This doesn't directly answer your question, but I always start from the analog part, and then work my way back to baseband, and then to symbols, when I think about power / gain / SNR scaling.

In digital, when you ignore overflow and quantization, everything is almost always correct up to a scaling factor, so conversely scaling factor almost always doesn't really matter unless you are doing fixed-point. It's the analog that matters.

"all of the science that you're learning is merely the pallet and paint
that you use as tools to exercise the art of communications system
design."

Never read such a good philosophical statement in a technical context.
Thanks.

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On Tue, 03 Sep 2013 18:13:49 -0500, commsignal wrote:

>>Hi All,
>>   Although it is a basic question but I couldn't find its answer in any
>>available reference. When we filter the signal at the Tx and Rx, how
> should
>>we adjust the filter gains or filter energies to keep the overall energy
>>figures correct *at every stage*. For example, should Tx filter gain be
>>necessarily set to the oversampling factor, or what should be the Rx
> filter
>>gain.
>>Thanks.
>>
>>_____________________________
>>Posted through www.DSPRelated.com
>>
>>
> There are many side-questions which I'm not clear about regarding the
> above.
> 1. Does convolution with a unit energy filter conserve the energy of the
> input signal?
> 2. The universal definition of the energy itself is \sum |x(n)^2.
> Shouldn't it be \sum |x(n)^2 * (sampling time)?
> 3. Should the square-root raised cosine pulse be unit energy, or the
> overall Tx/Rx combination (raised cosine) be unit energy? Also,
> according to which definition of energy in question 2 above.
> 4. I get correct BER results for many different Tx and Rx filter
> scalings. What is the correct method? It is important because any blocks
> before it will affect the energy entering the system blocks at each
> stage.

First, I feel you need to be very careful about the use of the word
"energy" in a signal-processing context.  "Energy" means something quite
waves) which happen to be carrying signals.  But even with analog
electronics, once you get those signals into your signal processing
hardware, the meaning of "energy" breaks down.

(Note, too, that in practical implementations you'll find yourself caring
more about power than energy -- yes, the energy of a specific bit is
important, but when you're trying to design a radio receiver it's the
power that impinges on the antenna, and the noise power of the
electronics, that you deal with directly.)

I think it is much more sensible once you're inside your signal
processing environment (be it analog electronics, digital hardware, or
that you think in terms of signal levels -- voltage, numbers, PSI,
whatever.  Your goal is to make sure that the signal is not corrupted on
the small end by noise, distortion, or sweat dripping into the hydraulic
fluid, and to make sure that the signal is not corrupted on the large end
by saturating amplifiers, numeric overflow, or muscle cramps.

1: No.  Try it.  But first do this thought experiment:

Take a unit-energy filter and a unit-energy signal (by whatever
definition of "unit energy" floats your boat).  Take the filter
to have a spectrum that is totally disjoint from the signal.
Now run the signal through the filter -- what is the resulting
energy?

2: It doesn't matter.  You're just using "energy" as a metaphor for
the real thing, here.

3: See my answer to (2) above, and guess at my opinion.

4: "The" correct method is to choose _a_ correct method out of
the infinite number possible that works well for you.  The
real stumbling block -- that you have to deal with no matter
what -- is that as soon as your signal is transmitted in the
_real world_, then energy (or more properly, power) does
matter.

What really matters is that you get the signal to your detector as
unmolested as possible, and that when it gets there you have a way to
predict the Eb/No.  You'll find that with real-world problems in radio
communication, you often can't do any better than to come up with a very
rough estimate of Eb/No, because both signal and noise are subject to
multiple effects that you have little control over.

At this point you will find that all of the science that you're learning
is merely the pallet and paint that you use as tools to exercise the art
of communications system design.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com


Hi,

thinking about samples, "power" is probably more appropriate. A sample
represents a certain power, valid over its duration. If you oversample (use
more samples), the duration of each sample scales down accordingly. The
energy per sample reduces, the sample value remains unchanged and so does
the overall power.

There is no right or wrong. One way to look at it is to see samples
representing a continuous-time waveform. Regardless how many samples you
take, the level of the waveform (and thus, individual samples) remain
unchanged.

One thing that needs attention is adding noise, because a given power
spreads over the whole covered bandwidth. So when you inject AWGN at an
oversampled rate, the noise power needs to scale accordingly, as you want a
given power density now over a wider bandwidth.

Defining "the" gain of a filter is quite a topic in itself, conceptually
simple but messy in calculations.
Often, 0 Hz is convenient (i.e. sum of taps in a FIR filter), but you'll
have to re-think the problem every time.

Yes, a pulse shaping filter dissipates some power, but if the noise
bandwidth equals the cutoff frequency, the effective gain is often 1 (check
case-by-case).

_____________________________
Posted through www.DSPRelated.com

>Hi All,
>   Although it is a basic question but I couldn't find its answer in any
>available reference. When we filter the signal at the Tx and Rx, how
should
>we adjust the filter gains or filter energies to keep the overall energy
>figures correct *at every stage*. For example, should Tx filter gain be
>necessarily set to the oversampling factor, or what should be the Rx
filter
>gain.
>Thanks.
>
>_____________________________
>Posted through www.DSPRelated.com
>

There are many side-questions which I'm not clear about regarding the
above.
1. Does convolution with a unit energy filter conserve the energy of the
input signal?
2. The universal definition of the energy itself is \sum |x(n)^2. Shouldn't
it be \sum |x(n)^2 * (sampling time)?
3. Should the square-root raised cosine pulse be unit energy, or the
overall Tx/Rx combination (raised cosine) be unit energy? Also, according
to which definition of energy in question 2 above.
4. I get correct BER results for many different Tx and Rx filter scalings.
What is the correct method? It is important because any blocks before it
will affect the energy entering the system blocks at each stage.

Thanks for any available feedback.

_____________________________
Posted through www.DSPRelated.com

Hi All,