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???
FIR filter
Started by ●January 7, 2016
Reply by ●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 ●January 8, 20162016-01-08
Vào 11:25:45 UTC+7 Thứ Sáu, ngày 08 tháng 1 năm 2016, Eric Jacobsen đã viết:> 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.comthe signal.
Reply by ●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
Reply by ●January 9, 20162016-01-09
On 09.01.2016 2:00, Tim Wescott wrote:> 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.
