminishing levels similar to how a square wave
>>>contains an infinite series of sine waves and yet is finite in amplitude.
>>
>> Only if the output of the DAC is filtered (including any zero-order
>> hold one has applied).
>>
>> An unadorned idealized DAC outputs an impulse "train", to which is
>> often applied a "boxcar" zero-older hold, but this second step
>> is a convenient practicality for typical systems which (by a
>> happy coincidence) do not need or require the higher-frequency
>> images.
>>
>> But other systems may want one of the higher images. Let's say the
>> sample rate at the DAC is 10 KHz, containing a signal of interest which
>> is narrowband and centered at 2.5 KHz. Construct a DAC which outputs a
>> square impulse (perhaps best achieved in the current domain) of
>> 1 usec duration. There is still a sinx/x rollof, but it is much
>> further out than if you had a zero-order hold (a 1 usec boxcar
>> instead of a 100 usec boxcar).
>>
>> In the frequency domain you now have a train of narrowband images,
>> gently rolling off and separated by 5 KHz, and you can isolate out
>> the image you desire with a bandpass filter.
>
> I actually saw this phenomenom on a spectrum analyzer at Sony Ericsson
> many years ago. For a minute or two I was confounded, but then I
> realized it was the images from the digital source. Yes, the images
> attenuated eventually, but at least the first couple were significant.
> I'm sorry but I can't remember the exact context (sample rate, etc.).
PS: When it hit me what I was looking at, it was quite a revelation:
where theory and reality crossed!
--
Randy Yates
Digital Signal Labs
http://www.digitalsignallabs.com
Reply by Randy Yates●June 6, 20152015-06-06
spope33@speedymail.org (Steve Pope) writes:
> rickman <gnuarm@gmail.com> wrote:
>
>>On 6/5/2015 7:07 AM, kaz wrote:
>
>>> A related question. A DAC device produces multiple (infinite) images of a
>>> frequency. How come energy be infinite or should we say a receiver can
>>> detect the frequency at any point that corresponds to an image.
>
>>Funny that the replies to your post are dealing with the DAC waveform
>>without responding to the fact that you are likely confusing the DAC
>>with the ADC in your question.
>
> I would take this question at face value; I don't think it's confused.
>
>>It is the sampled output of an ADC which
>>can be considered to contain infinite aliased copies of the baseband
>>signals at the various reflection points. The energy in that waveform
>>is not infinite because these are just alternate ways of looking at the
>>same signals, not added signals.
>
> Okay
>
>>The output waveform of a DAC does indeed have energy at higher
>>frequencies, but at diminishing levels similar to how a square wave
>>contains an infinite series of sine waves and yet is finite in amplitude.
>
> Only if the output of the DAC is filtered (including any zero-order
> hold one has applied).
>
> An unadorned idealized DAC outputs an impulse "train", to which is
> often applied a "boxcar" zero-older hold, but this second step
> is a convenient practicality for typical systems which (by a
> happy coincidence) do not need or require the higher-frequency
> images.
>
> But other systems may want one of the higher images. Let's say the
> sample rate at the DAC is 10 KHz, containing a signal of interest which
> is narrowband and centered at 2.5 KHz. Construct a DAC which outputs a
> square impulse (perhaps best achieved in the current domain) of
> 1 usec duration. There is still a sinx/x rollof, but it is much
> further out than if you had a zero-order hold (a 1 usec boxcar
> instead of a 100 usec boxcar).
>
> In the frequency domain you now have a train of narrowband images,
> gently rolling off and separated by 5 KHz, and you can isolate out
> the image you desire with a bandpass filter.
I actually saw this phenomenom on a spectrum analyzer at Sony Ericsson
many years ago. For a minute or two I was confounded, but then I
realized it was the images from the digital source. Yes, the images
attenuated eventually, but at least the first couple were significant.
I'm sorry but I can't remember the exact context (sample rate, etc.).
--
Randy Yates
Digital Signal Labs
http://www.digitalsignallabs.com
Reply by Steve Pope●June 6, 20152015-06-06
rickman <gnuarm@gmail.com> wrote:
>On 6/5/2015 7:07 AM, kaz wrote:
>> A related question. A DAC device produces multiple (infinite) images of a
>> frequency. How come energy be infinite or should we say a receiver can
>> detect the frequency at any point that corresponds to an image.
>Funny that the replies to your post are dealing with the DAC waveform
>without responding to the fact that you are likely confusing the DAC
>with the ADC in your question.
I would take this question at face value; I don't think it's confused.
>It is the sampled output of an ADC which
>can be considered to contain infinite aliased copies of the baseband
>signals at the various reflection points. The energy in that waveform
>is not infinite because these are just alternate ways of looking at the
>same signals, not added signals.
Okay
>The output waveform of a DAC does indeed have energy at higher
>frequencies, but at diminishing levels similar to how a square wave
>contains an infinite series of sine waves and yet is finite in amplitude.
Only if the output of the DAC is filtered (including any zero-order
hold one has applied).
An unadorned idealized DAC outputs an impulse "train", to which is
often applied a "boxcar" zero-older hold, but this second step
is a convenient practicality for typical systems which (by a
happy coincidence) do not need or require the higher-frequency
images.
But other systems may want one of the higher images. Let's say the
sample rate at the DAC is 10 KHz, containing a signal of interest which
is narrowband and centered at 2.5 KHz. Construct a DAC which outputs a
square impulse (perhaps best achieved in the current domain) of
1 usec duration. There is still a sinx/x rollof, but it is much
further out than if you had a zero-order hold (a 1 usec boxcar
instead of a 100 usec boxcar).
In the frequency domain you now have a train of narrowband images,
gently rolling off and separated by 5 KHz, and you can isolate out
the image you desire with a bandpass filter.
Steve
Reply by rickman●June 6, 20152015-06-06
On 6/5/2015 7:07 AM, kaz wrote:
> A related question. A DAC device produces multiple (infinite) images of a
> frequency. How come energy be infinite or should we say a receiver can
> detect the frequency at any point that corresponds to an image.
Funny that the replies to your post are dealing with the DAC waveform
without responding to the fact that you are likely confusing the DAC
with the ADC in your question. It is the sampled output of an ADC which
can be considered to contain infinite aliased copies of the baseband
signals at the various reflection points. The energy in that waveform
is not infinite because these are just alternate ways of looking at the
same signals, not added signals.
The output waveform of a DAC does indeed have energy at higher
frequencies, but at diminishing levels similar to how a square wave
contains an infinite series of sine waves and yet is finite in amplitude.
Heck, Tim was confused by your post enough to answer as if you were
asking about an ADC, but then went on to correct himself to respond to
the question regarding the DAC output. He should have realized he
answered the right question to begin with. It was your question that
was confused. No? :)
--
Rick
Reply by Steve Pope●June 6, 20152015-06-06
<radams2000@gmail.com> wrote:
>I'm not an expert on EM fields but there's a company out of MIT called
>WiTricity that transmits electrical power over a distance. It seems like
>placing a highly-resonant tuned coil in the field (where the field is
>narrowband at the same frequency as the resonator) somehow directs the
>field towards the coil and you get a lot more power than just computing
>the spherical surface area that you are intercepting.
Only in the near field.
This is why "dip meters" work, and also used in some earlier electronic
door locks.
Steve
Reply by Tim Wescott●June 5, 20152015-06-05
On Fri, 05 Jun 2015 02:32:18 -0700, gyansorova wrote:
> Suppose I have a transmitter working off a battery.
>
> I also have in the same room a receiver which does not have a power
> source but is a type crystal format with a set of headphones and I
> listen to the transmitted music.
>
> Then a second and third person comes into the room with identical
> wireless receivers (also no power). Does the volume on my receiver go
> down because the others are drawing more power from the transmitter? Or
> likewise does the battery of the transmitter run down quicker with more
> receivers?
I think that hanging an antenna out does distort the waves in the æther.
But unless it's much, much larger than one wavelength it's not going to
cast much of a shadow behind which other antennas won't work, and it
certainly won't affect antennas placed _beside_ it much.
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
Reply by Tim Wescott●June 5, 20152015-06-05
On Sat, 06 Jun 2015 00:12:53 +0000, glen herrmannsfeldt wrote:
> Tim Wescott <seemywebsite@myfooter.really> wrote:
>> On Fri, 05 Jun 2015 06:07:37 -0500, kaz wrote:
>
>>> A related question. A DAC device produces multiple (infinite) images
>>> of a frequency. How come energy be infinite or should we say a
>>> receiver can detect the frequency at any point that corresponds to an
>>> image.
>
>> Oooh, there's been entire flame wars dedicated to that subject here.
>> Mostly fueled by one individual who hasn't shown his head for a while,
>> so let me point out my view on this:
>
>> You're probably referring to the model of sampling where you treat the
>> sampling process as a multiplication by a train of impulses. That
>> model has two really salient points to it that are germane to this
>> discussion:
>
>> 1: It just ain't so. What comes out of a DAC isn't a train of impulses
>> of infinitesimal width in time and infinite height. What comes out of
>> a DAC is just a sequence of numbers, with no particular real-world
>> connection between actual fry-an-egg energy and the magnitude of the
>> numbers.
>
> Also, this isn't sampling (ADC) but reconstruction (DAC).
I got that backward: probably I was lead to it because the OP said
something that's more sensible to ADCs. Change everywhere that I said
"DAC" to "ADC" and it may sound like I'm less of an idiot.
I do that all the time. Weak dyslexia?
>
>> 2: It is exceedingly convenient from a mathematical standpoint, because
>> it unifies the discrete-time Fourier transform with the continuous-time
>> Fourier transform.
>
> For the usual DAC, holding the value for one sample period, and then
> instantaneously (ideal), or somewhat fast (actual) changing to the new
> value at the next sample point is more appropriate.
In the "sampling is multiplication by a train of impulses" model, you'd
model the DAC as a zero-order hold (which is just a continuous-time
successive average filter). But it's still just a _model_, not a
_reality_.
>> So by point 2 we want to keep it, but by point 1 we need to make sure
>> that any results we get are within the bounds of what the model
>> actually models.
>
> -- glen
On Fri, 05 Jun 2015 19:02:51 -0500, Tim Wescott
<seemywebsite@myfooter.really> wrote:
>On Fri, 05 Jun 2015 06:07:37 -0500, kaz wrote:
>
>> A related question. A DAC device produces multiple (infinite) images of
>> a frequency. How come energy be infinite or should we say a receiver can
>> detect the frequency at any point that corresponds to an image.
>
>Oooh, there's been entire flame wars dedicated to that subject here.
>Mostly fueled by one individual who hasn't shown his head for a while, so
>let me point out my view on this:
>
>You're probably referring to the model of sampling where you treat the
>sampling process as a multiplication by a train of impulses. That model
>has two really salient points to it that are germane to this discussion:
>
>1: It just ain't so. What comes out of a DAC isn't a train of impulses
>of infinitesimal width in time and infinite height. What comes out of a
>DAC is just a sequence of numbers, with no particular real-world
>connection between actual fry-an-egg energy and the magnitude of the
>numbers.
>
>2: It is exceedingly convenient from a mathematical standpoint, because
>it unifies the discrete-time Fourier transform with the continuous-time
>Fourier transform.
>
>So by point 2 we want to keep it, but by point 1 we need to make sure
>that any results we get are within the bounds of what the model actually
>models.
Most DACs are zero-order hold, which is also not hard to model
mathematically, and which has a sinx/x frequency response. Even with
no reconstruction filter, and an ideal zero-order hold DAC output, the
repeating images are of diminishing energy due to the decreasing
sidelobe amplitude of the sinx/x response.
Since a physical DAC output is naturally bandlimited by the output
amplifier technology, it only goes so far, and the images get pretty
small as you go up in frequency just due to the sinx/x response of the
zero-order hold.
We've built systems where we used an image as the IF output, but you
lose a little power (and SNR/EVM) since it's in a sidelobe, and you
have to correct for the tilt of the sidelobe response in whichever
image you plan to use (and if you don't want distortion, it needs to
be reasonably close to the baseband image). Plus, every other image
is spectrally inverted, so you have to keep track of that, too.
But, yeah, basically, no real device will produce anything close to an
infinite train of spectral images. I wish they did, though, 'cause
you could do some really cool things with it.
Reply by glen herrmannsfeldt●June 5, 20152015-06-05
Tim Wescott <seemywebsite@myfooter.really> wrote:
> On Fri, 05 Jun 2015 06:07:37 -0500, kaz wrote:
>> A related question. A DAC device produces multiple (infinite) images of
>> a frequency. How come energy be infinite or should we say a receiver can
>> detect the frequency at any point that corresponds to an image.
> Oooh, there's been entire flame wars dedicated to that subject here.
> Mostly fueled by one individual who hasn't shown his head for a while, so
> let me point out my view on this:
> You're probably referring to the model of sampling where you treat the
> sampling process as a multiplication by a train of impulses. That model
> has two really salient points to it that are germane to this discussion:
> 1: It just ain't so. What comes out of a DAC isn't a train of impulses
> of infinitesimal width in time and infinite height. What comes out of a
> DAC is just a sequence of numbers, with no particular real-world
> connection between actual fry-an-egg energy and the magnitude of the
> numbers.
Also, this isn't sampling (ADC) but reconstruction (DAC).
> 2: It is exceedingly convenient from a mathematical standpoint, because
> it unifies the discrete-time Fourier transform with the continuous-time
> Fourier transform.
For the usual DAC, holding the value for one sample period, and
then instantaneously (ideal), or somewhat fast (actual) changing
to the new value at the next sample point is more appropriate.
> So by point 2 we want to keep it, but by point 1 we need to make sure
> that any results we get are within the bounds of what the model actually
> models.