what is the energy of this signal?

Hi all,

Do you know how to calculate the energy of this signal?

r(t) = sum over k ( a(k) * h(t - kT - 0.1kT) ), where a(k)'s are +1, -1; and h = [1 4 6 4 1]. 
If there was no 0.1kT term(a time-variant shift), then the above is a convolution and since E(a(k)^2)=1, then the E(r(l)^2) is simply norm(h)^2 = 70. 
I don't know how to do this as it is above?

The discrete h can be interpolated by adding 5 "sinc"s like: sinc(t)+4*sinc(t-1)+...

Thanks,
Elnaz

On 20.2.14 17:12, Elnaz wrote:
> Hi all,
>
> Do you know how to calculate the energy of this signal?
>
> r(t) = sum over k ( a(k) * h(t - kT - 0.1kT) ), where a(k)'s are +1, -1; and h = [1 4 6 4 1].
> If there was no 0.1kT term(a time-variant shift), then the above is a convolution and since E(a(k)^2)=1, then the E(r(l)^2) is simply norm(h)^2 = 70.
> I don't know how to do this as it is above?
>
> The discrete h can be interpolated by adding 5 "sinc"s like: sinc(t)+4*sinc(t-1)+...
>
> Thanks,
> Elnaz


Please do not start a new thread on the same subject
with a different title.

You have two sequences with different sampling frequencies:
kT for a(k) and 1.1*kT for h(k). To do the convolution,
you have to get them on a common base. See the response
for the previous thread by Eric Jacobsen.

I read between the rows of your follow-up that you are
not happy implementing it on Matlab - right?
If you mean it, please say so.

-- 

Tauno Voipio

I have implemented it in Matlab. This is not the same question. The equation is the same. What I'm asking here is how to calculate the energy of this signal theoretically? This has nothing to do with how to implement it in Matlab or...however, it can help verify the implementation. 

Thanks,
Elnaz

On Thursday, February 20, 2014 10:57:08 AM UTC-5, Elnaz wrote:
> I have implemented it in Matlab. This is not the same question. The equation is the same. What I'm asking here is how to calculate the energy of this signal theoretically? This has nothing to do with how to implement it in Matlab or...however, it can help verify the implementation. 
> 
> 
> 
> Thanks,
> 
> Elnaz

Since energy is a physical thing, what are the units associated with your numbers? Often one may talk about the "energy" of a signal without regard to units, but then one still needs to clarify what your numbers represent. Bessel's theorem (special case of Parseval's) will use a sum of the squares of the magnitudes of each of the samples, but then this will relate the results of doing this in two different domains. I suspect the sum of squares is what you desire. Another way to compute the energy involves a signal and its first and second derivatives. Look up the Kaiser-Teager energy operator. Check out the following link:

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.216.4519&rep=rep1&type=pdf


Clay