Tim Wescott <tim@seemywebsite.really> writes:> [...] > My goal is to know the probability distribution of a measure of the > "magnitude" of noise, said measure being the maximum absolute value found > in a vector of samples of a colored (i.e., filtered white noise, > autocorrelation != impulse, etc.) random process. > > It is the mean (and variance, and pdf if I can get it) of this measure > that I am seeking.Tim, What is this for? -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Max absolute value of colored Gaussian noise
Started by ●July 12, 2014
Reply by ●July 15, 20142014-07-15
Reply by ●July 15, 20142014-07-15
On Tue, 15 Jul 2014 09:58:35 -0400, Randy Yates wrote:> Tim Wescott <tim@seemywebsite.really> writes: >> [...] >> My goal is to know the probability distribution of a measure of the >> "magnitude" of noise, said measure being the maximum absolute value >> found in a vector of samples of a colored (i.e., filtered white noise, >> autocorrelation != impulse, etc.) random process. >> >> It is the mean (and variance, and pdf if I can get it) of this measure >> that I am seeking. > > Tim, > > What is this for?I go over this elsewhere in this astonishingly long (to me) thread, but basically I'm receiving an on-off keyed signal with unknown noise levels and more or less unknown amplitude. I'm trying to set the threshold for detection by measuring the noise in a known quiet period, and setting the actual threshold proportional to that. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●July 15, 20142014-07-15
On Sat, 12 Jul 2014 17:03:55 -0500, Tim Wescott wrote:> I need a number, and I'm feeling lazy; has anyone worked this out > recently? > > I want to know the distribution of the maximum of the absolute value of > a vector of samples of a colored, zero-mean Gaussian process. > > Or, stated another way, I want to shove white noise into a filter, then > examine a finite chunk of the filter output for it's maximum absolute > value. > > Anyone know the answer? Or should I sharpen my pencil and get to work?I broke down and got an answer by simulation. It looks like -- at least for the vector lengths that I'm using -- using the max(abs) metric to estimate noise level is nearly as good as using the variance: the ratio of measured standard deviation to mean for the max (abs) measure is about 5% worse than using the "normal" variance estimate. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●August 12, 20142014-08-12
On July 12, Tim Wescott wrote:> I want to know the distribution of the maximum of the absolute > value of a vector of samples of a colored, zero-mean Gaussian > process. Or, stated another way, I want to shove white noise > into a filter, then examine a finite chunk of the filter output > for it's maximum absolute value.Look up the Gumbel distribution. My memory is hazy, but it applies to extreme value, worst case applications. As I recall, it's used in designs where there's some quantization error of a system parameter - not signal noise - and one needs to estimate the worst case performance. -- Rich
