zero padding and periodic waveform energy calculation

Consider a 100 Hz waveform sampled at 10kHz.  One period would consist of
100 samples.  I'm trying to better understand the energy of this waveform
and the same waveform with 28 zeros.  

I'm asking because I see two equations pertaining to the energy of a
periodic waveform. 

(1) is the summation of squares
(2) same as 1 with the addition of multiplying the sum by the duration of
the waveform

If (2) is the case, would the zeros be a part of the duration?  The
summation in both cases is for the entire waveform (in my case two
waveforms, one is 100 points and the other 128 points).  

Anyway, I thought I would ask while I continue to put this in the googles.
   


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helloworld <60772@dsprelated> wrote:
> Consider a 100 Hz waveform sampled at 10kHz.  One period would consist of
> 100 samples.  I'm trying to better understand the energy of this waveform
> and the same waveform with 28 zeros.  
 
> I'm asking because I see two equations pertaining to the energy of a
> periodic waveform. 

For a periodic waveform, you probably don't want energy, but power,
or energy per unit time.  (Or energy per period.) Otherwise it
will be infinite.
 
> (1) is the summation of squares
> (2) same as 1 with the addition of multiplying the sum by 
>     the duration of the waveform
 
> If (2) is the case, would the zeros be a part of the duration?  The
> summation in both cases is for the entire waveform (in my case two
> waveforms, one is 100 points and the other 128 points).  

In the case of a periodic waveform, the zeros would be part of it.

Zero padding is sometimes used to Fourier transform non-periodic
signals with a finite number of samples. A finite length signal
can have an energy, but again power might be a better choice.
 
> Anyway, I thought I would ask while I continue to put this 
> in the googles.

I would be interested to know what you learn from Google.

-- glen