Slightly OT - Wireless Energy

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

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

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

>Randy Yates <yates@digitalsignallabs.com> writes:
>
>> spope33@speedymail.org (Steve Pope) writes:
>>
>>> rickman  <gnuarm@gmail.com> wrote:

>>>>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
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