On Fri, 12 Mar 1999 09:28:06 -0500, Sean Breheny wrote: >Hi Zonn, > >At 07:29 AM 3/12/99 GMT, you wrote: >>You'll find no patterns in the thermo noise of a diode. Unless something's >wrong >>with your circuit, like outputting all ones? > >Well,I may not have been clear about what I meant by pattern: Take for >example, the white noise produced across a resistor due to thermal effects. >It has a Gaussian distribution. This means that values near zero are more >likely than say, 1 volt,across the resistor! This is an extreme example, >but it also means that values or around 1uV are more likely than 5uV,etc. >So,if you were to make a one time pade which was,say,the number of >microvolts times 16,most of he numbers in your one time pad would be in the >range 0 to 16 * sigma, where sigma was sqrt(4*k*T*R*B),which might be say >4uV. So, you would get almost NO values greater than 64. Upon thinking >about it more,I must admit that this probably could be minimized by >increasing the gain,so that our range of values was well within the sigma >range. Still,I would think it better to apply a little algorithm to the >data to make higher values more likely,so that ridiculously high gain >wasn't needed. > >I'm not saying that a diode is unsuitable, just warning that someone should >examine the distribution of their output to make sure that it is reasonably >random and uniform (not the same thing,since not all random processes show >no law-LIKE behavior,in this case,procuding lower voltages more than higher >ones). > >> >>When I've needed truly random patterns in the past, I've used a 16 bit sound >>card and sampled the hiss between FM radio stations, and then concatenated >the >>lowest order bit of the 16 bit words, into a string of bytes. >> > >Well, I think if you were to actually look at the whole 16 bits,you'd find >that very few times were the highest bits set(unless you had the volume up >very high or extra amplification),since the noise from the radio is almost >never putting 5V (or whatever was your Vref for the ADC) across the >speaker. You actually did something to fix the situation,by only using the >lowest bits,which were very close to the zero point on the Gaussian "bell", >therefore very close to a uniform (abs. level) distribution because the >slope of the Gaussian is very small near zero. Hi Sean, Actually the highest bit is also all over the place since the sample is a signed value and constantly jumping above and below zero, regardless of amplitude. But your point is taken. Of course given an infinite number of bits in the sample, the values will always be skewed towards zero. You can increase the gain to effect higher and higher bits, (beyond 64 counts in your diode example, and beyond +/- 32767 in my sound card example), and you can then argue given a 32 bit sample size it's doubtful the higher + or - values will be approached. By not using the bits as a whole sample, but by using only one bit per sample, you remove all skewing of data towards any value. It's mathematically impossible to predict exactly the value of a physical noise source (FM hiss, noisy diode) based on previous values. You of course can predict that the amplitude will be within a range supplied by you, but you will not know where in that range it will be. If you'd like to run some analysis of the white noise generated by the FM approach I'd be more than happy to send you a sample. You'll find that all values are just as likely as any other, +/- a few *random* counts on each value (which is also unpredictable). It is complete white noise. This is the case using the lowest bit, highest bit, any bit. (Remember it's signed, and regardless of it's amplitude you cannot know whether it will be above or below zero given on any particular sample, as long as the sample rate is lower than the frequency response of the FM radio being sampled.) I only used the lowest bit because I didn't trust my sound card, or FM radio, to have an exactly zero volt offset, and this could have an effect on the highest bit. -Zonn