SNR of signal perturbed by WGN

I am trying to analyze the variability of detection time by a
threshold detector for input signal perturbed by a White Gaussian Noise
(w[n]) N(0,sig^2).

My input to the detector is a ramp-signal x[n] with added WGN w[n].
The input signal is supposed to have a fixed SNR.

Now, I decide to use the input of duration/length L. Then compute the
input signal power as sigPower = sum(x[n].*x[n])/L (where n=1:L) and
using this value with my required SNR I can compute the noise power/
variance and eventually standard dev.

With current approach, for my input ramp the signal power depends on
the input duration and for a longer duration the input power is large
and vice-verse. with changing input powers, my noise power is also
changing keeping my SNR fixed.

Since the variability of detection time depends on the noise power and
here the noise power is changing with input signal duration I choose.
The detection time variability seems to depend on the input signal
duration too, but I am not sure about this dependence and hence my
doubt about the approach used. I this approach correct?

Secondly, would it be correct to find instantaneous signal power as
iSigPower(l) = sum(x[l].*x[l])/l where l is my present instance, and
compute noise power with this signal power. With this approach, my
signal power increases with time and noise power similarly. Would this
approach be correct instead?

Please present your ideas and help me clear it up.

M

On Jul 16, 7:32&#4294967295;pm, SRT <sauravtulad...@gmail.com> wrote:
> I am trying to analyze the variability of detection time by a
> threshold detector for input signal perturbed by a White Gaussian Noise
> (w[n]) N(0,sig^2).
>
> My input to the detector is a ramp-signal x[n] with added WGN w[n].
> The input signal is supposed to have a fixed SNR.
>
> Now, I decide to use the input of duration/length L. Then compute the
> input signal power as sigPower = sum(x[n].*x[n])/L (where n=1:L) and
> using this value with my required SNR I can compute the noise power/
> variance and eventually standard dev.
>
> With current approach, for my input ramp the signal power depends on
> the input duration and for a longer duration the input power is large
> and vice-verse. with changing input powers, my noise power is also
> changing keeping my SNR fixed.
>
> Since the variability of detection time depends on the noise power and
> here the noise power is changing with input signal duration I choose.
> The detection time variability seems to depend on the input signal
> duration too, but I am not sure about this dependence and hence my
> doubt about the approach used. I this approach correct?
>
> Secondly, would it be correct to find instantaneous signal power as
> iSigPower(l) = sum(x[l].*x[l])/l where l is my present instance, and
> compute noise power with this signal power. With this approach, my
> signal power increases with time and noise power similarly. Would this
> approach be correct instead?
>
> Please present your ideas and help me clear it up.
>
> M

hmm... is the power the function of time (either duration time or
detection in your context)? note that power definition is

P = 1/T \integrate {f^2(t)} dt with T goes to infinite.

and energy doesn't need to divide by T.

so can you compute a continuously running sine waveform's energy and
power?