> On Thu, 07 Jan 2016 16:37:36 -0800, zoro wrote:
>
>> The input signal is white Gaussian noise - 8000 sample (uniform power
>> across all frequencies). If I represent it by the histogram, the limit
>> of it is about [-3.5 3.9] also in a report I saw limit of it is [-8000
>> 8000], Where am I wrong???
>
> The Gaussian distribution is non-zero out to infinity. So no matter how
> small the deviation of the distribution, in theory one might get a sample
> of any magnitude.
>
> In reality, the probability of getting a sample greater than a few times
> the deviation is small. I don't have the numbers easily to hand, but
> it's something like a 1/1000 chance of getting 3*sigma, and 10^-6 to get
> 6*sigma (you can look up or calculate the real numbers yourself).
>
> At any rate, trying to measure the maximum of a Gaussian-distributed
> random variable may get a bit time consuming.
>
More like 10^-9 to get 6*sigma... As the Q-function is upper-bounded by
0.5*exp(-0.5*x^2), it falls more rapidly than an exponential...
Evgeny.
Reply by Tim Wescott●January 8, 20162016-01-08
On Thu, 07 Jan 2016 16:37:36 -0800, zoro wrote:
> The input signal is white Gaussian noise - 8000 sample (uniform power
> across all frequencies). If I represent it by the histogram, the limit
> of it is about [-3.5 3.9] also in a report I saw limit of it is [-8000
> 8000], Where am I wrong???
The Gaussian distribution is non-zero out to infinity. So no matter how
small the deviation of the distribution, in theory one might get a sample
of any magnitude.
In reality, the probability of getting a sample greater than a few times
the deviation is small. I don't have the numbers easily to hand, but
it's something like a 1/1000 chance of getting 3*sigma, and 10^-6 to get
6*sigma (you can look up or calculate the real numbers yourself).
At any rate, trying to measure the maximum of a Gaussian-distributed
random variable may get a bit time consuming.
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
> On Thu, 7 Jan 2016 16:37:36 -0800 (PST), zoro <md.sylinh93@gmail.com>
> wrote:
>
> >The input signal is white Gaussian noise - 8000 sample (uniform power across all frequencies). If I represent it by the histogram, the limit of it is about [-3.5 3.9] also in a report I saw limit of it is [-8000 8000], Where am I wrong???
>
>
> What is "it"? The signal? The filter impulse response? The
> histogram?
>
>
> Eric Jacobsen
> Anchor Hill Communications
> http://www.anchorhill.com
the signal.
Reply by Eric Jacobsen●January 7, 20162016-01-07
On Thu, 7 Jan 2016 16:37:36 -0800 (PST), zoro <md.sylinh93@gmail.com>
wrote:
>The input signal is white Gaussian noise - 8000 sample (uniform power across all frequencies). If I represent it by the histogram, the limit of it is about [-3.5 3.9] also in a report I saw limit of it is [-8000 8000], Where am I wrong???
What is "it"? The signal? The filter impulse response? The
histogram?
Eric Jacobsen
Anchor Hill Communications
http://www.anchorhill.com
Reply by zoro●January 7, 20162016-01-07
The input signal is white Gaussian noise - 8000 sample (uniform power across all frequencies). If I represent it by the histogram, the limit of it is about [-3.5 3.9] also in a report I saw limit of it is [-8000 8000], Where am I wrong???